German Breast Cancer Study Group 2

Description

A data frame containing the observations from the GBSG2 study.

Format

This data frame contains the observations of 686 women:

horTh

hormonal therapy, a factor at two levels no and yes.

age

of the patients in years.

menostat

menopausal status, a factor at two levels pre (premenopausal) and post (postmenopausal).

tsize

tumor size (in mm).

tgrade

tumor grade, a ordered factor at levels I < II < III.

pnodes

number of positive nodes.

progrec

progesterone receptor (in fmol).

estrec

estrogen receptor (in fmol).

time

recurrence free survival time (in days).

cens

censoring indicator (0- censored, 1- event).

References

M. Schumacher, G. Basert, H. Bojar, K. Huebner, M. Olschewski, W. Sauerbrei, C. Schmoor, C. Beyerle, R.L.A. Neumann and H.F. Rauschecker for the German Breast Cancer Study Group (1994), Randomized 2\times2 trial evaluating hormonal treatment and the duration of chemotherapy in node-positive breast cancer patients. Journal of Clinical Oncology, 12, 2086–2093.

Pbc3 data

Description

PBC3 was a multi-centre randomized clinical trial conducted in six European hospitals. Between 1 Jan. 1983 and 1 Jan. 1987, 349 patients with the liver disease primary biliary cirrhosis (PBC) were randomized to either treatment with Cyclosporin A (CyA, 176 patients) or placebo (173 patients). The purpose of the trial was to study the effect of treatment on the survival time. However, during the course of the trial an increased use of liver transplantation for patients with this disease made the investigators redefine the main response variable to be time to “failure of medical treatment” defined as either death or liver transplantation. Patients were then followed from randomization until treatment failure, drop-out or 1 Jan, 1989; 61 patients died (CyA: 30, placebo: 31), another 29 were transplanted (CyA: 14, placebo: 15) and 4 patients were lost to follow-up before 1 Jan. 1989. At entry a number of clinical, biochemical and histological variables, including serum bilirubin, serum albumin, sex, age were recorded.

Format

A data frame with 349 observations on the following 15 variables.

ptno

patient identification

unit

hospital (1: Hvidovre, 2: London, 3: Copenhagen, 4: Barcelona, 5: Munich, 6: Lyon)

tment

treatment (0: placebo, 1: CyA)

sex

(1: males, 0: females)

age

age in years

stage

histological stage (1, 2, 3, 4)

gibleed

previous gastrointestinal bleeding (1: yes, 0: no)

crea

creatinine (micromoles/L)

alb

albumin (g/L)

bili

bilirubin (micromoles/L)

alkph

alkaline phosphatase (IU/L)

asptr

aspartate transaminase (IU/L)

weight

body weight (kg)

days

observation time (days)

status

status at observation time (0: censored, 1: liver transplantation, 2 : dead)

Source

Andersen and Skovgaard. Regression with linear predictors.

References

Andersen and Skovgaard. Regression with linear predictors. Springer, 2010.

Examples

data(Pbc3)

Explained variation for survival models

Description

This function computes a time-dependent $R^2$ like measure of the variation explained by a survival prediction model, by dividing the mean squared error (Brier score) of the model by the mean squared error (Brier score) of a reference model which ignores all the covariates.

Usage

R2(object, models, what, times, reference = 1)

Arguments

Details

In survival analysis the prediction error of the Kaplan-Meier estimator plays a similar role as the total sum of squares in linear regression. Hence, it is a sensible reference model for $R^2$.

Value

A matrix where the first column holds the times and the following columns are the corresponding $R^2$ values for the requested prediction models.

Author(s)

Thomas A. Gerds tag@biostat.ku.dk

References

E. Graf et al. (1999), Assessment and comparison of prognostic classification schemes for survival data. Statistics in Medicine, vol 18, pp= 2529–2545.

Gerds TA, Cai T and Schumacher M (2008) The performance of risk prediction models Biometrical Journal, 50(4), 457–479

See Also

pec

Examples

set.seed(18713)
library(prodlim)
library(survival)
dat=SimSurv(100)
nullmodel=prodlim(Hist(time,status)~1,data=dat)
pmodel1=coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
pmodel2=coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE)
perror=pec(list(Cox1=pmodel1,Cox2=pmodel2),Hist(time,status)~1,data=dat,reference=TRUE)
R2(perror,times=seq(0,1,.1),reference=1)

Drawing bootstrapped cross-validation curves and the .632 or .632plus error of models. The prediction error for an optional benchmark model can be added together with bootstrapped cross-validation error and apparent errors.

Description

This function is invoked and controlled by plot.pec.

Usage

Special(
  x,
  y,
  addprederr,
  models,
  bench,
  benchcol,
  times,
  maxboot,
  bootcol,
  col,
  lty,
  lwd
)

Arguments

Details

This function should not be called directly. The arguments can be specified as Special.arg in the call to plot.pec.

Value

Invisible object.

See Also

plot.pec

Calibration plots for right censored data

Description

Calibration plots for risk prediction models in right censored survival and competing risks data

Usage

calPlot(
  object,
  time,
  formula,
  data,
  splitMethod = "none",
  B = 1,
  M,
  pseudo,
  type,
  showPseudo,
  pseudo.col = NULL,
  pseudo.pch = NULL,
  method = "nne",
  round = TRUE,
  bandwidth = NULL,
  q = 10,
  bars = FALSE,
  hanging = FALSE,
  names = "quantiles",
  showFrequencies = FALSE,
  jack.density = 55,
  plot = TRUE,
  add = FALSE,
  diag = !add,
  legend = !add,
  axes = !add,
  xlim = c(0, 1),
  ylim = c(0, 1),
  xlab,
  ylab,
  col,
  lwd,
  lty,
  pch,
  cause = 1,
  percent = TRUE,
  giveToModel = NULL,
  na.action = na.fail,
  cores = 1,
  verbose = FALSE,
  cex = 1,
  ...
)

Arguments

Details

For method "nne" the optimal bandwidth with respect to is obtained with the function dpik from the package KernSmooth for a box kernel function.

Value

list with elements: time, pseudoFrame and bandwidth (NULL for method quantile).

