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Type:

Package

Title:

Mixture and Non Mixture Parametric Cure Models to Estimate Cure Indicators

Version:

0.1.2

Author:

Juste Goungounga

[aut, cre], Judith Breaud

[aut], Olayide Boussari

[aut], Laura Botta

[ctb], Valerie Jooste

[aut]

Maintainer:

Juste Goungounga <juste.goungounga@ehesp.fr>

Description:

Fits a variety of cure models using excess hazard modeling methodology such as the mixture model proposed by Phillips et al. (2002) <doi:10.1002/sim.1101> The Weibull distribution is used to represent the survival function of the uncured patients; Fits also non-mixture cure model such as the time-to-null excess hazard model proposed by Boussari et al. (2020) <doi:10.1111/biom.13361>.

License:

GPL (≥ 3)

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.3.2

Depends:

R (≥ 3.5), stringr, survival

Imports:

numDeriv, stats, randtoolbox, bbmle, optimx, Formula, Deriv, statmod

Suggests:

testthat, knitr, rmarkdown, xhaz, survexp.fr

VignetteBuilder:

knitr

NeedsCompilation:

Packaged:

2025-03-07 12:39:20 UTC; jbreaud

Repository:

CRAN

Date/Publication:

2025-03-07 13:50:02 UTC

Mixture and Non Mixture Parametric Cure Models to Estimate Cure Indicators

Description

Fits cure models in net survival setting. It can be a mixture cure model with the survival of the uncured following a Weibull or an exponentiated Weibull. The package also implements non-mixture cure models such as the time-to-null excess hazard model proposed by Boussari et al (2021). If the modelling assumption of the comparability between expected hazard in the cohort under study and that related to the general population doesn't hold, an extra effect (due to life tables mismatch) can be estimated for these two classes of cure models. The overall survival setting can also be considered in this package.

Details

package: curesurv

     type: Package

     Version 0.1.2

     license: GPL 3 + LICENSE file

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

Boussari O, Bordes L, Romain G, Colonna M, Bossard N, Remontet L, Jooste V. Modeling excess hazard with time-to-cure as a parameter. Biometrics. 2021 Dec;77(4):1289-1302. doi: 10.1111/biom.13361. Epub 2020 Sep 12. PMID: 32869288. (pubmed)

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

De Angelis R, Capocaccia R, Hakulinen T, Soderman B, Verdecchia A. Mixture models for cancer survival analysis: application to population-based data with covariates. Stat Med. 1999 Feb 28;18(4):441-54. doi: 10.1002/(sici)1097-0258(19990228)18:4<441::aid-sim23>3.0.co;2-m. PMID: 10070685. (pubmed)

Akaike's An Information Criterion for cure models

Description

Calculates the Akaike's "An Information Criterion" for fitted models from curesurv

Usage

## S3 method for class 'curesurv'
AIC(object, ..., k = 2)

Arguments

object

a fitted model object obtained from curesurv

...

optionally more fitted model objects obtained from curesurv.

k

numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC.

Details

When comparing models fitted by maximum likelihood to the same data, the smaller the AIC, the better the fit.

However in our case, one should be careful when comparing the AIC. Specifically, when one implements a mixture cure model with curesurv without correcting the rate table (pophaz.alpha=FALSE), one is not obligated to specify cumpophaz. However, you cannot compare a model where cumpophaz is not specified with a model where cumpophaz is specified. If one wants to compare different models using AIC, one should always specify cumpophaz when using the curesurv function.

Value

the value corresponds to the AIC calculated from the log-likelihood of the fitted model if just one object is provided. If multiple objects are provided, a data.frame with columns corresponding to the objects and row representing the AIC

Examples



library("curesurv")
library("survival")

 testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 AIC(fit_m1_ad_tneh)

TTC_adtneh2 function

Description

calculates the probability Pi(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t from a Time-to-Null excess hazard model using numerical method, uniroot. In other words, Pi(t)=(probability of being cured and alive up to time t given xi)/ (probability of being alive up to time t given xi)

Usage

TTC_adtneh2(z_alpha, z_tau, xmax, object, epsilon = epsilon)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

xmax

time max at which Pi(t) is calculated.

object

ouput from a non mixture model with distribution "tneh" from curesurv function.

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

Boussari O, Romain G, Remontet L, Bossard N, Mounier M, Bouvier AM, Binquet C, Colonna M, Jooste V. A new approach to estimate time-to-cure from cancer registries data. Cancer Epidemiol. 2018 Apr;53:72-80. doi: 10.1016/j.canep.2018.01.013. Epub 2018 Feb 4. PMID: 29414635. (pubmed)

TTC_ic_Jakobsen_wei function

Description

calculates the confidence interval of the time TTC using the Jakobsen's approach. Note that this function is for mixture cure model with Weibull distribution considered for uncured patients.

Usage

TTC_ic_Jakobsen_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  epsilon = 0.05,
  level = 0.975
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

level

1-alpha/2-order quantile of a normal distribution

TTC_ic_adtneh2 function

Description

calculates confidence interval of the time TTC from a non-mixture model with distribution "tneh"

Usage

TTC_ic_adtneh2(
  z_alpha,
  z_tau,
  xmax,
  object,
  epsilon = epsilon,
  level = level,
  TTC,
  varTTC
)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

xmax

time max at which Pi(t) is calculated.

object

ouput from a model implemented in curesurv

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

level

1-alpha/2-order quantile of a normal distribution

TTC

time to cure TTC,if NULL then calculated

varTTC

variance of time to cure ,if NULL then calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

TTC_ic_adtneh2_log function

Description

Produce confidence interval of the time TTC with log method

Usage

TTC_ic_adtneh2_log(
  z_alpha,
  z_tau,
  xmax,
  object,
  epsilon = epsilon,
  level = level,
  TTC = NULL,
  varTTC = NULL
)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

xmax

time max at which Pi(t) is calculated.

object

ouput from a model implemented in curesurv

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

level

1-alpha/2-order quantile of a normal distribution

TTC

time to cure TTC,if NULL then calculated

varTTC

variance of time to cure ,if NULL then calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

TTC_ic_log_wei function

Description

calculates the confidence interval of the time TTC using delta method by assuming normality on log scale of TTC. IC = exp(log(TTC) +/- z*sqrt(var(log(TTC)))), where Var(log(TTC)) = (dlog(TTC)/dtheta)Var(theta)(dlog(TTC)/dtheta)^T.

Note that this function is for mixture cure model with Weibull distribution considered for uncured patients.

Usage

TTC_ic_log_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  epsilon = 0.05,
  level,
  TTC = NULL,
  Dttc = NULL
)

Arguments

object

An object of class curesurv.

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

level

1-alpha/2-order quantile of a normal distribution

TTC

time to cure calculated by TTC_wei

Dttc

partial derivates of TTC by dTTCdtheta_wei

TTC_ic_multneh function

Description

calculates confidence interval of the time TTC from a non-mixture model with distribution "tneh", link_tau="loglinear"

Usage

TTC_ic_multneh(
  z_alpha,
  z_tau,
  xmax,
  object,
  epsilon = epsilon,
  level = level,
  TTC = NULL,
  DpTTC = NULL,
  cumLexctopred = NULL
)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

xmax

time max at which Pi(t) is calculated.

object

ouput from a model implemented in curesurv

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

level

1-alpha/2-order quantile of a normal distribution

TTC

The time to cure, if NULL it is recalculated

DpTTC

partial derivatives, recalculated if not given

cumLexctopred

pre prediction, calculated if NULL

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

TTC_ic_multneh_log function

Description

Produce confidence interval of the time TTC with log method

Usage

TTC_ic_multneh_log(
  z_alpha,
  z_tau,
  xmax,
  object,
  epsilon = epsilon,
  level = level,
  TTC = NULL,
  DpTTC = NULL,
  cumLexctopred = NULL
)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

xmax

time max at which Pi(t) is calculated.

object

ouput from a model implemented in curesurv

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

level

1-alpha/2-order quantile of a normal distribution

TTC

The time to cure, if NULL it is recalculated

DpTTC

partial derivatives, recalculated if not given

cumLexctopred

pre prediction, calculated if NULL

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

TTC_ic_wei function

Description

calculates the confidence interval of the time TTC. Note that this function is for mixture cure model with Weibull distribution considered for uncured patients.

Usage

TTC_ic_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  epsilon = 0.05,
  level,
  TTC = NULL,
  Dttc = NULL
)

Arguments

object

An object of class curesurv.

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

level

1-alpha/2-order quantile of a normal distribution

TTC

time to cure calculated by TTC_wei

Dttc

partial derivates of TTC by dTTCdtheta_wei

TTC_multneh function

Description

Usage

TTC_multneh(z_alpha, z_tau, xmax, object, epsilon = epsilon)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

xmax

time max at which Pi(t) is calculated.

object

ouput from a non mixture model with distribution "tneh" from curesurv function, with link_tau="loglinear"

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

TTC_theoric_adtneh function

Description

Product the value of TTC with TNEH model

Usage

TTC_theoric_adtneh(newdata, object)

Arguments

newdata

newdata

object

An object of class curesurv.

TTC_wei function

Description

calculates the probability Pi(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t. In other words, Pi(t)=(probability of being cured and alive up to time t given xi)/ (probability of being alive up to time t given xi)

Note that this function is for mixture cure model with Weibull distribution considered for uncured patients.

