  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.