Author(s)

Thomas Alexander Gerds tag@biostat.ku.dk

Examples

library(prodlim)
library(lava)
library(riskRegression)
library(survival)
# survival
dlearn <- SimSurv(40)
dval <- SimSurv(100)
f <- coxph(Surv(time,status)~X1+X2,data=dlearn,x=TRUE,y=TRUE)
cf=calPlot(f,time=3,data=dval)
print(cf)
plot(cf)

g <- coxph(Surv(time,status)~X2,data=dlearn,x=TRUE,y=TRUE)
cf2=calPlot(list("Cox regression X1+X2"=f,"Cox regression X2"=g),
    time=3,
    type="risk",
    data=dval)
print(cf2)
plot(cf2)
calPlot(f,time=3,data=dval,type="survival")
calPlot(f,time=3,data=dval,bars=TRUE,pseudo=FALSE)
calPlot(f,time=3,data=dval,bars=TRUE,type="risk",pseudo=FALSE)

## show a red line which follows the hanging bars
calPlot(f,time=3,data=dval,bars=TRUE,hanging=TRUE)
a <- calPlot(f,time=3,data=dval,bars=TRUE,hanging=TRUE,abline.col=NULL)
lines(c(0,1,ceiling(a$xcoord)),
      c(a$offset[1],a$offset,a$offset[length(a$offset)]),
      col=2,lwd=5,type="s")

calPlot(f,time=3,data=dval,bars=TRUE,type="risk",hanging=TRUE)

set.seed(13)
m <- crModel()
regression(m, from = "X1", to = "eventtime1") <- 1
regression(m, from = "X2", to = "eventtime1") <- 1
m <- addvar(m,c("X3","X4","X5"))
distribution(m, "X1") <- binomial.lvm()
distribution(m, "X4") <- binomial.lvm()
d1 <- sim(m,100)
d2 <- sim(m,100)
csc <- CSC(Hist(time,event)~X1+X2+X3+X4+X5,data=d1)
fgr <- FGR(Hist(time,event)~X1+X2+X3+X4+X5,data=d1,cause=1)
if ((requireNamespace("cmprsk",quietly=TRUE))){
predict.crr <- cmprsk:::predict.crr
cf3=calPlot(list("Cause-specific Cox"=csc,"Fine-Gray"=fgr),
        time=5,
        legend.x=-0.3,
        legend.y=1.35,
        ylab="Observed event status",
        legend.legend=c("Cause-specific Cox regression","Fine-Gray regression"),
        legend.xpd=NA)
print(cf3)
plot(cf3)

b1 <- calPlot(list("Fine-Gray"=fgr),time=5,bars=TRUE,hanging=FALSE)
print(b1)
plot(b1)

calPlot(fgr,time=5,bars=TRUE,hanging=TRUE)
}

Concordance index for right censored survival time data

Description

In survival analysis, a pair of patients is called concordant if the risk of the event predicted by a model is lower for the patient who experiences the event at a later timepoint. The concordance probability (C-index) is the frequency of concordant pairs among all pairs of subjects. It can be used to measure and compare the discriminative power of a risk prediction models. The function provides an inverse of the probability of censoring weigthed estimate of the concordance probability to adjust for right censoring. Cross-validation based on bootstrap resampling or bootstrap subsampling can be applied to assess and compare the discriminative power of various regression modelling strategies on the same set of data.

Usage

cindex(
  object,
  formula,
  data,
  eval.times,
  pred.times,
  cause,
  lyl = FALSE,
  cens.model = "marginal",
  ipcw.refit = FALSE,
  ipcw.args = NULL,
  ipcw.limit,
  tiedPredictionsIn = TRUE,
  tiedOutcomeIn = TRUE,
  tiedMatchIn = TRUE,
  splitMethod = "noPlan",
  B,
  M,
  model.args = NULL,
  model.parms = NULL,
  keep.models = FALSE,
  keep.residuals = FALSE,
  keep.pvalues = FALSE,
  keep.weights = FALSE,
  keep.index = FALSE,
  keep.matrix = FALSE,
  multiSplitTest = FALSE,
  testTimes,
  confInt = FALSE,
  confLevel = 0.95,
  verbose = TRUE,
  savePath = NULL,
  slaveseed = NULL,
  na.action = na.fail,
  ...
)

Arguments

Details

Pairs with identical observed times, where one is uncensored and one is censored, are always considered usuable (independent of the value of tiedOutcomeIn), as it can be assumed that the event occurs at a later timepoint for the censored observation.

For uncensored response the result equals the one obtained with the functions rcorr.cens and rcorrcens from the Hmisc package (see examples).

Value

Estimates of the C-index.

Author(s)

Thomas A Gerds tag@biostat.ku.dk

References

TA Gerds, MW Kattan, M Schumacher, and C Yu. Estimating a time-dependent concordance index for survival prediction models with covariate dependent censoring. Statistics in Medicine, Ahead of print:to appear, 2013. DOI = 10.1002/sim.5681

Wolbers, M and Koller, MT and Witteman, JCM and Gerds, TA (2013) Concordance for prognostic models with competing risks Research report 13/3. Department of Biostatistics, University of Copenhagen

Andersen, PK (2012) A note on the decomposition of number of life years lost according to causes of death Research report 12/2. Department of Biostatistics, University of Copenhagen

Paul Blanche, Michael W Kattan, and Thomas A Gerds. The c-index is not proper for the evaluation of-year predicted risks. Biostatistics, 20(2): 347–357, 2018.

Examples

 # simulate data based on Weibull regression  
library(prodlim)
 set.seed(13)
 dat <- SimSurv(100)
 # fit three different Cox models and a random survival forest
 # note: low number of trees for the purpose of illustration 
 library(survival)
 cox12 <- coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
 cox1 <- coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE)
 cox2 <- coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE)
 #
 # compute the apparent estimate of the C-index at a single time point
 #
A1  <- pec::cindex(list("Cox X1"=cox1),
		  formula=Surv(time,status)~X1+X2,
		  data=dat,
		  eval.times=10)
 #
 # compute the apparent estimate of the C-index at different time points
 #
ApparrentCindex  <- pec::cindex(list("Cox X1"=cox1,
		       "Cox X2"=cox2,
		       "Cox X1+X2"=cox12),
		  formula=Surv(time,status)~X1+X2,
		  data=dat,
		  eval.times=seq(1,15,1))
  print(ApparrentCindex)
  plot(ApparrentCindex)
 #
 # compute the bootstrap-crossvalidation estimate of
 # the C-index at different time points
 #
set.seed(142)
bcvCindex  <- pec::cindex(list("Cox X1"=cox1,
		       "Cox X2"=cox2,
		       "Cox X1+X2"=cox12),
		  formula=Surv(time,status)~X1+X2,
		  data=dat,
                  splitMethod="bootcv",
                  B=5,
 		  eval.times=seq(1,15,1))
  print(bcvCindex)
  plot(bcvCindex)
 # for uncensored data the results are the same
 # as those obtained with the function rcorr.cens from Hmisc

