Title:	Simulation and Analysis of Platform Trials with Non-Concurrent Controls
Version:	1.0
Author:	Pavla Krotka [aut, cre], Marta Bofill Roig [aut, ths], Katharina Hees [aut], Peter Jacko [aut], Dominic Magirr [aut], Martin Posch [ctb]
Maintainer:	Pavla Krotka <pavla.krotka@meduniwien.ac.at>
Description:	Design and analysis of flexible platform trials with non-concurrent controls. Functions for data generation, analysis, visualization and running simulation studies are provided. The implemented analysis methods are described in: Bofill Roig et al. (2022) <doi:10.1186/s12874-022-01683-w>, Saville et al. (2022) <doi:10.1177/17407745221112013> and Schmidli et al. (2014) <doi:10.1111/biom.12242>.
URL:	https://pavlakrotka.github.io/NCC/, https://github.com/pavlakrotka/NCC
License:	MIT + file LICENSE
Encoding:	UTF-8
Imports:	rlang, stats, RBesT, rjags, ggplot2, lmerTest, parallel, doParallel, parallelly, foreach, iterators, spaMM, mgcv, splines, magick
RoxygenNote:	7.1.2
Suggests:	rmarkdown, knitr
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2023-03-02 20:16:03 UTC; pavla
Repository:	CRAN
Date/Publication:	2023-03-03 09:10:10 UTC

Analysis for binary data using the MAP Prior approach

Description

This function performs analysis of binary data using the Meta-Analytic-Predictive (MAP) Prior approach. The method borrows data from non-concurrent controls to obtain the prior distribution for the control response in the concurrent periods.

Usage

MAPprior_bin(
  data,
  arm,
  alpha = 0.025,
  opt = 2,
  prior_prec_tau = 4,
  prior_prec_eta = 0.001,
  n_samples = 1000,
  n_chains = 4,
  n_iter = 4000,
  n_adapt = 1000,
  robustify = TRUE,
  weight = 0.1,
  check = TRUE,
  ...
)

Arguments

Details

The MAP approach derives the prior distribution for the control response in the concurrent periods by combining the control information from the non-concurrent periods with a non-informative prior.

The model for the binary response y_{js} for the control patient j in the non-concurrent period s is defined as follows:

g(E(y_{js})) = \eta_s

where g(\cdot) denotes the logit link function and \eta_s represents the control log odds in the non-concurrent period s.

The log odds for the non-concurrent controls in period s are assumed to have a normal prior distribution with mean \mu_{\eta} and variance \tau^2:

\eta_s \sim \mathcal{N}(\mu_{\eta}, \tau^2)

For the hyperparameters \mu_{\eta} and \tau, normal and half-normal hyperprior distributions are assumed, with mean 0 and variances \sigma^2_{\eta} and \sigma^2_{\tau}, respectively:

\mu_{\eta} \sim \mathcal{N}(0, \sigma^2_{\eta})

\tau \sim HalfNormal(0, \sigma^2_{\tau})

The MAP prior distribution p_{MAP}(\eta_{CC}) for the control response in the concurrent periods is then obtained as the posterior distribution of the parameters \eta_s from the above specified model.

If robustify=TRUE, the MAP prior is robustified by adding a weakly-informative mixture component p_{\mathrm{non-inf}}, leading to a robustified MAP prior distribution:

p_{rMAP}(\eta_{CC}) = (1-w) \cdot p_{MAP}(\eta_{CC}) + w \cdot p_{\mathrm{non-inf}}(\eta_{CC})

where w (parameter weight) may be interpreted as the degree of skepticism towards borrowing strength.

In this function, the argument alpha corresponds to 1-\gamma, where \gamma is the decision boundary. Specifically, the posterior probability of the difference distribution under the null hypothesis is such that: P(p_{treatment}-p_{control}>0) \ge 1-alpha. In case of a non-informative prior this coincides with the frequentist type I error.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - posterior probability that the log-odds ratio is less than zero

• treat_effect - posterior mean of log-odds ratio

• lower_ci - lower limit of the (1-2*alpha)*100% credible interval for log-odds ratio

• upper_ci - upper limit of the (1-2*alpha)*100% credible interval for log-odds ratio

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

Author(s)

Katharina Hees

References

Robust meta-analytic-predictive priors in clinical trials with historical control information. Schmidli, H., et al. Biometrics 70.4 (2014): 1023-1032.

Applying Meta-Analytic-Predictive Priors with the R Bayesian Evidence Synthesis Tools. Weber, S., et al. Journal of Statistical Software 100.19 (2021): 1548-7660.

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

MAPprior_bin(data = trial_data, arm = 3)

Analysis for continuous data using the MAP Prior approach

Description

This function performs analysis of continuous data using the Meta-Analytic-Predictive (MAP) Prior approach. The method borrows data from non-concurrent controls to obtain the prior distribution for the control response in the concurrent periods.

Usage

MAPprior_cont(
  data,
  arm,
  alpha = 0.025,
  opt = 2,
  prior_prec_tau = 4,
  prior_prec_eta = 0.001,
  n_samples = 1000,
  n_chains = 4,
  n_iter = 4000,
  n_adapt = 1000,
  robustify = TRUE,
  weight = 0.1,
  check = TRUE,
  ...
)

Arguments

Details

The MAP approach derives the prior distribution for the control response in the concurrent periods by combining the control information from the non-concurrent periods with a non-informative prior.

The model for the continuous response y_{js} for the control patient j in the non-concurrent period s is defined as follows:

E(y_{js}) = \eta_s

where \eta_s represents the control mean in the non-concurrent period s.

The means for the non-concurrent controls in period s are assumed to have a normal prior distribution with mean \mu_{\eta} and variance \tau^2:

\eta_s \sim \mathcal{N}(\mu_{\eta}, \tau^2)

For the hyperparameters \mu_{\eta} and \tau, normal and half-normal hyperprior distributions are assumed, with mean 0 and variances \sigma^2_{\eta} and \sigma^2_{\tau}, respectively:

\mu_{\eta} \sim \mathcal{N}(0, \sigma^2_{\eta})

\tau \sim HalfNormal(0, \sigma^2_{\tau})

The MAP prior distribution p_{MAP}(\eta_{CC}) for the control response in the concurrent periods is then obtained as the posterior distribution of the parameters \eta_s from the above specified model.

