BOB: Bayesian Optimal Design for Biosimilar Trials with Co-Primary Endpoints

BOB design is a Bayesian optimal design proposed for biosimilar trials with co-primary endpoints.

This repository contains R codes used to implement numerical studies in the corresponding paper.

Table of Contents

• Simulation Settings
• Numerical Studies
  • Frequentist Fixed Designs
  • Bayesian Adaptive Designs
    • Design Calibration
    • power(type I error)

• Authors and Reference

Simulation Settings

Firstly, some important setting parameters and their meanings are explained in this document, as follows:

• maxnsample: $n_J$
• Tmax: $J$
• nsample: $n_j$
• tau2: $\tau^2$
• rho: $\rho$
• sn: number of replicated trials in this simulation study
• pR(pT): $p_R (p_T)$
• overallmuR(overallmuT): $\mu_R (\mu_T)$

Numerical Studies

Frequentist Fixed Designs

This folder contains R codes used to implement three fixed-sample designs considered in the paper.

Frequentist fixed-sample designs include two univariate designs such as FE and FS and a bivariate design FES. Among them, FE adopts a two-sample t-test approach for the scaled average bioequivalence test to evaluate the biosimilarity of the efficacy endpoint, FS applies the frequentist two one-sided tests (TOST) procedure for both sides to test the safety endpoints, and FES combines the FE and FS designs to test both efficacy and safety endpoints.

Bayesian Adaptive Designs

This folder contains R codes used to implement four Bayesian adaptive designs considered in the paper. The procedure of Bayesian designs requires two main steps: (1) design calibration and (2) design implementation.

Design Calibration

R codes in this folder help us to calibrate the design and return the optimal design parameters ($\lambda, \gamma$). We calibrate Bayesian adaptive designs including BAE, BAS, BOBs, and BOBavg. In detail, BAE and BAS are Bayesian group-sequential designs that consider the respective efficacy and safety as a single primary endpoint. BOBs and BOBavg are proposed BOB designs.

• calibration_bae.R: R codes used to calibrate the design BAE, and output the optimal design parameters.

• calibration_bas.R: R codes used to calibrate the design BAS, and output the optimal design parameters.

• calibration_bobs.R: R codes used to calibrate the design BOBs, and output the optimal design parameters.

• BOBavg

  This folder contains 3 files used to implement the whole calibration procedure of the design BOBavg with the following settings:

  • search_1.R: $\mu_T=\pm 0.32$, $p_T \sim unif(0.3,0.7)$
  • search_2.R: $\mu_T=0, p_T=0$ (i.e., power of the design)
  • search_3.R: $\mu_T \sim unif(-0.32,0.32)$, $p_T=0.5\pm 0.2$

  and the file output.R used to output the optimal design parameters.

For example, for the proposed BOBs design, simply run the corresponding R script like

Rscript calibration_bobs.R

the optimal design parameters will be output as follows:

#Optimal parameters for BOBs:

Design implementation: power(type I error)

Given the resulted optimal design parameters, simulation can be performed to obtain the operating characteristics such as the power (or the type I error rate) and the expected sample size.

For example, for the proposed BOBs design,

Rscript simu_bob.R

#The power (or type I error rate) of the design BOB:
#Expected Sample Size(EN):

Authors and Reference

• Chi X, Yu Z, Lin R. BOB: Bayesian optimal design for biosimilar trials with co-primary endpoints. Statistics in Medicine. 2022;1-16. doi: 10.1002/sim.9571