set.seed(16)
dat <- SimSurv(30)
dat$staus=1
fit12 <- coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
fit1 <- coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE)
fit2 <- coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE)
Cpec <- pec::cindex(list("Cox X1+X2"=fit12,"Cox X1"=fit1,"Cox X2"=fit2),
	       formula=Surv(time,status)~1,
	       data=dat) 	       
p1 <- predictSurvProb(fit1,newdata=dat,times=10)
p2 <- predictSurvProb(fit2,newdata=dat,times=10)
p12 <- predictSurvProb(fit12,newdata=dat,times=10)
if (requireNamespace("Hmisc",quietly=TRUE)){
library(Hmisc)
harrelC1 <- rcorr.cens(p1,with(dat,Surv(time,status)))
harrelC2 <- rcorr.cens(p2,with(dat,Surv(time,status)))
harrelC12 <- rcorr.cens(p12,with(dat,Surv(time,status)))
harrelC1[["C Index"]]==Cpec$AppCindex[["Cox.X1"]]
harrelC2[["C Index"]]==Cpec$AppCindex[["Cox.X2"]]
harrelC12[["C Index"]]==Cpec$AppCindex[["Cox.X1.X2"]]
}
 #
 # competing risks 
 #
library(riskRegression)
library(prodlim)
set.seed(30)
dcr.learn <- SimCompRisk(30)
dcr.val <- SimCompRisk(30)
pec::cindex(CSC(Hist(time,event)~X1+X2,data=dcr.learn),data=dcr.val)
fit <- CSC(Hist(time,event)~X1+X2,data=dcr.learn)
cif <- predictRisk(fit,newdata=dcr.val,times=3,cause=1)
pec::cindex(list(fit),data=dcr.val,times=3)

Copenhagen Stroke Study

Description

This data set contains a subset of the data from the Copenhagen stroke study.

Format

This data frame contains the observations of 518 stroke patients :

age

Age of the patients in years.

sex

A factor with two levels female and male.

hypTen

Hypertension, a factor with two levels no and yes.

ihd

History of ischemic heart disease at admission, a factor with two levels no and yes.

prevStroke

History of previous strokes before admission, a factor with two levels no and yes.

othDisease

History of other disabling diseases (e.g. severe dementia), a factor with two levels no and yes.

alcohol

Daily alcohol consumption, a factor with two levels no and yes.

diabetes

Diabetes mellitus status indicating if the glucose level was higher than 11 mmol/L, a factor with two levels no and yes.

smoke

Daily smoking status, a factor with two levels no and yes.

atrialFib

Atrial fibrillation, a factor with two levels no and yes.

hemor

Hemorrhage (stroke subtype), a factor with two levels no (infarction) and yes (hemorrhage).

strokeScore

Scandinavian stroke score at admission to the hospital. Ranges from 0 (worst) to 58 (best).

cholest

Cholesterol level

time

Survival time (in days).

status

Status (0: censored, 1: event).

References

Joergensen HS, Nakayama H, Reith J, Raaschou HO, and Olsen TS. Acute stroke with atrial fibrillation. The Copenhagen Stroke Study. Stroke, 27(10):1765-9, 1996.

Mogensen UB, Ishwaran H, and Gerds TA. Evaluating random forests for survival analysis using prediction error curves. Technical Report 8, University of Copenhagen, Department of Biostatistics, 2010.

Formula interface for function CoxBoost of package CoxBoost.

Description

Formula interface for function CoxBoost of package CoxBoost.

Usage

coxboost(formula, data, cv = TRUE, cause = 1, penalty, ...)

Arguments

Details

See CoxBoost.

Value

See CoxBoost.

Author(s)

Thomas Alexander Gerds tag@biostat.ku.dk

References

See CoxBoost.

See Also

See CoxBoost.

Summarizing prediction error curves

Description

Computes the cumulative prediction error curves, aka integrated Brier scores, in ranges of time.

Usage

crps(object, models, what, times, start)

Arguments

Details

The cumulative prediction error (continuous ranked probability score) is defined as the area under the prediction error curve, hence the alias name, ibs, which is short for integrated Brier score.

Value

A matrix with a column for the crps (ibs) at every requested time point and a row for each model

Author(s)

Thomas A. Gerds tag@biostat.ku.dk

References

E. Graf et al. (1999), Assessment and comparison of prognostic classification schemes for survival data. Statistics in Medicine, vol 18, pp= 2529–2545.

Gerds TA, Cai T & Schumacher M (2008) The performance of risk prediction models Biometrical Journal, 50(4), 457–479

See Also

pec

Examples

set.seed(18713)
library(prodlim)
library(survival)
dat=SimSurv(100)
pmodel=coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
perror=pec(list(Cox=pmodel),Hist(time,status)~1,data=dat)

## cumulative prediction error
crps(perror,times=1) # between min time and 1
## same thing:
ibs(perror,times=1) # between min time and 1
crps(perror,times=1,start=0) # between 0 and 1
crps(perror,times=seq(0,1,.2),start=0) # between 0 and seq(0,1,.2)

Estimation of censoring probabilities

Description

This function is used internally by the function pec to obtain inverse of the probability of censoring weights.

Usage

ipcw(
  formula,
  data,
  method,
  args,
  times,
  subjectTimes,
  subjectTimesLag = 1,
  what
)

Arguments

Details

Inverse of the probability of censoring weights (IPCW) usually refer to the probabilities of not being censored at certain time points. These probabilities are also the values of the conditional survival function of the censoring time given covariates. The function ipcw estimates the conditional survival function of the censoring times and derives the weights.

IMPORTANT: the data set should be ordered, order(time,-status) in order to get the values IPCW.subjectTimes in the right order for some choices of method.