Usage

TTC_wei(z_pcured = z_pcured, z_ucured = z_ucured, theta, epsilon = 0.05)

Arguments

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

theta

estimated parameters

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

anova.curesurv function for likelihood-ratio test of two nested models from curesurv function

Description

This function computes an analysis of deviance table for two excess hazard models fitted using the curesurv R package.

Usage

## S3 method for class 'curesurv'
anova(object, ..., test = "LRT")

Arguments

object

An object of class curesurv.

...

Additional object of class curesurv.

test

A character string. Computes the likelihood-ratio test for value "LRT". In case the two models are the same, but one with the correction of mortality tables and one without, the likelihood ratio test is computed for value "LRT_alpha" These are the only tests available for now.

Value

An object of class anova inheriting from class matrix. The different columns contain respectively the degrees of freedom and the log-likelihood values of the two nested models, the degree of freedom of the chi-square statistic, the chi-square statistic, and the p-value of the likelihood ratio test.

Note

The comparison between two or more models by anova or more excess hazard models will only be valid if they are fitted to the same dataset, and if the compared models are nested. This may be a problem if there are missing values.

Examples


library("curesurv")
library("survival")

testiscancer$age_crmin <- (testiscancer$age - min(testiscancer$age)) / sd(testiscancer$age)

fit_m0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

fit_m1 <- curesurv(Surv(time_obs, event) ~ age_crmin | 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

anova(fit_m0, fit_m1)

cumLexc_alphaeweibull function

Description

calculates the cumulative excess hazard from an exponentiated Weibull distribution

Usage

cumLexc_alphaeweibull(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  theta = theta,
  sign_delta = 1
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion.

x

the time arguments at which to calculate the cumulative excess hazard

theta

the parameters of the cumulative excess hazard from an exponentiated Weibull distribution

sign_delta

only used for mixture cure rate models to specify if the effects or minus the effects of covariates acting on uncured survival to be considered. Default will be sign_delta = "1". The alternative is sign_delta = "-1".

@keywords cumLexc_alphaeweibull

Value

An object of class curesurv. This object is a vector containing:

cumHazE

values of the cumulative excess hazard at the time points considered for the calculations

References

Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42, 299-302.

Mudholkar, G.S., Srivastava, D.K., and Freimer, M. (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data, Technometrics, 37, 436-445.doi:10.2307/1269735 (jstor)

cumLexc_alphaweibull function

Description

calculates the cumulative excess hazard from a Weibull distribution

Usage

cumLexc_alphaweibull(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  theta = theta,
  sign_delta = 1
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion.

x

the time arguments at which to calculate the cumulative excess hazard

theta

estimated parameters of the cumulative excess hazard from a mixture model using curesurv and uncured survival following a Weibull distribution

sign_delta

Value

This object is a list containing the following components:

cumhaz

cumulative excess hazard estimates

usurv

survival of uncured

SurvE

net survival estimates

cured

cure fraction

ptcure

the probability Pi(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t.

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

cumLexc_alphaweibull_topred function

Description

calculates the cumulative excess hazard from a Weibull distribution

Usage

cumLexc_alphaweibull_topred(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  theta = theta,
  sign_delta = 1
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion.

x

the time arguments at which to calculate the cumulative excess hazard

theta

the parameters of the cumulative excess hazard from a Weibull distribution

sign_delta

Value

This object is a list containing the following components:

cumhaz

cumulative excess hazard estimates

usurv

survival of uncured

SurvE

net survival estimates

cured

cure fraction

pt_cure

the conditionnal probability of being cured knowing they are alive at t

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

cumLexc_mul function

Description

returns the cumulative excess hazard for an TNEH model in case of parametrization of log the of the time to null excess hazard as function to fit the data

Usage

cumLexc_mul(z_tau, z_alpha, x, theta)

Arguments

z_tau

covariates depending on tau

z_alpha

covariates depending on alpha

x

time value

theta

of the coefficient of tneh parameters

Value

An object of class numeric containing the cumulative excess hazard with the same length as the time.

Fitting cure models using curesurv

Description

Fits the non-mixture cure model proposed by Boussari et al. (2020), or mixture cure model such as proposed by De Angelis et al. (1999) with the possibility to correct the background mortality as proposed by Phillips et al. (2002) in the net survival framework.

Non-mixture cure model

The Boussari model

This model allows for direct estimation of time-to-null-excess-hazard which can be interpreted as time-to-cure. The parametrization offers various link functions for the covariates effects on the time-to-null-excess-hazard: τ(z_k) = g(τ₀ + z_k τ_k). If link_tau=linear, then g is the identity function. If link_tau=loglinear then g is the exponential function. In this model, the cure proportion is expressed as: π(z;θ) = exp(−g(τ₀ + z_k τ_k) \text{Beta}((\alpha_{0} + Z_{k} \alpha_{k}), \beta)).

Mixture cure model

The user can choose the survival function modeling the uncured patients net survival among Weibull (default) and exponentiated Weibull. The parametrization for weibull distribution is S_u(t) = exp(−λt^γ)^exp(δZ). The related hazard function is expressed as: λ_u(t) = γλt^{γ− 1} exp(δz) The net survival and the excess hazard functions can be respectively expressed as S_E(t) = π(z;β) + (1 − π(z;β)) * S_u(t). and λ_E(t)=[((1−π(z;β))fu(t))/(π(z;β) + (1 − π(z;β))S_u(t))], with π(z;β) = [1/((1 + exp(−[β₀ + Zβ])))].

Correction of background mortality

Usually, in the net survival framework the expected hazard is directly obtained from life tables. However some patients in cancer registries can have some factors impacting their expected mortality rates (such as comorbidities, deprivation) that are not always accounted #' for in the available life tables, and there is a need to account for this problem. The correction proposed by Phillips et al (2002) assumes that λ_exp(t,z)=αλ_pop(t,z_k) with λ_exp(t,z) the patient expected hazard and λ_pop(t,z_k) the population hazard obtained from life table.

Usage

curesurv(
  formula,
  data,
  pophaz = NULL,
  cumpophaz = NULL,
  pophaz.alpha = FALSE,
  model = "nmixture",
  dist = "weib",
  link_tau = "linear",
  ncoor_des = NULL,
  init = NULL,
  maxit_opt = 10000,
  gradient = FALSE,
  hessian_varcov = TRUE,
  optim_func = "optim",
  optimizer = "optim",
  method_opt = "L-BFGS-B",
  trace = 0,
  nvalues = 10,
  iter_eps = 1e-08,
  optim_fixed = NULL,
  clustertype = NULL,
  nproc = 1,
  subset,
  na.action,
  sign_delta,
  ...
)

Arguments

formula

a formula object of the Surv function with the response on the left of a ~ operator and the terms on the right. The response must be a survival object as returned by the Surv function (time in first and status in second).

data

a data frame in which to interpret the variables named in the formula

pophaz

corresponds to the name of the column in the data representing the values of the population instantaneous mortality rates. If the pophaz argument is not specified, overall survival is fitted.

cumpophaz

corresponds to the name of the column in the data representing the values of the instantaneous population cumulative mortality rates. If not specified, the model cannot be compared with model with pophaz.alpha = TRUE using AIC.

pophaz.alpha

to be specified if user want an excess hazard model with correction of mortality rates by a scale parameter

model

To fit a mixture model, specify model = "mixture". To fit Time-To-Null Excess Hazard model the argument is model = "tneh".

dist

For mixture model, it corresponds to the function used to fit the uncured patients survival. By default, ("weib") is used. Another option is the exponentiated Weibull function ("eweib"). For non-mixture models, this argument corresponds to the name of the model. By default, ("tneh") is used to fit the time to null excess hazard model proposed by Boussari et al..

link_tau

must be specified only for model ="tneh". Default is linear link ("linear"). Another link is loglinear ("loglinear").

ncoor_des

if null, the initial parameters are defaults. If else, the initials parameters are obtained via coordinates descent algorithms

init

a list containing the vector of initial values theta_init, the vector of upper bounds theta_upper and the vector of the lower bounds theta_lower for the parameters to estimate. For each elements of the list, give the name of the covariate followed by the vector of the fixed initials values

maxit_opt

option for maximum of iteration in optimization function

gradient

True if optimization process requires gradient to be provided

hessian_varcov

TRUE if user wants variance covariance matrix using hessian function

optim_func

specify which function to be used for optimization purposes.

optimizer

only use this argument when optim_func="bbmle"

method_opt

optimization method used in optim function. The default algorithm is "L-BFGS-B".

trace

Non-negative integer corresponding to the trace argument as in optim

nvalues

number of set of initial values when using multiple initials values

iter_eps

this parameter only works when ncoor_des = "iter"; It allows to run coordinates descent algorithm until the stooping criteria equal at least to the specified value.

optim_fixed

to specify with parameter to not estimated in the estimation process

clustertype

related to cluster type in marqLevAlg package

nproc

number of processors for parallel computing as in marqLevAlg

subset

an expression indicating which subset of the data should be used in the modeling. All observations are included by default

na.action

as in the coxph function, a missing-data filter function.

sign_delta

...

additional parameters such z_alpha, and z_tau. For more details, use the help function.

