Model-based time trend adjustments in platform trials with non-concurrent controls

This repository contains the main code and R functions to reproduce the results of the simulation study in “On model-based time trend adjustments in platform trials with non-concurrent controls” [Paper] [Preprint].

We investigated frequentist, model-based approaches to adjust for time trends in platform trials utilizing non-concurrent controls. We investigated conditions under which the model-based approaches can successfully adjust for time trends in the simple case of a two-period trial with two experimental treatments and a shared control. Assuming that the second treatment arm is added at a later time period, we assess the robustness of recently proposed model-based approaches to adjust for time trends when utilizing non-concurrent controls. The following figure illustrates the design considered:

Next, we explain the R functions we created to simulate the data and to analyse it. After this, we describe the main simulation script and results and briefly summarize the supplementary material and the figures created.

R Functions

The folder functions contains all R functions necessary to reproduce the results and figures in the main paper and supplementary material:

Functions for data generation

• trend_functions.R: Contains functions linear_trend() and sw_trend() that are used to generate linear or stepwise trend in the main paper and the function linear_trend2() that is used to simulate linear trend that starts in the second period in the supplementary material.

• data_sim_block.R: The function data_sim_block() simulates continuous or binary data for two-stage platform trial using block randomization and deterministic patient entry times, based on given sample sizes, effect sizes and time trend specifications. This function is used for data generation in the main paper.

• data_sim_brdt.R: The function data_sim_brdt() simulates continuous or binary data for two-stage platform trial using block randomization and random patient entry times.

• data_sim.R: The function data_sim() simulates continuous or binary data for two-stage platform trial using simple randomization per period and deterministic patient entry times.

• data_sim_rdt.R: The function data_sim_rdt() simulates continuous or binary data for two-stage platform trial using simple randomization per period and random patient entry times.

Functions for tests and models

• z_test.R: Contains functions z_test_pol() and z_test_sep() that perform pooled or separate one-sided z-test with the given data.

• t_test.R: Contains functions t_test_pol() and t_test_sep() that perform pooled or separate one-sided t-test with the given data.

• linear_model.R: Contains functions linear_model_a1(), linear_model_a1_int(), linear_model_a2(), linear_model_a2_int(), linear_model_b1() and linear_model_b2() that are used to fit different linear regression models (ALLTC-Linear, ALLTCI-Linear, ALLTC-Step, ALLTCI-Step, TC-Linear and TC-Step) to given data.

• z_prop_test.R: Contains function z_prop_pol() and z_prop_sep() that perform pooled or separate one-sided two-proportions z-test for with the given data.

• log_model.R: Contains functions logistic_model_a1(), logistic_model_a1_int(), logistic_model_a2(), logistic_model_a2_int(), logistic_model_b1(), logistic_model_b2(), logistic_model_sep() and logistic_model_pol() that are used to fit different logistic regression models (ALLTC-Linear, ALLTCI-Linear, ALLTC-Step, ALLTCI-Step, TC-Linear, TC-Step and separate and pooled logistic model) to given data.

Functions for simulations

• allinone_model.R: The function allinone_model() is programmed to call all the aforementioned functions and return the calculated metrics (T/F for reject H02 and bias) from all considered tests and models.

• allinone_sim.R: The function allinone_simsce() takes a data frame with different simulation scenarios as input and performs nsim replications for each of them to simulate the type I error rate/power, bias and rMSE.

• allinone_sim_par.R: The function allinone_simsce_par() is a parallelized version of allinone_simsce().

Main paper

Main simulation script and results

• mainpaper_script.R: Script with all scenarios considered in the main study. Simulates given scenarios and saves the results as .csv files in the folder results.

Running this script results in 100 separate .csv files, named results_bin_trendpattern_parametrization_hypothesis_trendtype.csv or results_cont_trendpattern_hypothesis_trendtype.csv depending on whether the simulated data were binary or continuous.

• For binary endpoints, the given scenario is indicated in the file name as results_bin_trendpattern_parametrization_hypothesis_trendtype.csv, where

  • for trendpattern, we considered the options:

    • inv_1 - inverted-U trend with peak in the middle of period 1
    • inv_2 - inverted-U trend with peak between period 1 and 2
    • inv_3 - inverted-U trend with peak in the middle of period 2
    • lin - linear trend
    • step - stepwise trend

  • for parametrization, we considered:

    • add - additive parametrization
    • mult - multiplicative parametrization

  • for hypothesis, we considered:

    • alpha - simulations of the type I error under the null hypothesis
    • pow - simulations of the power under the alternative hypothesis

  • for trendtype, we considered:

    • eq - equal time trend in all arms
    • diff_pos - positive time trend in control and arm 2, varying trend in arm 1
    • diff_neg - negative time trend in control and arm 2, varying trend in arm 1

  • additionally, OR1 refers to scenarios with OR1>1, otherwise OR1<1 is used

• For continuous endpoints, the given scenario is indicated in the file name as follows: results_cont_trendpattern_hypothesis_trendtype.csv, where

  • for trendpattern, we considered:

    • inv_1 - inverted-U trend with peak in the middle of period 1
    • inv_2 - inverted-U trend with peak between period 1 and 2
    • inv_3 - inverted-U trend with peak in the middle of period 2
    • lin - linear trend
    • step - stepwise trend

  • for hypothesis, we considered:

    • alpha - simulations of the type I error under the null hypothesis
    • pow - simulations of the power under the alternative hypothesis

  • for trendtype, we considered:

    • eq - equal time trend in all arms
    • diff - time trend of lambda=0.1 in control and arm 2, varying trend in arm 1

Figures

• Plots_paper.Rmd: generates all figures used in the main paper and section E of the supplementary material and saves them in the folder figures.

Figures presented in the main paper have the suffix _main (e.g. cont_response_main.png), while figures included in the supplementary material are indicated by the suffix _supp (e.g. cont_all_eq_bias_supp.png).

Supplementary material

The folder Supp_mat contains additional simulation results for three-stage platform trials and additional results regarding different randomization procedures discussed in the supplementary material.

Results that are reported in section F.1 of the supplementary material are simulated in the Supp_mat_randomization.Rmd script and presented in the corresponding HTML file.

For section F.2 of the supplementary material (platform trials with three periods), there are analogous functions as for the main paper in the subfolder functions, which were adapted for the three-stage design. All considered three-stage scenarios can be simulated by running the additional_sim_script.R, while the results are again saved in the results subfolder. The files Plots_additional_sim.Rmd and the corresponding HTML file are used for visualization of the additional results. Figures presented in Section F.2 of the Supplementary material are saved in the figures subfolder.

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Funding

EU-PEARL (EU Patient-cEntric clinicAl tRial pLatforms) project has received funding from the Innovative Medicines Initiative (IMI) 2 Joint Undertaking (JU) under grant agreement No 853966. This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and EFPIA andChildren’s Tumor Foundation, Global Alliance for TB Drug Development non-profit organisation, Spring works Therapeutics Inc. This publication reflects the authors’ views. Neither IMI nor the European Union, EFPIA, or any Associated Partners are responsible for any use that may be made of the information contained herein.