Value

Author(s)

Thomas A. Gerds tag@biostat.ku.dk

See Also

pec

Examples

library(prodlim)
library(rms)
library(survival)
dat=SimSurv(30)

dat <- dat[order(dat$time),]

# using the marginal Kaplan-Meier for the censoring times

WKM=ipcw(Hist(time,status)~X2,
  data=dat,
  method="marginal",
  times=sort(unique(dat$time)),
  subjectTimes=dat$time)
plot(WKM$fit)
WKM$fit

# using the Cox model for the censoring times given X2
library(survival)
WCox=ipcw(Hist(time=time,event=status)~X2,
  data=dat,
  method="cox",
  times=sort(unique(dat$time)),
  subjectTimes=dat$time)
WCox$fit

plot(WKM$fit)
lines(sort(unique(dat$time)),
      1-WCox$IPCW.times[1,],
      type="l",
      col=2,
      lty=3,
      lwd=3)
lines(sort(unique(dat$time)),
      1-WCox$IPCW.times[5,],
      type="l",
      col=3,
      lty=3,
      lwd=3)

# using the stratified Kaplan-Meier
# for the censoring times given X2

WKM2=ipcw(Hist(time,status)~X2,
  data=dat,
  method="nonpar",
  times=sort(unique(dat$time)),
  subjectTimes=dat$time)
plot(WKM2$fit,add=FALSE)

Prediction error curves

Description

Evaluating the performance of risk prediction models in survival analysis. The Brier score is a weighted average of the squared distances between the observed survival status and the predicted survival probability of a model. Roughly the weights correspond to the probabilities of not being censored. The weights can be estimated depend on covariates. Prediction error curves are obtained when the Brier score is followed over time. Cross-validation based on bootstrap resampling or bootstrap subsampling can be applied to assess and compare the predictive power of various regression modelling strategies on the same set of data.

Usage

pec(
  object,
  formula,
  data,
  traindata,
  times,
  cause,
  start,
  maxtime,
  exact = TRUE,
  exactness = 100,
  fillChar = NA,
  cens.model = "cox",
  ipcw.refit = FALSE,
  ipcw.args = NULL,
  splitMethod = "none",
  B,
  M,
  reference = TRUE,
  model.args = NULL,
  model.parms = NULL,
  keep.index = FALSE,
  keep.matrix = FALSE,
  keep.models = FALSE,
  keep.residuals = FALSE,
  keep.pvalues = FALSE,
  noinf.permute = FALSE,
  multiSplitTest = FALSE,
  testIBS,
  testTimes,
  confInt = FALSE,
  confLevel = 0.95,
  verbose = TRUE,
  savePath = NULL,
  slaveseed = NULL,
  na.action = na.fail,
  ...
)

Arguments

Details

Note that package riskRegression provides very similar functionality (and much more) but not yet every feature of pec.

Missing data in the response or in the input matrix cause a failure.

The status of the continuous response variable at cutpoints (times), ie status=1 if the response value exceeds the cutpoint and status=0 otherwise, is compared to predicted event status probabilities which are provided by the prediction models on the basis of covariates. The comparison is done with the Brier score: the quadratic difference between 0-1 response status and predicted probability.

There are two different sources for bias when estimating prediction error in right censored survival problems: censoring and high flexibility of the prediction model. The first is controlled by inverse probability of censoring weighting, the second can be controlled by special Monte Carlo simulation. In each step, the resampling procedures reevaluate the prediction model. Technically this is done by replacing the argument object$call$data by the current subset or bootstrap sample of the full data.

For each prediction model there must be a predictSurvProb method: for example, to assess a prediction model which evaluates to a myclass object one defines a function called predictSurvProb.myclass with arguments object,newdata,cutpoints,...

Such a function takes the object and derives a matrix with predicted event status probabilities for each subject in newdata (rows) and each cutpoint (column) of the response variable that defines an event status.

Currently, predictSurvProb methods are readily available for various survival models, see methods(predictSurvProb)

Value

A pec object. See also the help pages of the corresponding print, summary, and plot methods. The object includes the following components:

Author(s)

Thomas Alexander Gerds tag@biostat.ku.dk

References

Gerds TA, Kattan MW. Medical Risk Prediction Models: With Ties to Machine Learning. Chapman and Hall/CRC https://www.routledge.com/9781138384477

Ulla B. Mogensen, Hemant Ishwaran, Thomas A. Gerds (2012). Evaluating Random Forests for Survival Analysis Using Prediction Error Curves. Journal of Statistical Software, 50(11), 1-23. DOI 10.18637/jss.v050.i11

E. Graf et al. (1999), Assessment and comparison of prognostic classification schemes for survival data. Statistics in Medicine, vol 18, pp= 2529–2545.

Efron, Tibshirani (1997) Journal of the American Statistical Association 92, 548–560 Improvement On Cross-Validation: The .632+ Bootstrap Method.

Gerds, Schumacher (2006), Consistent estimation of the expected Brier score in general survival models with right-censored event times. Biometrical Journal, vol 48, 1029–1040.

Thomas A. Gerds, Martin Schumacher (2007) Efron-Type Measures of Prediction Error for Survival Analysis Biometrics, 63(4), 1283–1287 doi:10.1111/j.1541-0420.2007.00832.x

Martin Schumacher, Harald Binder, and Thomas Gerds. Assessment of survival prediction models based on microarray data. Bioinformatics, 23(14):1768-74, 2007.

Mark A. van de Wiel, Johannes Berkhof, and Wessel N. van Wieringen Testing the prediction error difference between 2 predictors Biostatistics (2009) 10(3): 550-560 doi:10.1093/biostatistics/kxp011

See Also

plot.pec, summary.pec, R2, crps

Examples

# simulate an artificial data frame
# with survival response and two predictors

set.seed(130971)
library(prodlim)
library(survival)
dat <- SimSurv(100)

# fit some candidate Cox models and compute the Kaplan-Meier estimate 

Models <- list("Cox.X1"=coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE),
              "Cox.X2"=coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE),
              "Cox.X1.X2"=coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE))

# compute the apparent prediction error 
PredError <- pec(object=Models,
                  formula=Surv(time,status)~X1+X2,
                  data=dat,
                  exact=TRUE,
                  cens.model="marginal",
                  splitMethod="none",
                  B=0,
                  verbose=TRUE)

print(PredError,times=seq(5,30,5))
summary(PredError)
plot(PredError,xlim=c(0,30))