Value

An object of class curesurv. This object is a list containing the following components:

iter_coords

number of iterations performed to obtain initial values of the parameters in tneh model only

coefficients

estimates found for the model

estimates

estimates in the appropriate scale for the model

loglik

corresponds to the log-likelihood computed; if only the pophaz is provided, the log-likelihood doesn't correspond to the total log-likelihood. The part of the cumulative population hazard is a constant and is dropped for the computation as presented in Esteve et al. (1990); The total log-likekihood is calculed if the user specifies a column name equal expected cumulative mortality (cumpophaz)

iteractions

the number iterations attained to estimate the parameters of the related model

evaluations

the number of times the log-likelihood function was evaluated until to reach the convergence

convergence

an integer code as in optim when L-BFGS-B method is used in optim.

message

a character string returned by the optimizer

varcov

the variance covariance matrix of the parameters estimated

varcov_star

the variance covariance matrix of the coefficients of the model of interest

std_err

the standard errors of the estimated parameters

std_err_star

the standard errors of the coefficients of the model of interest

AIC

the Akaike information criteria from the model of interest

n.events

the number of events in the dataset. Events are considered

n.obs

the number of observations in the dataset.

model

if fitted model is a mixture model, it returns "mixture". If fitted model is Time-To-Null Excess Hazard model, it returns "nmixture".

Terms

the representation of the terms in the model

pophaz.alpha

logical value to indicate if fitted cure model requires correction of mortality rates by a scale parameter

pophaz

corresponds to the the population instantaneous mortality rates.

cumpophaz

corresponds to the population cumulative mortality rates.

frailtyhp

a booleen to be specified if a frailty correction is needed for the population hazard.

dist

For mixture model, it corresponds to the function used to fit the uncured patients survival. By default, ("weib") is used. Another option is the exponentiated Weibull function ("eweib"). For non-mixture models, this argument corresponds to the name of the model. By default, ("tneh") is used to fit the time to null excess hazard model proposed by Boussari et al.

xmax

maximum follow-up time to evaluate the TTC

z_tau

Covariates acting on parameter tau in non mixture cure model tneh

link_tau

returned only for model ="tneh"; returned by default is "linear" or "loglinear" for linear or loglinear link function of covariates acting on tau parameter.

z_alpha

Covariates acting on parameter alpha in non mixture cure model tneh

z_c

Covariates acting on cure fraction in mixture cure model

z_ucured

covariates acting on survival of uncured in mixture cure model

z_pcured

Covariates acting on cure fraction in mixture cure model

z_ucured

covariates acting on survival of uncured in mixture cure model

data

the dataset used to run the model

call

the function call based on model

formula

the formula as a formula object

Note

Note that all these models can be fitted in the overall survival setting.

time is OBLIGATORY in years

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

Botta L, Caffo O, Dreassi E, Pizzoli S, Quaglio F, Rugge M, Valsecchi MG. A new cure model that corrects for increased risk of non-cancer death: analysis of reliability and robustness, and application to real-life data. BMC Med Res Methodol. 2023 Mar 25;23(1):70. doi: 10.1186/s12874-023-01876-x. PMID: N/A. (pubmed)

Examples


library("curesurv")
library("survival")



# Net survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate

theta_init2 <- rep(0, 3)
theta_lower2 <- c(-Inf,-Inf,-Inf)
theta_upper2 <- c(Inf, Inf, Inf)


fit_m0_ml <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             pophaz = "ehazard",
             cumpophaz = "cumehazard",
             model = "mixture", dist = "weib",
             data = testiscancer,
             init = list(theta_init = theta_init2,
             theta_lower = theta_lower2,
             theta_upper = theta_upper2),
             method_opt = "L-BFGS-B")
fit_m0_ml



# Mixture cure model with Weibull function for the uncured patients survival:
#standardized age as covariate


fit_m2_ml <- curesurv(Surv(time_obs, event) ~ age_cr | age_cr,
                   pophaz = "ehazard",
                   cumpophaz = "cumehazard",
                   model = "mixture", dist = "weib",
                   data = testiscancer,
                   method_opt = "L-BFGS-B")

 fit_m2_ml



## Non mixture cure model
### TNEH Null model
#### loglinear effect of covariates on time-to-null excess hazard

theta_init2 <- rep(0, 3)
theta_lower2 <- c(-Inf,-Inf,-Inf)
theta_upper2 <- c(Inf, Inf, Inf)

fit_m0_mult_tneh <- curesurv(Surv(time_obs, event) ~ 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "loglinear",
                          data = testiscancer,
                          init = list(theta_init = theta_init2,
                                      theta_lower = theta_lower2,
                                      theta_upper = theta_upper2),
                          method_opt = "L-BFGS-B")


fit_m0_mult_tneh

#### Additive parametrization
theta_init2 <- c(1, 6, 6)
theta_lower2 <- c(0,1,0)
theta_upper2 <- c(Inf, Inf, Inf)

fit_m0_ad_tneh <- curesurv(Surv(time_obs, event) ~ 1,
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "linear",
                          data = testiscancer,
                          init = list(theta_init = theta_init2,
                                      theta_lower = theta_lower2,
                                      theta_upper = theta_upper2),
                          method_opt = "L-BFGS-B")



 fit_m0_ad_tneh

#### Additive parametrization, with covariates
fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_alpha(age_cr) +
                          z_tau(age_cr),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture",
                          dist = "tneh", link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")



 fit_m1_ad_tneh

dTTCdtheta_wei function

Description

function of partial derivates of time-to-cure (TTC) by theta (estimated parameters) from a mixture cure model with uncured survival following a Weibull distribution

Usage

dTTCdtheta_wei(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  theta = theta,
  epsilon = epsilon,
  TTC
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

theta

estimated parameters from the ouput of a mixture cure model implemented in curesurv

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

TTC

time-to-cure previously estimated using TTC_wei

Simulated data with vital status information from Weibull mixture cure model

Description

Simulated data

Usage

data(dataweib)

Format

This dataset contains the following variables:

age: Age at diagnosis
age_cr: centered and scaled age at diagnosis
age_classe: "<45", "45_59" and ">=60" age groups
sexe: "male", "female" gender groups
stage: "<0", "1" , "2" and "3" for stage I-IV groups
time_obs: Follow-up time (years)
event: Vital status
cumehazard: individual cumulative expected hazard
ehazard: individual instantaneous expected hazard

Examples

data(dataweib)
summary(dataweib)

dexhazdtheta_adtneh2 function

Description

Partial derivatives of excess hazard by theta from non-mixture model with distribution "tneh".

Usage

dexhazdtheta_adtneh2(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  cumLexctopred = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the estimates are predicted

object

ouput from model implemented in curesurv

cumLexctopred

a pre-prediction parameter, calculated if NULL

dexhazdtheta_multneh function

Description

@description Partial derivatives of excess hazard by theta from non-mixture model with distribution "tneh".

Usage

dexhazdtheta_multneh(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  cumLexctopred = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the estimates are predicted

object

ouput from model implemented in curesurv

cumLexctopred

a pre-prediction parameter, calculated if NULL

dexhazdtheta_wei function

Description

Produce partial derivatives of excess hazard

Usage

dexhazdtheta_wei(
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x = x,
  theta,
  cumLexctopred
)

Arguments

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

theta

estimated parameters from a mixture model using curesurv and uncured survival following a Weibull distribution

cumLexctopred

pre prediction obtained with cumLexc_alphaweibull_topred

digamma function

Description

digamma function

Usage

digamma(z)

Arguments

z

positive argument

Value

An object of type numeric. This object is a vector of the same length as x. The output element is :

psi

frac{d ln(\tau(x))}{dx} = \frac{\tau'(x)}{\tau(x)}. This equal to the output of base::digamma(x)

dlogCumHazdtheta_wei function

Description

function of partial derivates of log-log of net survival depending on theta (estimated parameters) from a mixture cure model with uncured survival following a Weibull distribution

Usage

dlogCumHazdtheta_wei(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  theta = theta,
  cumLexctopred
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

x

time at which the estimates are predicted

theta

estimated parameters from the ouput of a mixture cure model implemented in curesurv

cumLexctopred

a pre-prediction parameter obtained with cumLexc_alphaweibull_topred

dlogTTCdtheta_wei function

Description

function of partial derivates of log of time-to-cure log(TTC) by theta (estimated parameters) from a mixture cure model with uncured survival following a Weibull distribution

Usage

dlogTTCdtheta_wei(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  object = object,
  epsilon = epsilon,
  TTC
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

object

ouput from a model implemented in curesurv

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

TTC

time to cure previsouly estimated by TTC_wei

dloglogpdtheta_wei function

Description

Produce partial derivatives of log(log(p(t)))) the logarithm of the probability to be cured

Usage

dloglogpdtheta_wei(
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x = x,
  theta,
  cumLexctopred
)

Arguments

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

theta

estimated parameters of the cumulative excess hazard from a mixture model using curesurv and uncured survival following a Weibull distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_alphaweibull_topred

dlogpdtheta_wei function

Description

Produce partial derivatives of log(p(t)) the logarithm of the probability to be cured

Usage

dlogpdtheta_wei(
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x = x,
  theta,
  cumLexctopred
)

Arguments

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

theta

estimated parameters of the cumulative excess hazard from a mixture model using curesurv and uncured survival following a Weibull distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_alphaweibull_topred

dlogsndtheta_wei function

Description

function of partial derivates of log of net survival depending on theta (estimated parameters) from a mixture cure model with uncured survival following a Weibull distribution

Usage

dlogsndtheta_wei(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  theta = theta,
  cumLexctopred
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

x

time at which the estimates are predicted

theta

estimated parameters from the ouput of a mixture cure model implemented in curesurv

cumLexctopred

a pre-prediction parameter obtained with cumLexc_alphaweibull_topred

dpdtheta_adtneh2 function

Description

Partial derivatives of probability to be cure by theta from non-mixture model with distribution "tneh".

