## A bias-adjusted analysis of stratified clinical trials with multi-component endpoints using the Wei-Lachin test
##Background:
# A bias-adjusted analysis of stratified clinical trials with multi-component endpoints using the Wei-Lachin test
## Abstract
### Background:
The disease heterogeneity and geographic dispersions of patients in rare diseases often necessitates a multi-center design and the use of multi-component endpoints, which combine multiple outcome measures into a single score. A common issue in these trials is allocation bias, as trials in rare diseases are frequently unblinded or single-blinded. The ICH E9 guideline recommends assessing the potential contributions of bias to inference. Therefore, we aim to develop a bias-adjusted analysis strategy for stratified clinical trials with multi-component endpoints.
##Methods:
### Methods:
To model biased patient responses, we derived an allocation biasing policy based on the 'convergence strategy' of Blackwell and Hodges tailored to stratified clinical trials with multi-component endpoints. Using this policy, we developed a bias-adjusted analysis strategy for a stratified version of the Wei-Lachin test, integrating Fleiss's stratified test with the Wei-Lachin test.
##Results:
### Results:
When allocation bias is present, ignoring it during trial evaluation with the stratified Wei-Lachin test increases the type I error rate, potentially exceeding the 5% significance level and inflating power beyond the nominal power of 80%, leading to an overestimation of the treatment effect. In contrast, the bias-adjusted stratified Wei-Lachin test preserves the 5% significance level while maintaining approximately 75–80% power, depending on the randomization procedure and the extent of allocation bias.
##Conclusion:
### Conclusion:
In stratified clinical trials with multi-component endpoints that are susceptible to allocation bias — such as those that are unblinded or single-blinded, lack allocation concealment, involve numerous strata, or use restrictive randomization procedures such as stratified PBR — incorporating a bias-adjusted test as a sensitivity analysis enhances the validity of trial results. Accounting for allocation bias during the analysis phase strengthens the robustness of clinical trials, leading to more reliable and accurate conclusions.
##Simulation study
## Simulation Study Overview
This simulation study is divided into three parts and is designed to investigate allocation bias effects, assess the efficiency of a bias-adjusted analysis, and evaluate the accuracy of bias estimation. Below, we outline each part in detail, along with the corresponding R code files for replication.
### Part I: Impact of Allocation Bias on the Type I Error on Misspecification
In the first part we investigate the impact of allocation bias on the test decisions of the stratified Wei-Lachin test for several clinical scenarios to figure out which scenarios are most susceptible to allocation bias. Especially in scenarios at higher risk of allocation bias a bias-adjusted sensitivity analysis may be advisable. We quantify the impact of allocation bias on the misspecified type I error of the stratified Wei-Lachin test. The type I error under misspecification refers to the type I error that is calculated conditioned on a randomization list and that ignores allocation bias effects.
#### Key Aspects
- Assess the impact of allocation bias on the trial results for several clinical scenarios
- Simulate misspecified type I errors concerning various randomization procedures
- For simulations the R code _T1EstratWL.R_ is used
### Part II: Power Comparison of Bias Adjusted vs. Unadjusted stratified Wei-Lachin Tests
In the second part of the simulation study, we examine the power of a bias-adjusted version of the stratified Wei-Lachin test, which accounts for allocation bias, and compare it to the power of the unadjusted stratified WL test, which ignores bias is present. This comparison helps determine whether bias adjustment improves the test's ability to detect true treatment effects.
#### Key Aspects
- Compare the power of the bias-adjusted and bias-unadjusted stratified Wei-Lachin test concerning various randomization procedures and different extents of allocation bias
- Simulations based on the R code _power_biasadj_unadj_stratWL.R_
### Part III: Accuracy of Allocation Bias Estimation
In the third part, we evaluate the accuracy of an allocation bias estimator, which is crucial for implementing bias-adjusted analyses. We simulate 100 000 clinical trials across various clinical settings, estimate the bias effects, and assess the accuracy of these estimates using the mean estimate and mean squared error.
#### Key Aspects
- Simulate clinical trials with various settings and estimate bias effects.
- Assess estimation accuracy using mean squared error and mean bias estimates.
- Simulation based on the R code _biasestimate.R_.
## License
This project is free and open source software, licensed under GPL3.