If robustify=TRUE, the MAP prior is robustified by adding a weakly-informative mixture component p_{\mathrm{non-inf}}, leading to a robustified MAP prior distribution:

p_{rMAP}(\eta_{CC}) = (1-w) \cdot p_{MAP}(\eta_{CC}) + w \cdot p_{\mathrm{non-inf}}(\eta_{CC})

where w (parameter weight) may be interpreted as the degree of skepticism towards borrowing strength.

In this function, the argument alpha corresponds to 1-\gamma, where \gamma is the decision boundary. Specifically, the posterior probability of the difference distribution under the null hypothesis is such that: P(\mu_{treatment}-\mu_{control}>0) \ge 1-alpha. In case of a non-informative prior this coincides with the frequentist type I error.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - posterior probability that the difference in means is less than zero

• treat_effect - posterior mean of difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% credible interval for difference in means

• upper_ci - upper limit of the (1-2*alpha)*100% credible interval for difference in means

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

Author(s)

Katharina Hees

References

Robust meta-analytic-predictive priors in clinical trials with historical control information. Schmidli, H., et al. Biometrics 70.4 (2014): 1023-1032.

Applying Meta-Analytic-Predictive Priors with the R Bayesian Evidence Synthesis Tools. Weber, S., et al. Journal of Statistical Software 100.19 (2021): 1548-7660.

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "stepwise")

MAPprior_cont(data = trial_data, arm = 3)

Wrapper function for simulations performing inference on given treatment arms using given models

Description

This function analyzes given data using different models as indicated by the user. It performs inference for indicated experimental treatment arms.

Usage

all_models(
  data,
  arms,
  models = c("fixmodel", "sepmodel", "poolmodel"),
  endpoint,
  alpha = 0.025,
  unit_size = 250,
  ncc = TRUE,
  opt = 2,
  prior_prec_tau = 4,
  prior_prec_eta = 0.001,
  n_samples = 1000,
  n_chains = 4,
  n_iter = 4000,
  n_adapt = 1000,
  robustify = TRUE,
  weight = 0.1,
  ci = FALSE,
  prec_theta = 0.001,
  prec_eta = 0.001,
  tau_a = 0.1,
  tau_b = 0.01,
  prec_a = 0.001,
  prec_b = 0.001,
  bucket_size = 25,
  smoothing_basis = "tp",
  basis_dim = -1,
  gam_method = "GCV.Cp",
  bs_degree = 3,
  poly_degree = 3
)

Arguments

Value

List containing an indicator whether the null hypothesis was rejected or not, and the estimated treatment effect for all investigated treatment arms and all models.

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

all_models(data = trial_data, arms = c(2,3), endpoint = "bin")

Simulate binary data from a platform trial with a shared control arm and a given number of experimental treatment arms entering at given time points

Description

This function simulates data from a platform trial with a given number of experimental treatment arms entering at given time points and a shared control arm. The primary endpoint is a binary endpoint. The user specifies the timing of adding arms in terms of patients recruited to the trial so far and the sample size per experimental treatment arm.

Usage

datasim_bin(
  num_arms,
  n_arm,
  d,
  period_blocks = 2,
  p0,
  OR,
  lambda,
  trend,
  N_peak,
  n_wave,
  full = FALSE,
  check = TRUE
)

Arguments

Details

Design assumptions:

• The simulated platform trial consists of a given number of experimental treatment arms (specified by the argument num_arms) and one control arm that is shared across the whole platform.

• Participants are indexed by entry order, assuming that at each time unit exactly one participant is recruited and the time of recruitment and observation of the response are equal.

• All participants are assumed to be eligible for all arms in the trial, i.e. the same inclusion and exclusion criteria apply to all experimental and control arms.

• Equal sample sizes (given by parameter n_arm) in all experimental treatment arms are assumed.

• The duration of the trial is divided into so-called periods, defined as time intervals bounded by distinct time points of any treatment arm entering or leaving the platform. Hence, multiple treatment arms entering or leaving at the same time point imply the start of only one additional period.

• Allocation ratio of 1:1:...:1 in each period. Furthermore, block randomization is used to assign patients to the active arms. Block size in each period = period_blocks* (number of active arms in the period).

• If the period sample size is not a multiple of the block size, arms for the remaining participants are chosen by sampling without replacement from a vector containing the indices of active arms replicated times ⁠ceiling(remaining sample size/number of active arms)⁠.

Data generation:

The binary response y_j for patient j is generated according to:

g(E(y_j)) = \eta_0 + \sum_{k=1}^K \cdot I(k_j=k) + f(j)

where g(\cdot) is the logit link function, and \eta_0 (logit function of parameter p0) and \theta_k (log of the parameter OR) are the log odds in the control arm and the log odds ratio of treatment k. K is the total number of treatment arms in the trial (parameter num_arms) and k_j is an indicator of the treatment arm patient j is allocated to.

The function f(j) denotes the time trend, whose strength is indicated by \lambda_{k_j} (parameter lambda) and which can have the following patterns (parameter trend):

• "linear" - trend starts at the beginning of the trial and the log odds increases or decreases linearly with a slope of \lambda, according to the function f(j) = \lambda \cdot \frac{j-1}{N-1}, where N is the total sample size in the trial

• "linear_2" - trend starts after the first period (i.e. there is no time trend in the first period) and the log odds increases or decreases linearly with a slope of \lambda, according to the function f(j) = \lambda \cdot \frac{j-1}{N-1}, where N is the total sample size in the trial

• "stepwise" - the log odds is constant in each period and increases or decreases by \lambda each time any treatment arm enters or leaves the trial (i.e. in each period), according to the function f(j) = \lambda_{k_j} \cdot (c_j - 1), where c_j is an index of the period patient j was enrolled in