Usage

dpdtheta_adtneh2(
  z_alpha = z_alpha,
  z_tau = z_tau,
  x = x,
  object,
  cumLexctopred = NULL,
  Dpi = NULL,
  Dsn = NULL
)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

x

time at which the estimates are predicted

object

ouput from model implemented in curesurv

cumLexctopred

a pre-prediction obtained with cumLexc_ad2_topred, if NULL will be calculated

Dpi

partial derivatives of pi the cure proportion by theta calculated by dpidtheta_adtneh2, if NULL will be calculated

Dsn

partial derivatives of net survival by theta calculated by dsndtheta_adtneh2, if NULL will be calculated

dpdtheta_wei function

Description

Produce partial derivatives of p(t) the probability to be cured

Usage

dpdtheta_wei(
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x = x,
  theta,
  cumLexctopred
)

Arguments

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

theta

estimated parameters from a mixture model using curesurv and uncured survival following a Weibull distribution

cumLexctopred

description

dpidtheta_adtneh2 function

Description

Partial derivatives of pi (net survival at tau) by theta

#' @description Partial derivatives of cure fraction (or net survival at tau) by theta from non-mixture model with distribution "tneh".

Usage

dpidtheta_adtneh2(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  cumLexctopred = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the estimates are predicted

object

ouput from model implemented in curesurv

cumLexctopred

pre prediction (obtained from cumLexc_ad2_topred), if NULL then it is calculated

dpidtheta_multneh function

Description

@description Partial derivatives of cure fraction (or net survival at tau) by theta from non-mixture model with distribution "tneh" when link_tau="loglinear".

Usage

dpidtheta_multneh(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  cumLexctopred = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the estimates are predicted

object

ouput from model implemented in curesurv

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, calculated if NULL

dpitheta_wei function

Description

Produce partial derivatives of pi the cure proportion

Usage

dpidtheta_wei(
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x = x,
  theta,
  cumLexctopred
)

Arguments

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

theta

estimated parameters from a mixture model using curesurv and uncured survival following a Weibull distribution

cumLexctopred

description

dptdtheta_multneh function

Description

Partial derivatives of probability to be cure by theta from non-mixture model with distribution "tneh".

Usage

dptdtheta_multneh(
  z_alpha = z_alpha,
  z_tau = z_tau,
  x = x,
  object,
  cumLexctopred = NULL,
  Dpi = NULL,
  Dsn = NULL
)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

x

time at which the estimates are predicted

object

ouput from model implemented in curesurv

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, if NULL will be calculated

Dpi

partial derivative of pi according to theta, if NULL will be calculated

Dsn

partial derivative of net survival according to theta , if NULL will be calculated

dpttcdtheta_adtneh2 function

Description

Partial derivatives of probability to be cure by theta which can be evaluated at t = TTC, from predictions based on non-mixture model with distribution "tneh".

Usage

dpttcdtheta_adtneh2(
  z_tau,
  z_alpha,
  x = x,
  object,
  cumLexctopred = NULL,
  Dpi = NULL,
  Dsn = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

cumLexctopred

a pre-prediction parameter obtained with cumLexc_ad2_topred, if NULL will be calculated

Dpi

partial derivative of pi according to theta at time TTC, if NULL will be calculated

Dsn

partial derivative of net survival according to theta at time TTC, if NULL will be calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

dpttcdtheta_adtneh2 function

Description

Partial derivatives of probability to be cure by theta which can be evaluated at t = TTC, from predictions based on non-mixture model with distribution "tneh", link="loglinear".

Usage

dpttcdtheta_multneh(
  z_tau,
  z_alpha,
  x = x,
  object,
  res_pred = NULL,
  Dpi = NULL,
  Dsn = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

res_pred

a pre prediction parameter obtained with cumLexc_mul_topred

Dpi

Partial derivatives of Pi at time TTC, if NULL then calculated

Dsn

Partial derivatives of net survival at time TTC, if NULL then calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

dsndtheta_adtneh2 function

Description

Partial derivatives of sn (net survival) by theta

Usage

dsndtheta_adtneh2(z_tau, z_alpha, x, object, cumLexctopred = NULL, Dpi = NULL)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

cumLexctopred

pre prediction thing (obtained from cumLexc_ad2_topred), if NULL then it is calculated

Dpi

partial derivates of pi according to theta, if NULL it is calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

dsndtheta_multneh function

Description

Partial derivatives of sn (net survival) by theta for the link_tau="loglinear" model

Usage

dsndtheta_multneh(z_tau, z_alpha, x, object, cumLexctopred = NULL, Dpi = NULL)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, estimated if NULL

Dpi

partial derivative of pi according to theta, if NULL will be calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

dsndtheta_wei function

Description

function of partial derivates of net survival depending on theta (estimated parameters) from a mixture cure model with uncured survival following a Weibull distribution

Usage

dsndtheta_wei(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  theta = theta,
  cumLexctopred
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

x

time at which the estimates are predicted

theta

estimated parameters from the ouput of a mixture cure model implemented in curesurv

cumLexctopred

pre prediction obtained with cumLexc_alphaweibull_topred

exhaz_ic_adtneh2 function

Description

produces confidence interval of excess hazard using a time-to-null excess hazard model with linear effect on parameter tau The confidence intervals calculation is based on the plain method.

Usage

exhaz_ic_adtneh2(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  Dexhaz = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

Dexhaz

parital derivatives of exess hazard wrt theta obtained by dexhazdtheta_adtneh2, calculated if not given

exhaz_ic_adtneh2_log function

Description

produces confidence interval of excess hazard using a time-to-null excess hazard model with linear effect on parameter tau The confidence intervals calculation is based on the log method.

Usage

exhaz_ic_adtneh2_log(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  Dexhaz = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

Dexhaz

parital derivatives of exess hazard wrt theta obtained by dexhazdtheta_adtneh2, calculated if not given

exhaz_ic_adtneh2_loglog function

Description

produces confidence interval of excess hazard using a time-to-null excess hazard model with linear effect on parameter tau The confidence intervals calculation is based on the log-log method.

Usage

exhaz_ic_adtneh2_loglog(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  Dexhaz = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

Dexhaz

parital derivatives of exess hazard wrt theta obtained by dexhazdtheta_adtneh2, calculated if not given

exhaz_ic_multneh function

Description

produces confidence interval of excess hazard using a time-to-null excess hazard model with loglinear effect on parameter tau The confidence intervals calculation is based on the plain method.

Usage

exhaz_ic_multneh(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  Dexhaz = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

Dexhaz

parital derivatives of exess hazard wrt theta obtained by dexhazdtheta_multneh, calculated if not given

exhaz_ic_multneh_log function

Description

produces confidence interval of excess hazard using a time-to-null excess hazard model with loglinear effect on parameter tau The confidence intervals calculation is based on the log method.

Usage

exhaz_ic_multneh_log(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  Dexhaz = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

Dexhaz

parital derivatives of exess hazard wrt theta obtained by dexhazdtheta_multneh, calculated if not given

exhaz_ic_multneh_loglog function

Description

produces confidence interval of excess hazard using a time-to-null excess hazard model with loglinear effect on parameter tau The confidence intervals calculation is based on the log-log method.

Usage

exhaz_ic_multneh_loglog(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  Dexhaz = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

Dexhaz

parital derivatives of exess hazard wrt theta obtained by dexhazdtheta_multneh, calculated if not given

exhaz_ic_wei function

Description

Calculates the confidence intervals of excess hazard by Delta Method

Usage

exhaz_ic_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dexhaz,
  exhaz
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained with cumLexc_alphaweibull_topred

Dexhaz

partial derivatives of exhaz

exhaz

estimation of exhaz

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

exhaz_ic_wei_log function

Description

Calculates the confidence intervals of excess hazard by "log" Delta Method

Usage

exhaz_ic_wei_log(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dexhaz,
  exhaz
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained with cumLexc_alphaweibull_topred

Dexhaz

partial derivatives of exhaz

exhaz

estimation of exhaz

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

exhaz_ic_wei_loglog function

Description

Calculates the confidence intervals of excess hazard by "log-log" Delta Method

Usage

exhaz_ic_wei_loglog(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dexhaz,
  exhaz
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained with cumLexc_alphaweibull_topred

Dexhaz

partial derivatives of exhaz

exhaz

estimation of exhaz

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

inc_beta_deriv function

Description

computes the first and second derivatives of incomplete Beta function with respect of Beta parameters p and or q using algorithm differentiating the aproximants of I_{x,p,q} formula in terms of forward recurrence relations where the the n^{th} approximant can be expressed as :

I_{x,p,q} \approx K_{x,p,q} A_n/B_n

, n \geq 1

This technique was proposed by Moore (1982) to calculate the derivatives of incomplete gamma function.