# Comparison of Weibull model and Cox model
library(survival)
library(rms)
library(pec)
data(pbc)
pbc <- pbc[sample(1:NROW(pbc),size=100),]
f1 <- psm(Surv(time,status!=0)~edema+log(bili)+age+sex+albumin,data=pbc)
f2 <- coxph(Surv(time,status!=0)~edema+log(bili)+age+sex+albumin,data=pbc,x=TRUE,y=TRUE)
f3 <- cph(Surv(time,status!=0)~edema+log(bili)+age+sex+albumin,data=pbc,surv=TRUE)
brier <- pec(list("Weibull"=f1,"CoxPH"=f2,"CPH"=f3),data=pbc,formula=Surv(time,status!=0)~1)
print(brier)
plot(brier)

# compute the .632+ estimate of the generalization error
set.seed(130971)
library(prodlim)
library(survival)
dat <- SimSurv(100)
set.seed(17100)
PredError.632plus <- pec(object=Models,
                  formula=Surv(time,status)~X1+X2,
                  data=dat,
                  exact=TRUE,
                  cens.model="marginal",
                  splitMethod="Boot632plus",
                  B=3,
                  verbose=TRUE)

print(PredError.632plus,times=seq(4,12,4))
summary(PredError.632plus)
plot(PredError.632plus,xlim=c(0,30))
# do the same again but now in parallel
## Not run: set.seed(17100)
# library(doMC)
# registerDoMC()
PredError.632plus <- pec(object=Models,
                  formula=Surv(time,status)~X1+X2,
                  data=dat,
                  exact=TRUE,
                  cens.model="marginal",
                  splitMethod="Boot632plus",
                  B=3,
                  verbose=TRUE)

## End(Not run)
# assessing parametric survival models in learn/validation setting
learndat <- SimSurv(50)
testdat <- SimSurv(30)
library(survival)
library(rms)
f1 <- psm(Surv(time,status)~X1+X2,data=learndat)
f2 <- psm(Surv(time,status)~X1,data=learndat)
pf <- pec(list(f1,f2),formula=Surv(time,status)~1,data=testdat,maxtime=200)
plot(pf)
summary(pf)

# ---------------- competing risks -----------------

library(survival)
library(riskRegression)
if(requireNamespace("cmprsk",quietly=TRUE)){
library(cmprsk)
library(pec)
cdat <- SimCompRisk(100)
f1  <- CSC(Hist(time,event)~X1+X2,cause=2,data=cdat)
f2  <- CSC(Hist(time,event)~X1,data=cdat,cause=2)
f3  <- FGR(Hist(time,event)~X1+X2,cause=2,data=cdat)
f4  <- FGR(Hist(time,event)~X1+X2,cause=2,data=cdat)
p1 <- pec(list(f1,f2,f3,f4),formula=Hist(time,event)~1,data=cdat,cause=2)
}

S3-wrapper function for cforest from the party package

Description

S3-wrapper function for cforest from the party package

Usage

pecCforest(formula, data, ...)

Arguments

Details

See cforest of the party package.

Value

list with two elements: cforest and call

References

Ulla B. Mogensen, Hemant Ishwaran, Thomas A. Gerds (2012). Evaluating Random Forests for Survival Analysis Using Prediction Error Curves. Journal of Statistical Software, 50(11), 1-23. DOI 10.18637/jss.v050.i11

S3-Wrapper for ctree.

Description

The call is added to an ctree object

Usage

pecCtree(...)

Arguments

Value

list with two elements: ctree and call

Author(s)

Thomas A. Gerds <tag@biostat.ku.dk>

See Also

pecCforest

Examples

if (requireNamespace("party",quietly=TRUE)){
library(prodlim)
library(survival)
set.seed(50)
d <- SimSurv(50)
nd <- data.frame(X1=c(0,1,0),X2=c(-1,0,1))
f <- pecCtree(Surv(time,status)~X1+X2,data=d)
predictSurvProb(f,newdata=nd,times=c(3,8))
}

Predict survival based on rpart tree object

Description

Combines the rpart result with a stratified Kaplan-Meier (prodlim) to predict survival

Usage

pecRpart(formula, data, ...)

Arguments

Value

list with three elements: ctree and call

Examples

library(prodlim)
if (!requireNamespace("rpart",quietly=TRUE)){
library(rpart)
library(survival)
set.seed(50)
d <- SimSurv(50)
nd <- data.frame(X1=c(0,1,0),X2=c(-1,0,1))
f <- pecRpart(Surv(time,status)~X1+X2,data=d)
predictSurvProb(f,newdata=nd,times=c(3,8))
}

Plot objects obtained with calPlot

Description

Calibration plots

Usage

## S3 method for class 'calibrationPlot'
plot(x, ...)

Arguments

Value

Nothing

Author(s)

Thomas A. Gerds <tag@biostat.ku.dk>

See Also

calPlot

Plotting prediction error curves

Description

Plotting prediction error curves for one or more prediction models.

Usage

## S3 method for class 'pec'
plot(
  x,
  what,
  models,
  xlim = c(x$start, x$minmaxtime),
  ylim = c(0, 0.3),
  xlab = "Time",
  ylab,
  axes = TRUE,
  col,
  lty,
  lwd,
  type,
  smooth = FALSE,
  add.refline = FALSE,
  add = FALSE,
  legend = ifelse(add, FALSE, TRUE),
  special = FALSE,
  ...
)

Arguments

Details

From version 2.0.1 on the arguments legend.text, legend.args, lines.type, lwd.lines, specials are obsolete and only available for backward compatibility. Instead arguments for the invoked functions legend, axis, Special are simply specified as legend.lty=2. The specification is not case sensitive, thus Legend.lty=2 or LEGEND.lty=2 will have the same effect. The function axis is called twice, and arguments of the form axis1.labels, axis1.at are used for the time axis whereas axis2.pos, axis1.labels, etc. are used for the y-axis.

These arguments are processed via ...{} of plot.pec and inside by using the function resolveSmartArgs. Documentation of these arguments can be found in the help pages of the corresponding functions.

Value

The (invisible) object.