• "stepwise_2" - the log odds is constant in each period and increases or decreases by \lambda each time a new treatment arm is added to the trial, according to the function f(j) = \lambda_{k_j} \cdot (w_j - 1), where w_j is an indicator of how many treatment arms have already entered the ongoing trial, when patient j was enrolled

• "inv_u" - the log odds increases up to the point N_p (parameter N_peak) and decreases afterwards, linearly with a slope of \lambda, according to the function f(j) = \lambda \cdot \frac{j-1}{N-1} (I(j \leq N_p) - I(j > N_p)), where N_p indicates the point at which the trend turns from positive to negative in terms of the sample size (note that for negative \lambda, the log odds ratio decreases first and increases after)

• "seasonal" - the log odds increases and decreases periodically with a magnitude of \lambda, according to the function f(j) = \lambda \cdot \mathrm{sin} \big( \psi \cdot 2\pi \cdot \frac{j-1}{N-1} \big), where \psi indicates how many cycles should the time trend have (parameter n_wave)

Trials with no time trend can be simulated too, by setting all elements of the vector lambda to zero and choosing an arbitrary pattern.

Value

Data frame: simulated trial data (if full=FALSE, i.e. default) with the following columns:

• j - patient recruitment index

• response - binary response for patient j

• treatment- index of the treatment patient j was allocated to

• period - index of the period patient j was recruited in

or List (if full=TRUE) containing the following elements:

• Data - simulated trial data, including an additional column p with the probability used for simulating the response for patient j

• n_total - total sample size in the trial

• n_arm - sample size per arm (assumed equal)

• num_arms - number of experimental treatment arms in the trial

• d - timings of adding new arms

• SS_matrix - matrix with the sample sizes per arm and per period

• period_blocks - number to multiply the number of active arms with, in order to get the block size per period

• p0 - response probability in the control arm

• OR - odds ratios for each experimental treatment arm

• lambda - strength of time trend in each arm

• time_dep_effect - time dependent treatment effects for each experimental treatment arm (for computing the bias)

• trend - time trend pattern

Author(s)

Pavla Krotka, Marta Bofill Roig

Examples

head(datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise"))

Simulate continuous data from a platform trial with a shared control arm and a given number of experimental treatment arms entering at given time points

Description

This function simulates data from a platform trial with a given number of experimental treatment arms entering at given time points and a shared control arm. The primary endpoint is a continuous endpoint. The user specifies the timing of adding arms in terms of patients recruited to the trial so far and the sample size per arm.

Usage

datasim_cont(
  num_arms,
  n_arm,
  d,
  period_blocks = 2,
  mu0 = 0,
  theta,
  lambda,
  sigma,
  trend,
  N_peak,
  n_wave,
  full = FALSE,
  check = TRUE
)

Arguments

Details

Design assumptions:

• The simulated platform trial consists of a given number of experimental treatment arms (specified by the argument num_arms) and one control arm that is shared across the whole platform.

• Participants are indexed by entry order, assuming that at each time unit exactly one participant is recruited and the time of recruitment and observation of the response are equal.

• All participants are assumed to be eligible for all arms in the trial, i.e. the same inclusion and exclusion criteria apply to all experimental and control arms.

• Equal sample sizes (given by parameter n_arm) in all experimental treatment arms are assumed.

• The duration of a platform trial is divided into so-called periods, defined as time intervals bounded by distinct time points of any treatment arm entering or leaving the platform. Hence, multiple treatment arms entering or leaving at the same time point imply the start of only one additional period.

• Allocation ratio of 1:1:...:1 in each period. Furthermore, block randomization is used to assign patients to the active arms. Block size in each period = period_blocks* (number of active arms in the period).

• If the period sample size is not a multiple of the block size, arms for the remaining participants are chosen by sampling without replacement from a vector containing the indices of active arms replicated times ⁠ceiling(remaining sample size/number of active arms)⁠.

Data generation:

The continuous response y_j for patient j is generated according to:

E(y_j) = \eta_0 + \sum_{k=1}^K \cdot I(k_j=k) + f(j)

where \eta_0 (parameter mu0) and \theta_k (parameter theta) are the response in the control arm and the effect of treatment k. K is the total number of treatment arms in the trial (parameter num_arms) and k_j is an indicator of the treatment arm patient j is allocated to.

The function f(j) denotes the time trend, whose strength is indicated by \lambda_{k_j} (parameter lambda) and which can have the following patterns (parameter trend):

• "linear" - trend starts at the beginning of the trial and the mean response increases or decreases linearly with a slope of \lambda, according to the function f(j) = \lambda \cdot \frac{j-1}{N-1}, where N is the total sample size in the trial

• "linear_2" - trend starts after the first period (i.e. there is no time trend in the first period) and the mean response increases or decreases linearly with a slope of \lambda, according to the function f(j) = \lambda \cdot \frac{j-1}{N-1}, where N is the total sample size in the trial

• "stepwise" - the mean response is constant in each period and increases or decreases by \lambda each time any treatment arm enters or leaves the trial (i.e. in each period), according to the function f(j) = \lambda_{k_j} \cdot (c_j - 1), where c_j is an index of the period patient j was enrolled in

• "stepwise_2" - the mean response is constant in each period and increases or decreases by \lambda each time a new treatment arm is added to the trial, according to the function f(j) = \lambda_{k_j} \cdot (w_j - 1), where w_j is an indicator of how many treatment arms have already entered the ongoing trial, when patient j was enrolled

• "inv_u" - the mean response increases up to the point N_p (parameter N_peak) and decreases afterwards, linearly with a slope of \lambda, according to the function f(j) = \lambda \cdot \frac{j-1}{N-1} (I(j \leq N_p) - I(j > N_p)), where N_p indicates the point at which the trend turns from positive to negative in terms of the sample size (note that for negative \lambda, the mean response decreases first and increases after)

• "seasonal" - the mean response increases and decreases periodically with a magnitude of \lambda, according to the function f(j) = \lambda \cdot \mathrm{sin} \big( \psi \cdot 2\pi \cdot \frac{j-1}{N-1} \big), where \psi indicates how many cycles should the time trend have (parameter n_wave)

Trials with no time trend can be simulated too, by setting all elements of the vector lambda to zero and choosing an arbitrary pattern.