Usage

inc.beta.deriv(
  x,
  p = stop("p must be specified"),
  q = stop("q must be specified"),
  err = .Machine$double.eps * 10000,
  minapp = 2,
  maxapp = 1000
)

Arguments

x

vector of length k containing values to which the beta function is to be integrated

p

Beta shape1 parameter

q

Beta shape2 parameter. shape1 and shape2 can be vertors in the same dimension as x or scalars

err

value for error

minapp

minimal bound value

maxapp

external noud value

Value

An object of class FD.inc.beta. This object is a list containing 15 components. The first 13 components in the list are each a vector of the same length as x (u in the model). The two last elements are scalar terms. The output elements are:

I

I_{x,p,q}. This equal to the output of pbeta(x,shape1,shape2)

Ip

I_{x,p,q}^{p} denotes the first derivative of the incomplete beta function with respect to p

Ipp

I_{x,p,q}^{pp} denotes the second derivative of the incomplete beta function with respect to p

Iq

I_{x,p,q}^{q} denotes the first derivative of the incomplete beta function with respect to q

Iqq

I_{x,p,q}^{qq} denotes the second derivative of the incomplete beta function with respect to q

Ipq

I_{x,p,q}^{pq} denotes the first derivative of the incomplete beta function with respect to p and q

log.Beta

\log[\mathrm{Beta}(p,q)]

digamma.p

\psi_p

trigamma.p

\psi_p'

digamma.q

\psi_q

trigamma.q

\psi_q'

digamma.pq

\psi_{p+q}

trigamma.pq

\psi_{p+q}'

nappx

highest order approximant evaluated. Iteration stops if nappx>maxappx

errapx

approximate maximum absolute error of computed derivatives

References

Boik, Robert J., and James F. Robison-Cox. "Derivatives of the incomplete beta function." Journal of Statistical Software 3.1 (1998): 1-20. (arXiv)

lexc_alphaeweibull function

Description

calculates the instantaneous excess hazard from an exponentiated Weibull distribution

Usage

lexc_alphaeweibull(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  theta = theta,
  sign_delta = 1
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion.

x

the time arguments at which to calculate the cumulative excess hazard

theta

the parameters of the cumulative excess hazard from an exponentiated Weibull distribution

sign_delta

Value

An object of class curesurv. This object is a vector containing:

References

Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42, 299-302.

Mudholkar, G.S., Srivastava, D.K., and Freimer, M. (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data, Technometrics, 37, 436–445.doi:10.2307/1269735 (jstor)

lexc_alphaweibull function

Description

calculates the instantaneous excess hazard from a Weibull distribution

Usage

lexc_alphaweibull(
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  theta = theta,
  sign_delta = 1
)

Arguments

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion.

x

the time arguments at which to calculate the cumulative excess hazard

theta

the parameters of the cumulative excess hazard from a Weibull distribution

sign_delta

Value

An object of class curesurv. This object is a vector containing:

References

Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42, 299–302.

Mudholkar, G.S., Srivastava, D.K., and Freimer, M. (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data, Technometrics, 37, 436-445.doi:10.2307/1269735 (jstor)

logCumHaz_ic_wei function

Description

calculates the confidence intervals of the log of cumulative excess hazard log(-log(Sn(t))) using variances of log(-log(Sn(t))). In this formula, the variance of log of the cumulative excess hazard is obtained using delta method at the scale of log-log of net survival, and with the expression Var(log(log(Sn(t)))) = (dlog(-log(Sn(t)))/dtheta)Var(theta)(dlog(-log(Sn(t)))/dtheta)^T; the Var(theta) is the variance-covariance matrix of theta (estimated parameters).

Usage

logCumHaz_ic_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre prediction obtained with cumLexc_alphaweibull

Simulated pancreas data with vital status information

Description

Simulated data

Usage

data(pancreas_data)

Format

This dataset contains the following variables:

age: Age at diagnosis
age_cr: centered and scaled age at diagnosis
age_classe: "<45", "45_59" and ">=60" age groups
time_obs: Follow-up time (years)
event: Vital status
cumehazard: individual cumulative expected hazard
ehazard: individual instantaneous expected hazard

Examples

data(pancreas_data)
summary(pancreas_data)

pcured function

Description

calculates cure fraction of mixture and non mixture cure models.

Usage

pcured(
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object
)

Arguments

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

Value

An object of class c("cure_fraction", "data.frame"). This object is a list containing the following components:

time

time in the input new data

netsurv

predicted net survival at the time provided in the new data

pi

pi or net survival at time tau

pi_ic_adtneh2 function

Description

produces confidence interval of cure fraction pi using a time-to-null excess hazard model with linear effect on parameter tau The confidence intervals calculation is based on the plain method.

Usage

pi_ic_adtneh2(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexc_topred = NULL,
  Dpi = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexc_topred

a pre prediction, if NULL it is calculated

Dpi

partial derivative of pi by theta obtained by dpidtheta_adtneh2 function, if NULL it is calculated

pi_ic_adtneh2_log function

Description

produces confidence interval of cure fraction pi using a time-to-null excess hazard model with linear effect on parameter tau The confidence intervals based on log method.

Usage

pi_ic_adtneh2_log(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexc_topred = NULL,
  Dpi = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexc_topred

a pre prediction, if NULL it is calculated

Dpi

partial derivative of pi by theta obtained by dpidtheta_adtneh2 function, if NULL it is calculated

pi_ic_adtneh2_loglog function

Description

produces confidence interval of cure fraction pi using a time-to-null excess hazard model with linear effect on parameter tau The confidence intervals based on log-log method.

Usage

pi_ic_adtneh2_loglog(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexc_topred = NULL,
  Dpi = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexc_topred

a pre prediction, if NULL it is calculated

Dpi

partial derivative of pi by theta obtained by dpidtheta_adtneh2 function, if NULL it is calculated

pi_ic_log_wei function

Description

calculates the confidence intervals of the cure proportion pi using variances of log(pi) by delta method

Usage

pi_ic_log_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dpi
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre prediction obtained with cumLexc_alphaweibull_topred

Dpi

Partial derivative of Pi calculated by dpidtheta_wei function

pi_ic_loglog_wei function

Description

calculates the confidence intervals of the cure proportion pi using variances of log(-log(pi)) by delta method

Usage

pi_ic_loglog_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dpi
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre prediction obtained with cumLexc_alphaweibull_topred

Dpi

Partial derivative of Pi calculated by dpidtheta_wei function

pi_ic_multneh function

Description

produces confidence interval of cure fraction pi using a time-to-null excess hazard model with loglinear effect on parameter tau The confidence intervals calculation is based on the plain method.

Usage

pi_ic_multneh(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpi = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, calculated if NULL

Dpi

partial derivative of pi according to theta, if NULL calculated

pi_ic_multneh_log function

Description

produces confidence interval of cure fraction pi using a time-to-null excess hazard model with loglinear effect on parameter tau The confidence intervals based on log method.

Usage

pi_ic_multneh_log(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpi = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, calculated if NULL

Dpi

partial derivative of pi according to theta, if NULL calculated

pi_ic_multneh_loglog function

Description

produces confidence interval of cure fraction pi using a time-to-null excess hazard model with log linear effect on parameter tau The confidence intervals based on log-log method.

Usage

pi_ic_multneh_loglog(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpi = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, calculated if NULL

Dpi

partial derivative of pi according to theta, if NULL calculated

pi_ic_wei function

Description

Calculates the confidence intervals of the cure proportion by Delta Method on pi

Usage

pi_ic_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dpi
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_alphaweibull

Dpi

partial derivatives of pi by theta, obtained with dpidtheta_wei function

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste#'

plot method for curesurv prediction objects

Description

Produces figures of (excess) hazard, (net) survival and probability P(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t.

Usage

## S3 method for class 'predCuresurv'
plot(
  x,
  fun = "all",
  conf.int = FALSE,
  conf.type = c("log", "log-log", "plain"),
  legend.out = TRUE,
  xlab = "Time since diagnosis",
  ylab.haz = "excess hazard",
  ylab.surv = "net survival",
  ylab.ptcure = "P(t)",
  ylab.cumhaz = "cumulative excess hazard",
  ylab.logcumhaz = "logarithm of cumulative excess hazard",
  col.haz = "black",
  col.surv = "black",
  col.ptcure = "black",
  col.cumhaz = "black",
  col.logcumhaz = "black",
  col.tau = "red",
  col.ttc = "green4",
  col.p95 = "black",
  col.pi = "blue",
  lty.surv = 1,
  lty.haz = 1,
  lty.ptcure = 1,
  lty.cumhaz = 1,
  lty.logcumhaz = 1,
  lty.pi = 2,
  lty.tau = 2,
  lty.ttc = 3,
  lty.p95 = 4,
  lty.ic = 5,
  lwd.main = 1,
  lwd.sub = 1,
  lwd.ic = 1,
  ...
)

Arguments

x

result of the predCuresurv function

fun

in "haz" or "surv" or "pt_cure", "cumhaz", "logcumhaz", the plot produced is that of (excess) hazard, or that of (net) survival, or that of the probability P(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t is provided, or that of cumulative hazard or that of the logarithm of the cumulative hazard; if fun = "all", the plots of the three first indicators are produced.

