The treatment effects of the same therapy observed from multiple clinical trials can often be very different. Yet the patient characteristics accounting for these differences may not be identifiable in real world practice. There needs to be an unbiased way to combine the results from multiple trials and report the overall treatment effect for the general population 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. Thus we are proposing efficient estimates and 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.
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