Value

Data frame: simulated trial data (if full=FALSE, i.e. default) with the following columns:

• j - patient recruitment index

• response - continuous response for patient j

• treatment- index of the treatment patient j was allocated to

• period - index of the period patient j was recruited in

or List (if full=TRUE) containing the following elements:

• Data - simulated trial data, including an additional column means with the theoretical means used for the simulation of the response for patient j

• n_total - total sample size in the trial

• n_arm - sample size per arm (assumed equal)

• num_arms - number of experimental treatment arms in the trial

• d - timings of adding new arms

• SS_matrix - matrix with the sample sizes per arm and per period

• period_blocks - number to multiply the number of active arms with, in order to get the block size per period

• mu0 - response in the control arm

• theta - treatment effects for each experimental treatment arm

• lambda - strength of time trend in each arm

• time_dep_effect - time dependent treatment effects for each experimental treatment arm (for computing the bias)

• sigma - standard deviation of the responses

• trend - time trend pattern

Author(s)

Pavla Krotka, Marta Bofill Roig

Examples

head(datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear"))

Frequentist logistic regression model analysis for binary data adjusting for periods

Description

This function performs logistic regression taking into account all trial data until the arm under study leaves the trial and adjusting for periods as factors.

Usage

fixmodel_bin(data, arm, alpha = 0.025, ncc = TRUE, check = TRUE, ...)

Arguments

Details

The model-based analysis adjusts for the time effect by including the factor period (defined as a time interval bounded by any treatment arm entering or leaving the platform). The time is then modelled as a step-function with jumps at the beginning of each period. Denoting by y_j the response probability for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

g(E(y_j)) = \eta_0 + \sum_{k \in \mathcal{K}_M} \theta_k \cdot I(k_j=k) + \sum_{s=2}^{S_M} \tau_s \cdot I(t_j \in T_{S_s})

where g(\cdot) denotes the logit link function and \eta_0 is the log odds in the control arm in the first period; \theta_k represents the log odds ratio of treatment k and control for k\in\mathcal{K}_M, where \mathcal{K}_M is the set of treatments that were active in the trial during periods prior or up to the time when the investigated treatment arm left the trial; \tau_s indicates the stepwise period effect in terms of the log odds ratio between periods 1 and s (s = 2, \ldots, S_M), where S_M denotes the period, in which the investigated treatment arm left the trial.

If the data consists of only one period (e.g. in case of a multi-arm trial), the period in not used as covariate.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the log-odds ratio

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

References

On model-based time trend adjustments in platform trials with non-concurrent controls. Bofill Roig, M., Krotka, P., et al. BMC Medical Research Methodology 22.1 (2022): 1-16.

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

fixmodel_bin(data = trial_data, arm = 3)

Frequentist logistic regression model analysis for binary data adjusting for calendar time units

Description

This function performs logistic regression taking into account all trial data until the arm under study leaves the trial and adjusting for calendar time units as factors.

Usage

fixmodel_cal_bin(
  data,
  arm,
  alpha = 0.025,
  unit_size = 25,
  ncc = TRUE,
  check = TRUE,
  ...
)

Arguments

Details

The model-based analysis adjusts for the time effect by including the factor calendar time unit (defined as time units of fixed length, defined by ùnit_size). The time is then modelled as a step-function with jumps at the beginning of each calendar time unit. Denoting by y_j the response probability for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

g(E(y_j)) = \eta_0 + \sum_{k \in \mathcal{K}_M} \theta_k \cdot I(k_j=k) + \sum_{c=2}^{C_M} \tau_c \cdot I(t_j \in T_{C_c})

where g(\cdot) denotes the logit link function and \eta_0 is the log odds in the control arm in the first calendar time unit; \theta_k represents the log odds ratio of treatment k and control for k\in\mathcal{K}_M, where \mathcal{K}_M is the set of treatments that were active in the trial during calendar time units prior or up to the time when the investigated treatment arm left the trial; \tau_c indicates the stepwise calendar time effect in terms of the log odds ratio between calendar time units 1 and c (c = 2, \ldots, C_M), where C_M denotes the calendar time unit, in which the investigated treatment arm left the trial.

If the data consists of only one calendar time unit, the calendar time unit in not used as covariate.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the log-odds ratio

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

fixmodel_cal_bin(data = trial_data, arm = 3)

Frequentist linear regression model analysis for continuous data adjusting for calendar time units

Description

This function performs linear regression taking into account all trial data until the arm under study leaves the trial and adjusting for calendar time units as factors.

Usage

fixmodel_cal_cont(
  data,
  arm,
  alpha = 0.025,
  unit_size = 25,
  ncc = TRUE,
  check = TRUE,
  ...
)

Arguments

Details

The model-based analysis adjusts for the time effect by including the factor calendar time unit (defined as time units of fixed length, defined by ùnit_size). The time is then modelled as a step-function with jumps at the beginning of each calendar time unit. Denoting by y_j the continuous response for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

E(y_j) = \eta_0 + \sum_{k \in \mathcal{K}_M} \theta_k \cdot I(k_j=k) + \sum_{c=2}^{C_M} \tau_c \cdot I(t_j \in T_{C_c})

where \eta_0 is the response in the control arm in the first calendar time unit; \theta_k represents the effect of treatment k compared to control for k\in\mathcal{K}_M, where \mathcal{K}_M is the set of treatments that were active in the trial during calendar time units prior or up to the time when the investigated treatment arm left the trial; \tau_c indicates the stepwise calendar time effect between calendar time units 1 and c (c = 2, \ldots, C_M), where C_M denotes the calendar time unit, in which the investigated treatment arm left the trial.

If the data consists of only one calendar time unit, the calendar time unit in not used as covariate.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

fixmodel_cal_cont(data = trial_data, arm = 3)

Frequentist linear regression model analysis for continuous data adjusting for periods

Description

This function performs linear regression taking into account all trial data until the arm under study leaves the trial and adjusting for periods as factors.