conf.int

an argument expected to be TRUE if the confidence intervals of the related-indicator specified by the argument "fun" are needed. The default option is FALSE. Confidence intervals are not available for fun="cumhaz" and fun="logcumhaz"

conf.type

One of "plain", "log", "log-log". The first option causes the standard intervals curve +- k *se(curve), where k is determined from conf.int. The log option calculates intervals based on log(curve). The log-log option bases the intervals on the log(-log(curve)).

legend.out

an argument deciding the place of the legend if fun="all". The default value is TRUE and forces most of the legend on the empty bottom-right plot slot. If value is FALSE, the legend will be printed entirely in each subplot.

xlab

label for the x-axis of the plot.

ylab.haz

optional label for the y-axis of the plot of excess hazard

ylab.surv

optional label for the y-axis of the plot of net survival

ylab.ptcure

optional label for the y-axis of the plot of the probability P(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t

ylab.cumhaz

optional label for the y-axis of the plot of cumulative excess hazard

ylab.logcumhaz

optional label for the y-axis of the plot of logarithm of cumulative excess hazard

col.haz

optional argument to specify the color of curve of the excess hazard

col.surv

optional argument to specify the color of curve of the net survival

col.ptcure

optional argument to specify the color of curve of probability P(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t.

col.cumhaz

optional argument to specify the color of curve of cumulative excess hazard

col.logcumhaz

optional argument to specify the color of curve of the logarithm of cumulative excess hazard

col.tau

optional argument to specify the color of curve of time-to-null excess hazard

col.ttc

optional argument to specify the color of curve of time-to-cure

col.p95

optional argument to specify the color for the line highlighting \epsilon when P(t) \ge 1-\epsilon

col.pi

optional argument to specify the color of cure proportion

lty.surv

stands for line types for net survival

lty.haz

stands for line types for excess hazard

lty.ptcure

stands for line types for probability P(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t.

lty.cumhaz

stands for line types for cumulative excess hazard

lty.logcumhaz

stands for line types for logarithm cumulative excess hazard

lty.pi

stands for line types for cure proportion

lty.tau

stands for line types for time-to-null excess hazard

lty.ttc

stands for line types for time-to-cure

lty.p95

stands for line types for the line highlighting \epsilon when P(t) \ge 1-\epsilon

lty.ic

stands for line types for confidence intervals

lwd.main

line width for the main line (haz, surv, pt_cure, cumhaz, logcumhaz)

lwd.sub

line width for the additionnal lines (ttc, p95, tau...)

lwd.ic

line width for the confidence intervals lines

...

additional options as in the classical plot method.

ylab

optional label for the y-axis of the plot. Depending to the curve of interest (hazard, survival, probability of being cured at a given time t, or all),the argument must be named ylab.haz, ylab.surv, ylab.ptcure. If missing some default labels are provided depending on the curve of interest. This name can be found in the data.frame from the result of the predict.curesurv function.

Value

No value is returned.

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

Examples




library("curesurv")
library("survival")

 testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 fit_m1_ad_tneh


#'  #mean of age
 newdata1 <- with(testiscancer,
 expand.grid(event = 0, age_crmin = mean(age_crmin), time_obs  = seq(0.001,10,0.1)))

 pred_agemean <- predict(object = fit_m1_ad_tneh, newdata = newdata1)


 #max of age
 newdata2 <- with(testiscancer,
 expand.grid(event = 0,
 age_crmin = max(age_crmin),
  time_obs  = seq(0.001,10,0.1)))

 pred_agemax <- predict(object = fit_m1_ad_tneh, newdata = newdata2)

   # predictions at time 2 years and  of age

   newdata3 <- with(testiscancer,
      expand.grid(event = 0,
      age_crmin = seq(min(testiscancer$age_crmin),max(testiscancer$age_crmin), 0.1),
      time_obs  = 2))

   pred_age_val <- predict(object = fit_m1_ad_tneh, newdata = newdata3)

 #plot of 3 indicators for mean age

 plot(pred_agemean, fun="all")


 #plot of net survival for mean and maximum age (comparison)

oldpar <- par(no.readonly = TRUE)

par(mfrow = c(2, 2),
    cex = 1.0)
plot(pred_agemax$time,
    pred_agemax$ex_haz,
    type = "l",
    lty = 1,
    lwd = 2,
    xlab = "Time since diagnosis",
    ylab = "excess hazard")
lines(pred_agemean$time,
     pred_agemean$ex_haz,
     type = "l",
     lty = 2,
     lwd = 2)

legend("topright",
      horiz = FALSE,
      legend = c("hE(t) age.max = 79.9", "hE(t) age.mean = 50.8"),
      col = c("black", "black"),
      lty = c(1, 2, 1, 1, 2, 2))
grid()

plot(pred_agemax$time,
    pred_agemax$netsurv,
    type = "l",
    lty = 1,
    lwd = 2,
    ylim = c(0, 1),
    xlab = "Time since diagnosis",
    ylab = "net survival")
lines(pred_agemean$time,
     pred_agemean$netsurv,
     type = "l",
     lty = 2,
     lwd = 2)
legend("bottomleft",
       horiz = FALSE,
       legend = c("Sn(t) age.max = 79.9", "Sn(t) age.mean = 50.8"),
       col = c("black", "black"),
      lty = c(1, 2, 1, 1, 2, 2))
grid()

plot(pred_agemax$time,
    pred_agemax$pt_cure,
    type = "l",
    lty = 1,
    lwd = 2,
    ylim = c(0, 1), xlim = c(0,30),
    xlab = "Time since diagnosis",
    ylab = "probability of being cured P(t)")

lines(pred_agemean$time,
     pred_agemean$pt_cure,
     type = "l",
     lty = 2,
     lwd = 2)


abline(v = pred_agemean$tau[1],
      lty = 2,
      lwd = 2,
      col = "blue")
abline(v = pred_agemean$TTC[1],
       lty = 2,
       lwd = 2,
       col = "red")
abline(v = pred_agemax$tau[1],
       lty = 1,
       lwd = 2,
       col = "blue")
abline(v = pred_agemax$TTC[1],
       lty = 1,
       lwd = 2,
      col = "red")
grid()

legend("bottomright",
       horiz = FALSE,
       legend = c("P(t) age.max = 79.9",
                 "P(t) age.mean = 50.8",
                 "TNEH age.max = 79.9",
                 "TTC age.max = 79.9",
                 "TNEH age.mean = 50.8",
                 "TTC age.mean = 50.8"),
      col = c("black", "black", "blue", "red", "blue", "red"),
      lty = c(1, 2, 1, 1, 2, 2))


 val_age <- seq(min(testiscancer$age_crmin),
                max(testiscancer$age_crmin), 0.1) * sd(testiscancer$age) +
                min(testiscancer$age)


 pred_age_val <- predict(object = fit_m1_ad_tneh, newdata = newdata3)


par(mfrow=c(2,2))
 plot(val_age,
     pred_age_val$ex_haz, type = "l",
     lty=1, lwd=2,
     xlab = "age",
     ylab = "excess hazard")
grid()

 plot(val_age,
     pred_age_val$netsurv, type = "l", lty=1,
     lwd=2, xlab = "age", ylab = "net survival")
     grid()

 plot(val_age,
     pred_age_val$pt_cure, type = "l", lty=1, lwd=2,
     xlab = "age",
     ylab = "P(t)")
     grid()
par(oldpar)

predcall_tneh function

Description

calculates the predicted cure indicators from a Time to null excess hazard model.

Usage

predcall_tneh(
  object,
  pred,
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  xmax = NULL,
  level = level,
  epsilon = epsilon,
  cumLexc_topred
)

Arguments

object

ouput from a model implemented in curesurv

pred

some predicted estimates

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

xmax

time max at which Pi(t) is calculated.

level

(1-alpha/2)-order quantile of a normal distribution

epsilon

value fixed by user to estimate the \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

cumLexc_topred

pre prediction obtained either from cumLexc_adtneh2_topred or cumLexc_mul_topred

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

predcall_wei function

Description

calculates the predicted cure indicators from a mixture cure model with the survival of uncured specified by a Weibull distribution.

Usage

predcall_wei(
  object,
  pred,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x = x,
  level = level,
  epsilon = epsilon,
  sign_delta = 1,
  cumLexctopred
)

Arguments

object

ouput from a model implemented using curesurv

pred

some predicted estimates

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the predictions are provided

level

(1-alpha/2)-order quantile of a normal distribution

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

sign_delta

cumLexctopred

pre prediction obtained by cumLexc_alphaweibull_topred

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

Prediction for a curesurv cure model

Description

return predicted (excess) hazard, (net) survival, cure fraction and time to null excess hazard or time to cure.