Author(s)

Ulla B. Mogensen ulmo@biostat.ku.dk, Thomas A. Gerds tag@biostat.ku.dk

See Also

pecsummary.pecSpecialprodlim

Examples

# simulate data
# with a survival response and two predictors
library(prodlim)
library(survival)
set.seed(280180)
dat <- SimSurv(100)

# fit some candidate Cox models and
# compute the Kaplan-Meier estimate 

Models <- list("Kaplan.Meier"=survfit(Surv(time,status)~1,data=dat),
               "Cox.X1"=coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE),
               "Cox.X2"=coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE),
               "Cox.X1.X2"=coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE))
Models <- list("Cox.X1"=coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE),
               "Cox.X2"=coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE),
               "Cox.X1.X2"=coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE))


# compute the .632+ estimate of the generalization error 
set.seed(17100)
PredError.632plus <- pec(object=Models,
                         formula=Surv(time,status)~X1+X2,
                         data=dat,
                         exact=TRUE,
                         cens.model="marginal",
                         splitMethod="boot632plus",
                         B=5,
                         keep.matrix=TRUE,
                         verbose=TRUE)

# plot the .632+ estimates of the generalization error 
plot(PredError.632plus,xlim=c(0,30))

# plot the bootstrapped curves, .632+ estimates of the generalization error
# and Apparent error for the Cox model 'Cox.X1' with the 'Cox.X2' model
# as benchmark
plot(PredError.632plus,
     xlim=c(0,30),
     models="Cox.X1",
     special=TRUE,
     special.bench="Cox.X2",
     special.benchcol=2,
     special.addprederr="AppErr")

Plotting predicted survival curves.

Description

Ploting time-dependent event risk predictions.

Usage

plotPredictEventProb(
  x,
  newdata,
  times,
  cause = 1,
  xlim,
  ylim,
  xlab,
  ylab,
  axes = TRUE,
  col,
  density,
  lty,
  lwd,
  add = FALSE,
  legend = TRUE,
  percent = FALSE,
  ...
)

Arguments

Details

Arguments for the invoked functions legend and axis are simply specified as legend.lty=2. The specification is not case sensitive, thus Legend.lty=2 or LEGEND.lty=2 will have the same effect. The function axis is called twice, and arguments of the form axis1.labels, axis1.at are used for the time axis whereas axis2.pos, axis1.labels, etc. are used for the y-axis.

These arguments are processed via ...{} of plotPredictEventProb and inside by using the function SmartControl.

Value

The (invisible) object.

Author(s)

Ulla B. Mogensen ulmo@biostat.ku.dk, Thomas A. Gerds tag@biostat.ku.dk

References

Ulla B. Mogensen, Hemant Ishwaran, Thomas A. Gerds (2012). Evaluating Random Forests for Survival Analysis Using Prediction Error Curves. Journal of Statistical Software, 50(11), 1-23. DOI 10.18637/jss.v050.i11

See Also

predictEventProbprodlim

Examples

# competing risk data
library(riskRegression)
library(pec)
set.seed(9)
d=sampleData(80)
csc1 <- CSC(Hist(time,event)~X1+X8, data=d)
nd=sampleData(3)
plotPredictEventProb(csc1, newdata=nd, cause=1, col=1:3)

Plotting predicted survival curves.

Description

Ploting prediction survival curves for one prediction model using predictSurvProb .

Usage

plotPredictSurvProb(
  x,
  newdata,
  times,
  xlim,
  ylim,
  xlab,
  ylab,
  axes = TRUE,
  col,
  density,
  lty,
  lwd,
  add = FALSE,
  legend = TRUE,
  percent = FALSE,
  ...
)

Arguments

Details

Arguments for the invoked functions legend and axis are simply specified as legend.lty=2. The specification is not case sensitive, thus Legend.lty=2 or LEGEND.lty=2 will have the same effect. The function axis is called twice, and arguments of the form axis1.labels, axis1.at are used for the time axis whereas axis2.pos, axis1.labels, etc. are used for the y-axis.

These arguments are processed via ...{} of plotPredictSurvProb and inside by using the function SmartControl.

Value

The (invisible) object.

Author(s)

Ulla B. Mogensen ulmo@biostat.ku.dk, Thomas A. Gerds tag@biostat.ku.dk

References

Ulla B. Mogensen, Hemant Ishwaran, Thomas A. Gerds (2012). Evaluating Random Forests for Survival Analysis Using Prediction Error Curves. Journal of Statistical Software, 50(11), 1-23. DOI 10.18637/jss.v050.i11

See Also

predictSurvProbprodlim

Examples

# generate some survival data
library(prodlim)
d <- SimSurv(100)
# then fit a Cox model
library(survival)
library(rms)
coxmodel <- cph(Surv(time,status)~X1+X2,data=d,surv=TRUE)
# plot predicted survival probabilities for all time points
ttt <- sort(unique(d$time))
# and for selected predictor values:
 ndat <- data.frame(X1=c(0.25,0.25,-0.05,0.05),X2=c(0,1,0,1))
plotPredictSurvProb(coxmodel,newdata=ndat,times=ttt)

Predicting event probabilities (cumulative incidences) in competing risk models.

Description

Function to extract event probability predictions from various modeling approaches. The most prominent one is the combination of cause-specific Cox regression models which can be fitted with the function cumincCox from the package compRisk.

Usage

predictEventProb(object, newdata, times, cause, ...)

Arguments

Details

The function predictEventProb is a generic function that means it invokes specifically designed functions depending on the 'class' of the first argument.

See predictSurvProb.

Value

A matrix with as many rows as NROW(newdata) and as many columns as length(times). Each entry should be a probability and in rows the values should be increasing.

Author(s)

Thomas A. Gerds tag@biostat.ku.dk

See Also

See predictSurvProb.

Examples

library(pec)
library(survival)
library(riskRegression)
library(prodlim)
train <- SimCompRisk(100)
test <- SimCompRisk(10)
cox.fit  <- CSC(Hist(time,cause)~X1+X2,data=train)
predictEventProb(cox.fit,newdata=test,times=seq(1:10),cause=1)

## with strata
cox.fit2  <- CSC(list(Hist(time,cause)~strata(X1)+X2,Hist(time,cause)~X1+X2),data=train)
predictEventProb(cox.fit2,newdata=test,times=seq(1:10),cause=1)

Predicting life years lost (cumulative cumulative incidences) in competing risk models.

Description

Function to extract predicted life years lost from various modeling approaches. The most prominent one is the combination of cause-specific Cox regression models which can be fitted with the function cumincCox from the package compRisk.

Usage

predictLifeYearsLost(object, newdata, times, cause, ...)