Usage

fixmodel_cont(data, arm, alpha = 0.025, ncc = TRUE, check = TRUE, ...)

Arguments

Details

The model-based analysis adjusts for the time effect by including the factor period (defined as a time interval bounded by any treatment arm entering or leaving the platform). The time is then modelled as a step-function with jumps at the beginning of each period. Denoting by y_j the continuous response for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

E(y_j) = \eta_0 + \sum_{k \in \mathcal{K}_M} \theta_k \cdot I(k_j=k) + \sum_{s=2}^{S_M} \tau_s \cdot I(t_j \in T_{S_s})

where \eta_0 is the response in the control arm in the first period; \theta_k represents the effect of treatment k compared to control for k\in\mathcal{K}_M, where \mathcal{K}_M is the set of treatments that were active in the trial during periods prior or up to the time when the investigated treatment arm left the trial; \tau_s indicates the stepwise period effect between periods 1 and s (s = 2, \ldots, S_M), where S_M denotes the period, in which the investigated treatment arm left the trial.

If the data consists of only one period (e.g. in case of a multi-arm trial), the period in not used as covariate.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

References

On model-based time trend adjustments in platform trials with non-concurrent controls. Bofill Roig, M., Krotka, P., et al. BMC Medical Research Methodology 22.1 (2022): 1-16.

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

fixmodel_cont(data = trial_data, arm = 3)

Generalized additive model analysis for continuous data

Description

This function performs analysis using a generalized additive model taking into account all trial data until the arm under study leaves the trial and smoothing over the patient entry index.

Usage

gam_cont(
  data,
  arm,
  alpha = 0.025,
  ci = FALSE,
  smoothing_basis = "tp",
  basis_dim = -1,
  gam_method = "GCV.Cp",
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

gam_cont(data = trial_data, arm = 3, ci = TRUE)

Sample size matrix for a platform trial with a given number of treatment arms

Description

This function computes the matrix with sample sizes per arm and period. It is used in the functions datasim_bin() and datasim_cont().

Usage

get_ss_matrix(num_arms, n_arm, d)

Arguments

Value

Sample size matrix, consisting of the sample size per arm and per period, where the arms are represented in the rows (with the control arm in the first row and the experimental arms coming after ordered by entry time) and the periods are represented in the columns.

Author(s)

Pavla Krotka

Examples

get_ss_matrix(num_arms = 3, n_arm = 100, d = c(0, 100, 250))

Generation of an inverted-u trend

Description

This function generates a time trend for given time points in the trial according to an inverted-u function.

Usage

inv_u_trend(j, lambda, N_peak, n_total)

Arguments

Details

The time trend is generated according to the function f(j) = \lambda \cdot \frac{j-1}{N-1} (I(j \leq N_p) - I(j > N_p)), where N is the total sample size (parameter n_total) and N_p (parameter N_peak) indicates the point at which the trend switches direction.

Value

Time trend for time points j.

Author(s)

Marta Bofill Roig, Pavla Krotka

Generation of a linear trend that starts in a given period

Description

This function generates a time trend for given time points in the trial according to a linear function.

Usage

linear_trend(j, lambda, sample_size)

Arguments

Details

The time trend is generated according to the function f(j) = \lambda \cdot \frac{j-1}{N-1}, where N is the total sample size.

Value

Time trend for time points j.

Author(s)

Marta Bofill Roig, Pavla Krotka

Mixed regression model analysis for continuous data adjusting for calendar time units as a random factor with AR1 correlation structure

Description

This function performs linear mixed model regression taking into account all trial data until the arm under study leaves the trial and adjusting for calendar time units as random factors with AR1 correlation structure.

Usage

mixmodel_AR1_cal_cont(
  data,
  arm,
  alpha = 0.025,
  ci = FALSE,
  unit_size = 25,
  ncc = TRUE,
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

mixmodel_AR1_cal_cont(data = trial_data, arm = 3, ci = TRUE)

Mixed regression model analysis for continuous data adjusting for periods as a random factor with AR1 correlation structure

Description

This function performs linear mixed model regression taking into account all trial data until the arm under study leaves the trial and adjusting for periods as random factors with AR1 correlation structure.

Usage

mixmodel_AR1_cont(
  data,
  arm,
  alpha = 0.025,
  ci = FALSE,
  ncc = TRUE,
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

mixmodel_AR1_cont(data = trial_data, arm = 3, ci = TRUE)

Mixed regression model analysis for continuous data adjusting for calendar time units as a random factor

Description

This function performs linear mixed model regression taking into account all trial data until the arm under study leaves the trial and adjusting for calendar time units as random factors.

Usage

mixmodel_cal_cont(
  data,
  arm,
  alpha = 0.025,
  ci = FALSE,
  unit_size = 25,
  ncc = TRUE,
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

mixmodel_cal_cont(data = trial_data, arm = 3, ci = TRUE)

Mixed regression model analysis for continuous data adjusting for periods as a random factor

Description

This function performs linear mixed model regression taking into account all trial data until the arm under study leaves the trial and adjusting for periods as random factors.

Usage

mixmodel_cont(
  data,
  arm,
  alpha = 0.025,
  ci = FALSE,
  ncc = TRUE,
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

mixmodel_cont(data = trial_data, arm = 3, ci = TRUE)

Model-based analysis for continuous data using discontinuous piecewise polynomials per calendar time unit

Description

This function performs linear regression taking into account all trial data until the arm under study leaves the trial and adjusting for time using discontinuous piecewise polynomials in each calendar time unit.

Usage

piecewise_cal_cont(
  data,
  arm,
  alpha = 0.025,
  unit_size = 25,
  ncc = TRUE,
  poly_degree = 3,
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

piecewise_cal_cont(data = trial_data, arm = 3)

Model-based analysis for continuous data using discontinuous piecewise polynomials per period

Description

This function performs linear regression taking into account all trial data until the arm under study leaves the trial and adjusting for time using discontinuous piecewise polynomials in each period.