Usage

## S3 method for class 'curesurv'
predict(
  object,
  newdata = NULL,
  xmax = 10^9,
  level = 0.975,
  epsilon = 0.05,
  sign_delta = 1,
  ...
)

Arguments

object

Output from curesurv function

newdata

the new data to be specified for predictions; If else, predictions are made using the data provided during the estimation step in order to obtain the output from curesurv function.

xmax

maximum time at which Time-to-Cure is evaluated numerically.

level

1-\frac{\alpha}{2}-order quantile of a normal distribution for the confidence intervals

epsilon

value fixed by user to estimate the TTC Pi(t) \ge 1-\epsilon. By default epsilon = 0.05.

sign_delta

sign of effect of delta on covariates acting on survival function, positive by default "sign_delta = 1" and alternative is "sign_delta = -1"

...

additional parameters

Value

An object of class c("pred_curesurv", "data.frame"). This object is a list containing the following components:

time

time in the input new data

ex_haz

predicted excess hazard at the time provided in the new data

netsurv

predicted net survival at the time provided in the new data

pt_cure

probability to be cured

tau

time to null in model TNEH when object corresponds to the results from Boussari model or its extension.

netsurv_tau

pi or net survival at time tau when object corresponds to the results from Boussari model or its extension.

time_to_cure_ttc

time to cure (TTC)

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

Examples


library("curesurv")
library("survival")

fit_m2_ml <- curesurv(Surv(time_obs, event) ~ age_cr|age_cr,
                   pophaz = "ehazard",
                   cumpophaz = "cumehazard",
                   model = "mixture",
                   data = pancreas_data,
                   method_opt = "L-BFGS-B")

 fit_m2_ml

 newdata <- pancreas_data[2,]

 predict(object = fit_m2_ml, newdata = newdata)

## Non mixture cure model
### TNEH model

#### Additive parametrization

testiscancer$age_crmin <- (testiscancer$age- min(testiscancer$age)) /
              sd(testiscancer$age)

fit_m1_ad_tneh <- curesurv(Surv(time_obs, event) ~ z_tau(age_crmin) +
                          z_alpha(age_crmin),
                          pophaz = "ehazard",
                          cumpophaz = "cumehazard",
                          model = "nmixture", dist = "tneh",
                          link_tau = "linear",
                          data = testiscancer,
                          method_opt = "L-BFGS-B")

 fit_m1_ad_tneh

 predict(object = fit_m1_ad_tneh, newdata = testiscancer[3:6,])

 #mean of age
 newdata1 <- with(testiscancer,
 expand.grid(event = 0, age_crmin = mean(age_crmin), time_obs  = seq(0.001,10,0.1)))

 pred_agemean <- predict(object = fit_m1_ad_tneh, newdata = newdata1)


 #max of age
 newdata2 <- with(testiscancer,
 expand.grid(event = 0,
 age_crmin = max(age_crmin),
  time_obs  = seq(0.001,10,0.1)))

 pred_agemax <- predict(object = fit_m1_ad_tneh, newdata = newdata2)
 head(pred_agemax)

print a curesurv object

Description

Print an object of class "curesurv"

Usage

## S3 method for class 'curesurv'
print(x, digits = max(1L, getOption("digits") - 3L), signif.stars = FALSE, ...)

Arguments

x

an object of class "curesurv".

digits

minimum number of significant digits to be used for most numbers.

signif.stars

logical; if TRUE, P-values are additionally encoded visually as "significance stars" in order to help scanning of long coefficient tables.

...

additional options

Value

an object of class "curesurv" representing the fit. See curesurv for details.

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

Boussari O, Bordes L, Romain G, Colonna M, Bossard N, Remontet L, Jooste V. Modeling excess hazard with time-to-cure as a parameter. Biometrics. 2020 Aug 31. doi: 10.1111/biom.13361. Epub ahead of print. PMID: 32869288. (pubmed)

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

Examples


library("curesurv")
library("survival")



# overall survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate



fit_ml0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             model = "mixture", dist = "weib",
             data = testiscancer,
             method_opt = "L-BFGS-B")


print(fit_ml0)

pt_cure_ic_adtneh2 function

Description

calculates the probability Pi(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t. It also provides the related confidence intervals using plain_method.

Usage

pt_cure_ic_adtneh2(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpt_cure = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_ad2_topred, if NULL it will be calculated here

Dpt_cure

Partial derivatives of the cure propability according to theta, if NULL it will be calculated here

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

pt_cure_ic_adtneh2_log function

Description

calculates the probability of the probability Pi(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t. It also provides the related confidence intervals using log method.

Usage

pt_cure_ic_adtneh2_log(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpt_cure = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_ad2_topred, if NULL it will be calculated here

Dpt_cure

Partial derivatives of the cure propability according to theta, if NULL it will be calculated here

pt_cure_ic_adtneh2_loglog function

Description

Usage

pt_cure_ic_adtneh2_loglog(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpt_cure = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_ad2_topred, if NULL it will be calculated here

Dpt_cure

Partial derivatives of the cure propability according to theta, if NULL it will be calculated here

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

pt_cure_ic_log_wei function

Description

confidence intervals of the probability to be cured at time t by Delta Method on logarithm of P(t)

Usage

pt_cure_ic_log_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dpt_cure
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_alphaweibull

Dpt_cure

partial derivatives of pt_cure by theta, obtained with dpdtheta_wei function

pt_cure_ic_loglog_wei function

Description

confidence intervals of the probability to be cured at time t by delta method on log(-log(p(t)))

Usage

pt_cure_ic_loglog_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dpt_cure
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_alphaweibull

Dpt_cure

partial derivatives of pt_cure by theta, obtained with dpdtheta_wei function

pt_cure_ic_multneh function

Description

calculates the probability Pi(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t. It also provides the related confidence intervals using plain_method.

Usage

pt_cure_ic_multneh(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpt_cure = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, if NULL will be calculated

Dpt_cure

partial derivative of pt_cure according to theta, if NULL will be calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

pt_cure_ic_multneh_log function

Description

Usage

pt_cure_ic_multneh_log(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpt_cure = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, if NULL will be calculated

Dpt_cure

partial derivative of pt_cure according to theta, if NULL will be calculated

pt_cure_ic_multneh_loglog function

Description

Usage

pt_cure_ic_multneh_loglog(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object,
  level = level,
  cumLexctopred = NULL,
  Dpt_cure = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, if NULL will be calculated

Dpt_cure

partial derivative of pt_cure according to theta, if NULL will be calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

pt_cure_ic_noDM function

Description

Variance of p(t) without delta method

Usage

pt_cure_ic_noDM(x, z_pcured, t, level = 0.975, theta)

Arguments

x

fit ouput from curesurv

z_pcured

covariates

t

time

level

level of confidence

theta

estimated parameters

pt_cure_ic_wei function

Description

Calculates the confidence intervals of the probability Pi(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t. by Delta Method on P(t)

Usage

pt_cure_ic_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dpt_cure
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction parameter obtained with cumLexc_alphaweibull

Dpt_cure

partial derivatives of pt_cure by theta, obtained with dpdtheta_wei function

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

pt_cure_wei function

Description

calculates the probability Pi(t) of being cured at a given time t after diagnosis knowing that he/she was alive up to time t. The predictions are based on a mixture cure model with weibull distribution for the survival of uncured patients.

Usage

pt_cure_wei(z_pcured = z_pcured, z_ucured = z_ucured, x, theta)

Arguments

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

theta

estimated parameters of the cumulative excess hazard from a mixture model using curesurv and uncured survival following a Weibull distribution

sn_ic_adtneh2 function

Description

calculates the net survival at time t. It also provides the related confidence intervals using plain_method.

Usage

sn_ic_adtneh2(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object = object,
  level = level,
  cumLexctopred = NULL,
  Dsn = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction thing obtained from cumLexc_ad2_topred, calculated if not NULL

Dsn

partial derivatives of Sn obtained from dsndtheta_adtneh2 function, calculated if not NULL

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

sn_ic_adtneh2_log function

Description

calculates the net survival at time t. It also provides the related confidence intervals using log method.

Usage

sn_ic_adtneh2_log(
  z_tau,
  z_alpha,
  x,
  object,
  level = 0.975,
  cumLexctopred = NULL,
  Dsn = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction thing obtained from cumLexc_ad2_topred, calculated if not NULL

Dsn

partial derivatives of Sn obtained from dsndtheta_adtneh2 function, calculated if not NULL

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

sn_ic_adtneh2_loglog function

Description

calculates the net survival at time t. It also provides the related confidence intervals using log-log method.

Usage

sn_ic_adtneh2_loglog(
  z_tau,
  z_alpha,
  x,
  object,
  level = 0.975,
  cumLexctopred = NULL,
  Dsn = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre-prediction thing obtained from cumLexc_ad2_topred, calculated if not NULL

Dsn

partial derivatives of Sn obtained from dsndtheta_adtneh2 function, calculated if not NULL

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

sn_ic_log_wei function

Description

calculates the confidence intervals of the net survival (Sn(t)) using variances of log(Sn(t)). In this formula, the variance of net survival is obtained using delta method at the scale of log of net survival, and with the expression Var(log(Sn(t))) = (dlog(Sn)/dtheta)Var(theta)(dlog(Sn)/dtheta)^T; the Var(theta) is the variance-covariance matrix of theta (estimated parameters).

Usage

sn_ic_log_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dsn
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

a pre prediction obtained with cumLexc_alphaweibull_topred

Dsn

Partial derivative of Sn calculated by dsndtheta_wei function

sn_ic_multneh function

Description

calculates the net survival at time t. It also provides the related confidence intervals using plain_method.

