Comparison of treatment regimes with adjustment for auxiliary variables

Abstract

Treatment regimes are algorithms for assigning treatments to patients with complex diseases, where treatment consists of more than one episode of therapy, potentially with different dosages of the same agent or different agents. Sequentially randomized clinical trials are usually designed to evaluate and compare the effect of different treatment regimes. In such designs, eligible patients are first randomly assigned to receive one of the initial treatments. Patients meeting some criteria (e.g. no progressive disease) are then randomized to receive one of the maintenance treatments. Usually, the procedure continues until all treatment options are exhausted. Such multistage treatment assignment results in treatment regimes consisting of initial treatments, intermediate responses and second-stage treatments. However, methods for efficient analysis of sequentially randomized trials have only been developed very recently. As a result, earlier clinical trials reported results based only on the comparison of stage-specific treatments. In this article, we propose a model that applies to comparisons of any combination of any number of treatment regimes regardless of the number of stages of treatment adjusted for auxiliary variables. Contrasts of treatment regimes are tested using the Wald chi-square method. Both the model and Wald chi-square tests of contrasts are illustrated through a simulation study and an application to a high-risk neuroblastoma study to complement the earlier results reported on this study.

Keywords:

• auxiliary variables
• treatment regime
• high-risk neuroblastoma study
• sequentially randomized design
• time-dependent covariates

Acknowledgements

We would like to thank COG Neuroblastoma Disease Committee for their kind permission to use the neuroblastoma data set, especially Dr Wendy London for her help during the application process. We also thank the referees of this article for their helpful comments.