Usage

piecewise_cont(
  data,
  arm,
  alpha = 0.025,
  ncc = TRUE,
  poly_degree = 3,
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

piecewise_cont(data = trial_data, arm = 3)

Function for visualizing the simulated trial

Description

This function creates a plot visualizing the trial progress over time.

Usage

plot_trial(treatments)

Arguments

Value

ggplot showing trial progress over time.

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

plot_trial(treatments = trial_data$treatment)

Pooled analysis for binary data

Description

This function performs pooled analysis (naively pooling concurrent and non-concurrent controls without adjustment) using a logistic model.

Usage

poolmodel_bin(data, arm, alpha = 0.025, check = TRUE, ...)

Arguments

Details

The pooled analysis takes into account only the data from the evaluated experimental treatment arm and the whole control arm and uses a logistic regression model to evaluate the given treatment arm. Denoting by y_j the response probability for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

g(E(y_j)) = \eta_0 + \theta_M \cdot I(k_j=M)

where g(\cdot) denotes the logit link function and \eta_0 is the log odds in the control arm; \theta_M represents the log odds ratio of treatment M and control.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the log-odds ratio

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

poolmodel_bin(data = trial_data, arm = 3)

Pooled analysis for continuous data

Description

This function performs pooled analysis (naively pooling concurrent and non-concurrent controls without adjustment) using a linear model.

Usage

poolmodel_cont(data, arm, alpha = 0.025, check = TRUE, ...)

Arguments

Details

The pooled analysis takes into account only the data from the evaluated experimental treatment arm and the whole control arm and uses a linear regression model to evaluate the given treatment arm. Denoting by y_j the continuous response for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

E(y_j) = \eta_0 + \theta_M \cdot I(k_j=M)

where \eta_0 is the response in the control arm; \theta_M represents the treatment effect of treatment M as compared to control.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

poolmodel_cont(data = trial_data, arm = 3)

Generation of a seasonal trend

Description

This function generates a time trend for given time points in the trial according to a periodic function.

Usage

seasonal_trend(j, lambda, n_wave, n_total)

Arguments

Details

The time trend is generated according to the function f(j) = \lambda \cdot \mathrm{sin} \big( \psi \cdot 2\pi \cdot \frac{j-1}{N-1} \big), where N is the total sample size (parameter n_total) and the parameter \psi corresponds to the input parameter n_wave.

Value

Time trend for time points j.

Author(s)

Marta Bofill Roig, Pavla Krotka

Separate analysis for binary data adjusted for periods

Description

This function performs separate analysis (only taking into account concurrent controls) using a logistic model and adjusting for periods, if the treatment arm stays in the trial for more than one period.

Usage

sepmodel_adj_bin(data, arm, alpha = 0.025, check = TRUE, ...)

Arguments

Details

The adjusted separate analysis takes into account only the data from the evaluated experimental treatment arm and its concurrent controls and adjusts for the time effect by including the factor period (defined as a time interval bounded by any treatment arm entering or leaving the platform). The time is then modelled as a step-function with jumps at the beginning of each period. Denoting by y_j the response probability for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

g(E(y_j)) = \eta_0 + \theta_M \cdot I(k_j=M) + \sum_{s=S_{M_1}+1}^{S_{M_2}} \tau_s \cdot I(t_j \in T_{S_s})

where g(\cdot) denotes the logit link function and \eta_0 is the log odds in the concurrent controls; \theta_M represents the log odds ratio of treatment M and control; \tau_s indicates the stepwise period effect in terms of the log odds ratio between periods S_{M_1} and s (s = S_{M_1}+1, \ldots, S_{M_2}), where S_{M_1} and S_{M_2} denote the periods, in which the investigated treatment arm joined and left the trial, respectively.

If the data consists of only one period, the period in not used as covariate.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the log-odds ratio

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

sepmodel_adj_bin(data = trial_data, arm = 3)

Separate analysis for continuous data adjusted for periods

Description

This function performs separate analysis (only taking into account concurrent controls) using a linear model and adjusting for periods, if the treatment arm stays in the trial for more than one period.

Usage

sepmodel_adj_cont(data, arm, alpha = 0.025, check = TRUE, ...)

Arguments

Details

The adjusted separate analysis takes into account only the data from the evaluated experimental treatment arm and its concurrent controls and adjusts for the time effect by including the factor period (defined as a time interval bounded by any treatment arm entering or leaving the platform). The time is then modelled as a step-function with jumps at the beginning of each period. Denoting by y_j the response probability for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

E(y_j) = \eta_0 + \theta_M \cdot I(k_j=M) + \sum_{s=S_{M_1}+1}^{S_{M_2}} \tau_s \cdot I(t_j \in T_{S_s})

where \eta_0 is the response in the concurrent controls; \theta_M represents the treatment effect of treatment M as compared to control; \tau_s indicates the stepwise period effect between periods S_{M_1} and s (s = S_{M_1}+1, \ldots, S_{M_2}), where S_{M_1} and S_{M_2} denote the periods, in which the investigated treatment arm joined and left the trial, respectively.

If the data consists of only one period, the period in not used as covariate.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

sepmodel_adj_cont(data = trial_data, arm = 3)

Separate analysis for binary data

Description

This function performs separate analysis (only taking into account concurrent controls) using a logistic model.

Usage

sepmodel_bin(data, arm, alpha = 0.025, check = TRUE, ...)

Arguments

Details

The separate analysis takes into account only the data from the evaluated experimental treatment arm and its concurrent controls and uses a logistic regression model to evaluate the given treatment arm. Denoting by y_j the response probability for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

g(E(y_j)) = \eta_0 + \theta_M \cdot I(k_j=M)

where g(\cdot) denotes the logit link function and \eta_0 is the log odds in the concurrent controls; \theta_M represents the log odds ratio of treatment M and control.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the log-odds ratio

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

sepmodel_bin(data = trial_data, arm = 3)

Separate analysis for continuous data

Description

This function performs separate analysis (only taking into account concurrent controls) using a linear model.

Usage

sepmodel_cont(data, arm, alpha = 0.025, check = TRUE, ...)

