The estimation of average hazard ratios by weighted Cox regression

Often the effect of at least one of the prognostic factors in a Cox regression model changes over time. which violates the proportional hazards assumption of this model. As a consequence. the average hazard ratio for such a prognostic factor is under- or overestimated. While there are several methods to appropriately cope with non-proportional hazards, in particular by including parameters for time-dependent effects, weighted estimation in Cox regression is a parsimonious alternative without additional parameters. The methodology, which extends the weighted k-sample logrank tests of the Tarone-Ware scheme to models With multiple, binary and continuous covariates, has been introduced ill the nineties of the last century and is further developed and re-evaluated ill this contribution. The notion of all average hazard ratio is defined and its connection to the effect size measure P(X<Y) is emphasized. The suggested approach accomplishes estimation of intuitively interpretable average hazard ratios and provides tools for inference. A Monte Carlo study confirms the satisfactory performance. Advantages of the approach arc exemplified by comparing standard and weighted analyses of an international lung cancer Study. SAS and R programs facilitate application. Copyright (C) 2009 John Wiley &, Sons, Ltd.