Usage

sn_ic_multneh(
  z_tau = z_tau,
  z_alpha = z_alpha,
  x = x,
  object = object,
  level = level,
  cumLexctopred = NULL,
  Dsn = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, if NULL will be calculated

Dsn

partial derivates of net survival, if NULL will be calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

sn_ic_multneh_log function

Description

calculates the net survival at time t. It also provides the related confidence intervals using log method.

Usage

sn_ic_multneh_log(
  z_tau,
  z_alpha,
  x,
  object,
  level = 0.975,
  cumLexctopred = NULL,
  Dsn = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, if NULL will be calculated

Dsn

partial derivates of net survival, if NULL will be calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

sn_ic_multneh_loglog function

Description

calculates the net survival at time t. It also provides the related confidence intervals using log-log method.

Usage

sn_ic_multneh_loglog(
  z_tau,
  z_alpha,
  x,
  object,
  level = 0.975,
  cumLexctopred = NULL,
  Dsn = NULL
)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained from cumLexc_mul_topred, if NULL will be calculated

Dsn

partial derivates of net survival, if NULL will be calculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

sn_ic_wei function

Description

calculates the confidence intervals of the net survival (Sn(t)) using variances of Sn(t). In this formula, the variance of net survival is obtained using the expression Var(Sn(t)) = (dSn/dtheta)Var(theta)(dSn/dtheta)^T where Var(theta) is the variance-covariance matrix of theta.

Usage

sn_ic_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x,
  level,
  cumLexctopred,
  Dsn
)

Arguments

object

ouput from a model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

level

(1-alpha/2)-order quantile of a normal distribution

cumLexctopred

pre prediction obtained with cumLexc_alphaweibull_topred

Dsn

Partial derivative of Sn calculated by dsndtheta_wei function

summary for a curesurv cure model

Description

summary an object of class "curesurv"

Usage

## S3 method for class 'curesurv'
summary(
  object,
  digits = max(1L, getOption("digits") - 3L),
  signif.stars = FALSE,
  ...
)

Arguments

object

an object of class "curesurv".

digits

minimum number of significant digits to be used for most numbers.

signif.stars

logical; if TRUE, P-values are additionally encoded visually as "significance stars" in order to help scanning of long coefficient tables.

...

additional options

Value

an object of class "curesurv" representing the fit. See curesurv for details.

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

Phillips N, Coldman A, McBride ML. Estimating cancer prevalence using mixture models for cancer survival. Stat Med. 2002 May 15;21(9):1257-70. doi: 10.1002/sim.1101. PMID: 12111877. (pubmed)

Examples


library("curesurv")
library("survival")



# overall survival setting
# Mixture cure model with Weibull function for the uncured patients survival:
# no covariate



fit_ml0 <- curesurv(Surv(time_obs, event) ~ 1 | 1,
             model = "mixture", dist = "weib",
             data = testiscancer,
             method_opt = "L-BFGS-B")


 summary(fit_ml0)

Simulated testis cancer data using a cure model

Description

Simulated dataset of 2000 individuals as in Boussari et al. (2020), following setting 1 sub-scenario design.

Usage

data(testiscancer)

Format

This dataset contains the following variables:

age: Age at diagnosis
age_cr: centered and scaled age at diagnosis
age_classe: "<40", "40_65" and ">=65" age groups
time_obs: Follow-up time (years)
event: Vital status
cumehazard: individual cumulative expected hazard
ehazard: individual instantaneous expected hazard
weisurvpop: individual expected survival

Examples

data(testiscancer)
summary(testiscancer)

trigamma function

Description

trigamma function

Usage

trigamma(z)

Arguments

z

positive parameter

var_TTC_Jakobsen_wei function

Description

Calculates the variance of TTC from a mixture cure model with uncured survival as Weibull distribution using the Jakobsen approach.

Usage

var_TTC_Jakobsen_wei(
  object,
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  epsilon = epsilon,
  TTC,
  cumLexc_topred_TTC
)

Arguments

object

ouput from a model implemented in curesurv

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

TTC

time to cure TTC

cumLexc_topred_TTC

a pre prediction given by cumLexc_alphaweibull_topred

var_TTC_multneh function

Description

calculates the variance of TTC in a non-mixture model with distribution "TNEH", link_tau="loglinear"

Usage

var_TTC_multneh(
  z_alpha,
  z_tau,
  xmax,
  object,
  epsilon = epsilon,
  TTC = NULL,
  cumLexctopred = NULL,
  DpTTC = NULL
)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

xmax

time max at which Pi(t) is calculated.

object

ouput from a model implemented in curesurv

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

TTC

The time to cure, if NULL it is recalculated

cumLexctopred

pre prediction, calculated if NULL

DpTTC

partial derivatives, recalculated if not given

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

var_TTC_tneh2 function

Description

calculates the variance of TTC in a non-mixture model with distribution "TNEH"

Usage

var_TTC_tneh2(
  z_alpha,
  z_tau,
  xmax,
  object,
  epsilon = epsilon,
  TTC,
  cumLexctopred = NULL,
  Dpttc = NULL
)

Arguments

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

z_tau

Covariates matrix acting on time-to-null parameter.

xmax

time max at which Pi(t) is calculated.

object

ouput from a model implemented in curesurv

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

TTC

time to cure calculated by TTC_adtneh2

cumLexctopred

pre prediction, if NULL recalculated

Dpttc

Partial derivatives of probability to be cure by theta which can be evaluated at t = TTC, if NULL it is recalculated

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

var_TTC_wei function

Description

Calculates the variance of TTC with delta method. The expression of this variance is expressed as Var(TTC) = (dTTC/dtheta)Var(theta)(dTTC/dtheta)^T where Var(theta) is the variance-covariance matrix of theta.

Usage

var_TTC_wei(
  object,
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  epsilon = epsilon,
  TTC
)

Arguments

object

ouput from a model implemented in curesurv

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

TTC

time to cure previously calculated using TTC_wei

var_logCumHaz_wei function

Description

Calculates the variance of log of cumulative excess hazard with delta method on the log-log of net survival scale.

Usage

var_logCumHaz_wei(
  object,
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  x = x,
  cumLexctopred
)

Arguments

object

ouput from a model implemented in curesurv

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

x

time at which the estimates are predicted

cumLexctopred

pre prediction obtained with cumLexc_alphaweibull_topred

var_pt_cure_wei function

Description

Variance of p(t) with delta method. Var(p(t)) = (dp/dtheta)Var(theta)(dp/dtheta)^T where Var(theta) is the variance-covariance matrix of theta.

Usage

var_pt_cure_wei(
  object,
  z_pcured = z_pcured,
  z_ucured = z_ucured,
  x = x,
  cumLexctopred
)

Arguments

object

ouput from mixture cure model implemented in curesurv

z_pcured

covariates matrix acting on cure proportion

z_ucured

covariates matrix acting on survival function of uncured

x

time at which the estimates are predicted

cumLexctopred

pre prediction obtained with cumLexc_alphaweibull_topred

varexhaz_adtneh2 function

Description

variance of excess hazard in non-mixture cure model with distribution "tneh".

Usage

varexhaz_adtneh2(z_tau = z_tau, z_alpha = z_alpha, x = x, object)

Arguments

z_tau

Covariates matrix acting on time-to-null parameter.

z_alpha

Covariates matrix acting on parameter alpha of the density of time-to-null excess hazard model

x

time at which the predictions are provided

object

ouput from a model implemented in curesurv

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

varlogTTC_Jakobsen_wei function

Description

Calculates the variance of log(TTC) from a mixture cure model with uncured survival as Weibull distribution using the Jakobsen approach.

Usage

varlogTTC_Jakobsen_wei(
  object,
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  epsilon = epsilon,
  TTC,
  cumLexc_topred_TTC
)

Arguments

object

ouput from a model implemented in curesurv

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

TTC

time to cure estimatec by TTC_wei

cumLexc_topred_TTC

a pre prediction given by cumLexc_alphaweibull_topred

varlogTTC_wei function

Description

Calculates the variance of log(TTC) with delta method. The expression of this variance is expressed as: Var(log(TTC)) = (dlog(TTC)/dtheta)Var(theta)(dlog(TTC)/dtheta)^T

where Var(theta) is the variance-covariance matrix of theta.

Usage

varlogTTC_wei(
  object = object,
  z_ucured = z_ucured,
  z_pcured = z_pcured,
  epsilon = epsilon,
  TTC
)

Arguments

object

ouput from a model implemented in curesurv

z_ucured

covariates matrix acting on survival function of uncured

z_pcured

covariates matrix acting on cure proportion

epsilon

value fixed by user to estimate the TTC \text{Pi}(t)\geq (1-\epsilon). By default \epsilon = 0.05.

TTC

time to cure previsouly estimated by TTC_wei

z_alpha function identifying variables acting on alpha parameter

Description

variables adjusted on alpha parameter in non-mixture cure model with "tneh" specified for the distribution.

Usage

z_alpha(x)

Arguments

x

a simple formula.

Value

the variable x

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

z_riskpop.alpha function

Description

indicator variable.

Usage

z_riskpop.alpha(x)

Arguments

x

a simple formula.

Value

the variable x

Author(s)

Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste

References

z_tau function identifying variables acting on tau parameter

Description

variables adjusted on tau parameter in non-mixture cure model with "tneh" specified for the distribution.

Usage

z_tau(x)

Arguments

x

the name of the column in the dataset representing the variable that will act on tau parameter of the "tneh" model