Arguments

Details

The separate analysis takes into account only the data from the evaluated experimental treatment arm and its concurrent controls and uses a linear regression model to evaluate the given treatment arm. Denoting by y_j the continuous response for patient j, by k_j the arm patient j was allocated to, and by M the treatment arm under evaluation, the regression model is given by:

E(y_j) = \eta_0 + \theta_M \cdot I(k_j=M)

where \eta_0 is the response in the concurrent controls; \theta_M represents the treatment effect of treatment M as compared to control.

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

sepmodel_cont(data = trial_data, arm = 3)

Wrapper function performing simulation studies for a given set of scenarios (not parallelized)

Description

This function performs a simulation study for a given set of scenarios, analyzing simulated data using different models as indicated by the user. Performs inference for indicated experimental treatment arms. Simulates the probability to reject H_0 based on a given number of replications.

Usage

sim_study(
  nsim,
  scenarios,
  arms,
  models = c("fixmodel", "sepmodel", "poolmodel"),
  endpoint,
  verbose = TRUE
)

Arguments

Value

Data frame with all considered scenarios and corresponding results - the probability to reject H_0.

Author(s)

Pavla Krotka

Examples

# Create data frame with all parameters:
sim_scenarios <- data.frame(num_arms = 4,
n_arm = 250,
d1 = 250*0,
d2 = 250*1,
d3 = 250*2,
d4 = 250*3,
period_blocks = 2,
mu0 = 0,
sigma = 1,
theta1 = 0,
theta2 = 0,
theta3 = 0,
theta4 = 0,
lambda0 = rep(seq(-0.15, 0.15, length.out = 9), 2),
lambda1 = rep(seq(-0.15, 0.15, length.out = 9), 2),
lambda2 = rep(seq(-0.15, 0.15, length.out = 9), 2),
lambda3 = rep(seq(-0.15, 0.15, length.out = 9), 2),
lambda4 = rep(seq(-0.15, 0.15, length.out = 9), 2),
trend = c(rep("linear", 9), rep("stepwise_2", 9)),
alpha = 0.025,
ncc = TRUE)

# Run simulation study:
sim_results <- sim_study(nsim = 100, scenarios = sim_scenarios, arms = c(3, 4),
models = c("fixmodel", "sepmodel", "poolmodel"), endpoint = "cont")

Wrapper function performing simulation studies for a given set of scenarios (parallelized on replication level)

Description

This function performs a simulation study for a given set of scenarios, analyzing simulated data using different models as indicated by the user. Performs inference for indicated experimental treatment arms. Simulates the probability to reject H_0, and the bias, as well as the mean squared error (MSE) of the treatment effect estimates based on a given number of replications.

Usage

sim_study_par(
  nsim,
  scenarios,
  arms,
  models = c("fixmodel", "sepmodel", "poolmodel"),
  endpoint,
  perc_cores = 0.9,
  verbose = TRUE
)

Arguments

Value

Data frame with all considered scenarios and corresponding results - the probability to reject H_0, and the bias, as well as the mean squared error (MSE) of the treatment effect estimates.

Author(s)

Pavla Krotka

Examples

# Create data frame with all parameters:
sim_scenarios <- data.frame(num_arms = 4,
n_arm = 250,
d1 = 250*0,
d2 = 250*1,
d3 = 250*2,
d4 = 250*3,
period_blocks = 2,
mu0 = 0,
sigma = 1,
theta1 = 0,
theta2 = 0,
theta3 = 0,
theta4 = 0,
lambda0 = rep(seq(-0.15, 0.15, length.out = 9), 2),
lambda1 = rep(seq(-0.15, 0.15, length.out = 9), 2),
lambda2 = rep(seq(-0.15, 0.15, length.out = 9), 2),
lambda3 = rep(seq(-0.15, 0.15, length.out = 9), 2),
lambda4 = rep(seq(-0.15, 0.15, length.out = 9), 2),
trend = c(rep("linear", 9), rep("stepwise_2", 9)),
alpha = 0.025,
ncc = TRUE)

# Run simulation study:
sim_results <- sim_study_par(nsim = 100, scenarios = sim_scenarios, arms = c(3, 4),
models = c("fixmodel", "sepmodel", "poolmodel"), endpoint = "cont")

Spline regression analysis for continuous data with knots placed according to calendar time units

Description

This function performs linear regression taking into account all trial data until the arm under study leaves the trial and adjusting for time using regression splines with knots placed according to calendar time units.

Usage

splines_cal_cont(
  data,
  arm,
  alpha = 0.025,
  unit_size = 25,
  ncc = TRUE,
  bs_degree = 3,
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• knots - positions of the knots in terms of patient index

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

splines_cal_cont(data = trial_data, arm = 3)

Spline regression analysis for continuous data with knots placed according to periods

Description

This function performs linear regression taking into account all trial data until the arm under study leaves the trial and adjusting for time using regression splines with knots placed according to periods.

Usage

splines_cont(
  data,
  arm,
  alpha = 0.025,
  ncc = TRUE,
  bs_degree = 3,
  check = TRUE,
  ...
)

Arguments

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - p-value (one-sided)

• treat_effect - estimated treatment effect in terms of the difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% confidence interval

• upper_ci - upper limit of the (1-2*alpha)*100% confidence interval

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

• knots - positions of the knots in terms of patient index

• model - fitted model

Author(s)

Pavla Krotka

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

splines_cont(data = trial_data, arm = 3)

Generation of stepwise trend with equal jumps between periods

Description

This function generates a stepwise trend for a given period. No time trend is assumed in the first period.

Usage

sw_trend(cj, lambda)

Arguments

Details

The time trend is generated according to the function f(j) = \lambda \cdot (c_j - 1), where c_j is an index of the period patient j was enrolled in.

Value

Time trend in period c_j.

Author(s)

Marta Bofill Roig, Pavla Krotka

Time machine analysis for binary data

Description

This function performs analysis of binary data using the Time Machine approach. It takes into account all data until the investigated arm leaves the trial. It is based on logistic regression with treatment as a categorical variable and covariate adjustment for time via a second-order Bayesian normal dynamic linear model (separating the trial into buckets of pre-defined size).

