Combining Survival Trials Using Aggregate Data Based on Misspecified Models

Abstract

The treatment effects of the same therapy observed from multiple clinical trials can be very different. Yet the patient characteristics accounting for the differences may not be identifiable in real practice so that it is necessary to estimate and report the overall treatment effect for the general popoulation during the development and validation of a new therapy. The non-linear structure of the maximum partial likelihood estimates for the (log) hazard ratio defined with a Cox proportional hazard model leads to challenges in the statistical analyses for combining such clinical trials. In this paper, we formulated the expected overall treatment effects using various modeling assumptions. Then we proceeded to propose efficient estimates together with a version of Wald test for the combined hazard ratio using only aggregate data. Interpretation of the methods are provided in the framework of robust data analyses involving misspecified models.