Arguments

Details

The function predictLifeYearsLost is a generic function that means it invokes specifically designed functions depending on the 'class' of the first argument.

See predictSurvProb.

Value

A matrix with as many rows as NROW(newdata) and as many columns as length(times). Each entry should be a positive value and in rows the values should be increasing.

Author(s)

Thomas A. Gerds tag@biostat.ku.dk

See Also

predictSurvProb, predictEventProb.

Examples

library(pec)
library(riskRegression)
library(survival)
library(prodlim)
train <- SimCompRisk(100)
test <- SimCompRisk(10)
fit <- CSC(Hist(time,cause)~X1+X2,data=train,cause=1)
predictLifeYearsLost(fit,newdata=test,times=seq(1:10),cv=FALSE,cause=1)

Predicting restricted mean time

Description

Function to extract predicted mean times from various modeling approaches.

Usage

## S3 method for class 'aalen'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'riskRegression'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'cox.aalen'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'cph'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'coxph'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'matrix'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'selectCox'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'prodlim'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'psm'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'survfit'
predictRestrictedMeanTime(object,newdata,times,...)
## S3 method for class 'pecRpart'
predictRestrictedMeanTime(object,newdata,times,...)
#' \method{predictRestrictedMeanTime}{pecCtree}(object,newdata,times,...)

Arguments

Details

The function predictRestrictedMeanTime is a generic function, meaning that it invokes a different function dependent on the 'class' of the first argument.

See also predictSurvProb.

Value

A matrix with as many rows as NROW(newdata) and as many columns as length(times). Each entry should be a probability and in rows the values should be decreasing.

Note

In order to assess the predictive performance of a new survival model a specific predictRestrictedMeanTime S3 method has to be written. For examples, see the bodies of the existing methods.

The performance of the assessment procedure, in particular for resampling where the model is repeatedly evaluated, will be improved by supressing in the call to the model all the computations that are not needed for probability prediction. For example, se.fit=FALSE can be set in the call to cph.

Author(s)

Thomas A. Gerds tag@biostat.ku.dk

References

Ulla B. Mogensen, Hemant Ishwaran, Thomas A. Gerds (2012). Evaluating Random Forests for Survival Analysis Using Prediction Error Curves. Journal of Statistical Software, 50(11), 1-23. DOI 10.18637/jss.v050.i11

See Also

predict,survfit

Examples

# generate some survival data
library(prodlim)
set.seed(100)
d <- SimSurv(100)
# then fit a Cox model
library(rms)
library(survival)
coxmodel <- cph(Surv(time,status)~X1+X2,data=d,surv=TRUE)

# predicted survival probabilities can be extracted
# at selected time-points:
ttt <- quantile(d$time)
# for selected predictor values:
ndat <- data.frame(X1=c(0.25,0.25,-0.05,0.05),X2=c(0,1,0,1))
# as follows
predictRestrictedMeanTime(coxmodel,newdata=ndat,times=ttt)

# stratified cox model
sfit <- coxph(Surv(time,status)~strata(X1)+X2,data=d,x=TRUE,y=TRUE)
predictRestrictedMeanTime(sfit,newdata=d[1:3,],times=c(1,3,5,10))

## simulate some learning and some validation data
learndat <- SimSurv(100)
valdat <- SimSurv(100)
## use the learning data to fit a Cox model
library(survival)
fitCox <- coxph(Surv(time,status)~X1+X2,data=learndat,x=TRUE,y=TRUE)
## suppose we want to predict the survival probabilities for all patients
## in the validation data at the following time points:
## 0, 12, 24, 36, 48, 60
psurv <- predictRestrictedMeanTime(fitCox,newdata=valdat,times=seq(0,60,12))
## This is a matrix with survival probabilities
## one column for each of the 5 time points
## one row for each validation set individual

Predicting survival probabilities

Description

Function to extract survival probability predictions from various modeling approaches. The most prominent one is the Cox regression model which can be fitted for example with ‘coxph’ and with ‘cph’.

Usage

## S3 method for class 'aalen'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'riskRegression'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'cox.aalen'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'cph'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'coxph'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'matrix'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'selectCox'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'pecCforest'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'prodlim'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'psm'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'survfit'
predictSurvProb(object,newdata,times,...)
## S3 method for class 'pecRpart'
predictSurvProb(object,newdata,times,...)
#' \method{predictSurvProb}{pecCtree}(object,newdata,times,...)

Arguments

Details

The function predictSurvProb is a generic function that means it invokes specifically designed functions depending on the 'class' of the first argument.

The function pec requires survival probabilities for each row in newdata at requested times. These probabilities are extracted from a fitted model of class CLASS with the function predictSurvProb.CLASS.

Currently there are predictSurvProb methods for objects of class cph (library rms), coxph (library survival), aalen (library timereg), cox.aalen (library timereg), rpart (library rpart), product.limit (library prodlim), survfit (library survival), psm (library rms)

Value

A matrix with as many rows as NROW(newdata) and as many columns as length(times). Each entry should be a probability and in rows the values should be decreasing.

Note

In order to assess the predictive performance of a new survival model a specific predictSurvProb S3 method has to be written. For examples, see the bodies of the existing methods.

The performance of the assessment procedure, in particular for resampling where the model is repeatedly evaluated, will be improved by supressing in the call to the model all the computations that are not needed for probability prediction. For example, se.fit=FALSE can be set in the call to cph.

Author(s)

Thomas A. Gerds tag@biostat.ku.dk

References

Ulla B. Mogensen, Hemant Ishwaran, Thomas A. Gerds (2012). Evaluating Random Forests for Survival Analysis Using Prediction Error Curves. Journal of Statistical Software, 50(11), 1-23. DOI 10.18637/jss.v050.i11

See Also

predict,survfit

Examples

# generate some survival data
library(prodlim)
set.seed(100)
d <- SimSurv(100)
# then fit a Cox model
library(survival)
library(rms)
coxmodel <- cph(Surv(time,status)~X1+X2,data=d,surv=TRUE)

# Extract predicted survival probabilities 
# at selected time-points:
ttt <- quantile(d$time)
# for selected predictor values:
ndat <- data.frame(X1=c(0.25,0.25,-0.05,0.05),X2=c(0,1,0,1))
# as follows
predictSurvProb(coxmodel,newdata=ndat,times=ttt)