Usage

timemachine_bin(
  data,
  arm,
  alpha = 0.025,
  prec_theta = 0.001,
  prec_eta = 0.001,
  tau_a = 0.1,
  tau_b = 0.01,
  bucket_size = 25,
  check = TRUE,
  ...
)

Arguments

Details

The Time Machine divides the trial duration into C calendar time intervals of equal length ("buckets"), which are indexed backwards in time. That is to say, the most recent time interval is denoted by c=1 and the time interval corresponding to the beginning of the trial by c=C. The analysis is performed as soon as the analyzed treatment arm finishes in the trial.

The model is defined as follows:

g(E(y_j)) = \eta_0 + \theta_{k_j} + \alpha_{c_j}

where y_j is the binary response for patient j and g(\cdot) is the logit link function, which maps the expected value of the patient response to the linear predictors in the model. The model intercept \eta_0 denotes the response of the control group at time of the analysis, \theta_{k_j} is the effect of the treatment arm k that patient j was enrolled in, relative to control in terms of the log odds ratio. For the parameters \eta_0 and \theta_{k_j}, normal prior distributions are assumed, with mean 0 and variances \sigma^2_{\eta_0} and \sigma^2_{\theta}, respectively:

\eta_0 \sim \mathcal{N}(0, \sigma^2_{\eta_0})

\theta_{k_j} \sim \mathcal{N}(0, \sigma^2_{\theta})

In the Time Machine, time effect is represented by \alpha_{c_j}, which is the change in the response in time bucket c_j (which denotes the time bucket in which patient j is enrolled) compared to the most recent time bucket c=1 and is modeled using a Bayesian second-order normal dynamic linear model. This creates a smoothing over the control response, such that closer time buckets are modeled with more similar response rates:

\alpha_1 = 0

\alpha_2 \sim \mathcal{N}(0, 1/\tau)

\alpha_c \sim \mathcal{N}(2 \alpha_{c-1} - \alpha_{c-2}, 1/\tau), 3 \le c \le C

where \tau denotes the drift parameter that controls the degree of smoothing over the time buckets and is assumed to have a Gamma hyperprior distribution:

\tau \sim Gamma(a_{\tau}, b_{\tau})

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - posterior probability that the log-odds ratio is less than zero

• treat_effect - posterior mean of log-odds ratio

• lower_ci - lower limit of the (1-2*alpha)*100% credible interval for log-odds ratio

• upper_ci - upper limit of the (1-2*alpha)*100% credible interval for log-odds ratio

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

Author(s)

Dominic Magirr, Peter Jacko

References

The Bayesian Time Machine: Accounting for Temporal Drift in Multi-arm Platform Trials. Saville, B. R., Berry, D. A., et al. Clinical Trials 19.5 (2022): 490-501.

Examples

trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

timemachine_bin(data = trial_data, arm = 3)

Time machine analysis for continuous data

Description

This function performs analysis of continuous data using the Time Machine approach. It takes into account all data until the investigated arm leaves the trial. It is based on linear regression with treatment as a categorical variable and covariate adjustment for time via a second-order Bayesian normal dynamic linear model (separating the trial into buckets of pre-defined size).

Usage

timemachine_cont(
  data,
  arm,
  alpha = 0.025,
  prec_theta = 0.001,
  prec_eta = 0.001,
  tau_a = 0.1,
  tau_b = 0.01,
  prec_a = 0.001,
  prec_b = 0.001,
  bucket_size = 25,
  check = TRUE,
  ...
)

Arguments

Details

The Time Machine divides the trial duration into C calendar time intervals of equal length ("buckets"), which are indexed backwards in time. That is to say, the most recent time interval is denoted by c=1 and the time interval corresponding to the beginning of the trial by c=C. The analysis is performed as soon as the analyzed treatment arm finishes in the trial.

The model is defined as follows:

E(y_j) = \eta_0 + \theta_{k_j} + \alpha_{c_j}

where y_j is the continuous response for patient j. The model intercept \eta_0 denotes the response of the control group at time of the analysis, \theta_{k_j} is the effect of the treatment arm k that patient j was enrolled in, relative to control. For the parameters \eta_0 and \theta_{k_j}, normal prior distributions are assumed, with mean 0 and variances \sigma^2_{\eta_0} and \sigma^2_{\theta}, respectively:

\eta_0 \sim \mathcal{N}(0, \sigma^2_{\eta_0})

\theta_{k_j} \sim \mathcal{N}(0, \sigma^2_{\theta})

In the Time Machine, time effect is represented by \alpha_{c_j}, which is the change in the response in time bucket c_j (which denotes the time bucket in which patient j is enrolled) compared to the most recent time bucket c=1 and is modeled using a Bayesian second-order normal dynamic linear model. This creates a smoothing over the control response, such that closer time buckets are modeled with more similar response rates:

\alpha_1 = 0

\alpha_2 \sim \mathcal{N}(0, 1/\tau)

\alpha_c \sim \mathcal{N}(2 \alpha_{c-1} - \alpha_{c-2}, 1/\tau), 3 \le c \le C

where \tau denotes the drift parameter that controls the degree of smoothing over the time buckets and is assumed to have a Gamma hyperprior distribution:

\tau \sim Gamma(a_{\tau}, b_{\tau})

The precision of the individual patient responses (1/\sigma^2) is also assumed to have a Gamma hyperprior distribution:

1/\sigma^2 \sim Gamma(a_{\sigma^2}, b_{\sigma^2})

Value

List containing the following elements regarding the results of comparing arm to control:

• p-val - posterior probability that the difference in means is less than zero

• treat_effect - posterior mean of difference in means

• lower_ci - lower limit of the (1-2*alpha)*100% credible interval for difference in means

• upper_ci - upper limit of the (1-2*alpha)*100% credible interval for difference in means

• reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)

Author(s)

Dominic Magirr, Peter Jacko

Examples

trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

timemachine_cont(data = trial_data, arm = 3)