# stratified cox model
sfit <- coxph(Surv(time,status)~strata(X1)+X2,data=d,,x=TRUE,y=TRUE)
predictSurvProb(sfit,newdata=d[1:3,],times=c(1,3,5,10))

## simulate some learning and some validation data
learndat <- SimSurv(100)
valdat <- SimSurv(100)
## use the learning data to fit a Cox model
library(survival)
fitCox <- coxph(Surv(time,status)~X1+X2,data=learndat,x=TRUE,y=TRUE)
## suppose we want to predict the survival probabilities for all patients
## in the validation data at the following time points:
## 0, 12, 24, 36, 48, 60
psurv <- predictSurvProb(fitCox,newdata=valdat,times=seq(0,60,12))
## This is a matrix with survival probabilities
## one column for each of the 5 time points
## one row for each validation set individual

## Cox with ridge option
f1 <- coxph(Surv(time,status)~X1+X2,data=learndat,x=TRUE,y=TRUE)
f2 <- coxph(Surv(time,status)~ridge(X1)+ridge(X2),data=learndat,x=TRUE,y=TRUE)
plot(predictSurvProb(f1,newdata=valdat,times=10),
     pec:::predictSurvProb.coxph(f2,newdata=valdat,times=10),
     xlim=c(0,1),
     ylim=c(0,1),
     xlab="Unpenalized predicted survival chance at 10",
     ylab="Ridge predicted survival chance at 10")

Printing a ‘pec’ (prediction error curve) object.

Description

Print the important arguments of call and the prediction error values at selected time points.

Usage

## S3 method for class 'pec'
print(x, times, digits = 3, what = NULL, ...)

Arguments

Value

The first argument in the invisible cloak.

Author(s)

Thomas A. Gerds tag@biostat.ku.dk

See Also

pec

Retrospective risk reclassification table

Description

Retrospective table of risks predicted by two different methods, models, algorithms

Usage

reclass(
  object,
  reference,
  formula,
  data,
  time,
  cause,
  cuts = seq(0, 100, 25),
  digits = 2
)

Arguments

Details

All risks are multiplied by 100 before

Value

reclassification tables: overall table and one conditional table for each cause and for subjects event free at time interest.

Author(s)

Thomas A. Gerds <tag@biostat.ku.dk>

See Also

predictStatusProb

Examples

## Not run: 
library(survival)
set.seed(40)
d <- prodlim::SimSurv(400)
nd <- prodlim::SimSurv(400)
Models <- list("Cox.X2"=coxph(Surv(time,status)~X2,data=d,x=TRUE,y=TRUE),
               "Cox.X1.X2"=coxph(Surv(time,status)~X1+X2,data=d,x=TRUE,y=TRUE))
rc <- reclass(Models,formula=Surv(time,status)~1,data=nd,time=5)
print(rc)
plot(rc)

set.seed(40)
library(riskRegression)
library(prodlim)
dcr <- prodlim::SimCompRisk(400)
ndcr <- prodlim::SimCompRisk(400)
crPred5 <- list("X2"=predictEventProb(CSC(Hist(time,event)~X2,data=dcr),newdata=ndcr,times=5),
                "X1+X2"=predictEventProb(CSC(Hist(time,event)~X1+X2,data=dcr),newdata=ndcr,times=5))
rc <- reclass(crPred5,Hist(time,event)~1,data=ndcr,time=3)
print(rc)

reclass(crPred5,Hist(time,event)~1,data=ndcr,time=5,cuts=100*c(0,0.05,0.1,0.2,1))

## End(Not run)

Resolve the splitMethod for estimation of prediction performance

Description

The function computes a matrix of random indices obtained by drawing from the row numbers of a data set either with or without replacement. The matrix can be used to repeatedly set up independent training and validation sets.

Usage

resolvesplitMethod(splitMethod, B, N, M)

Arguments

Value

A list with the following components

Author(s)

Thomas Alexander Gerds tag@biostat.ku.dk

Examples

  # BootstrapCrossValidation: Sampling with replacement   
  resolvesplitMethod("BootCv",N=10,B=10)

  # 10-fold cross-validation: repeated 2 times
  resolvesplitMethod("cv10",N=10,B=2)

  # leave-one-out cross-validation
  resolvesplitMethod("loocv",N=10)

  resolvesplitMethod("bootcv632plus",N=10,B=2)
  
  

Backward variable selection in the Cox regression model

Description

This is a wrapper function which first selects variables in the Cox regression model using fastbw from the rms package and then returns a fitted Cox regression model with the selected variables.

Usage

selectCox(formula, data, rule = "aic")

Arguments

Details

This function first calls cph then fastbw and finally cph again.

References

Ulla B. Mogensen, Hemant Ishwaran, Thomas A. Gerds (2012). Evaluating Random Forests for Survival Analysis Using Prediction Error Curves. Journal of Statistical Software, 50(11), 1-23. DOI 10.18637/jss.v050.i11

Examples

data(GBSG2)
library(survival)
f <- selectCox(Surv(time,cens)~horTh+age+menostat+tsize+tgrade+pnodes+progrec+estrec ,
	       data=GBSG2)

Simulate COST alike data

Description

Simulate data alike the data from the Copenhagen stroke study (COST)

Usage

simCost(N)

Arguments

Details

This uses functionality of the lava package.

Value

Data frame

Author(s)

Thomas Alexander Gerds

threecity data

Description

Extracted data from a french population based cohort (Three-City cohort). The dataset includes followup information on dementia outcome and predicted 5-year risks based on based on the subject specific information which includes age, gender, education level and cognitive decline measured by a psychometric test (Mini Mental State Examination). The prediction model from which the predictions have been computed has been fitted on independent training data from the Paquid cohort, another french population based cohort with similar design (see Reference Blanche et al. 2015 for details) .

Format

A subsample consisting of 2000 observations on the following 3 variables.

pi

5-year absolute risk predictions of dementia.

status

0=censored, 1=dementia, 2=death dementia free

time

time to event (i.e., time to either dementia, death dementia free or loss of follow-up)

Source

Web-appendix of Blanche et al. (2015).

References

Blanche, P., Proust-Lima, C., Loubere, L., Berr, C., Dartigues, J. F., Jacqmin-Gadda, H. (2015). Quantifying and comparing dynamic predictive accuracy of joint models for longitudinal marker and time-to-event in presence of censoring and competing risks. Biometrics, 71(1), 102-113.

Examples

data(threecity)