Hierarchical proportional hazards regression models for highly stratified data

In clinical trials conducted over several data collection centers, the most common statistically defensible analytic method, a stratified Cox model an alysis, suffers from two important defects. First, identification of units that are outlying with respect to the baseline hazard is awkward since this hazard is implicit (rather than explicit) in the Cox partial likelihood. S econd land more seriously), identification of modest treatment effects is o ften difficult since the model fails to acknowledge any similarity across t he strata. We consider a number of hierarchical modeling approaches that pr eserve the integrity of the stratified design while offering a middle groun d between traditional stratified and unstratified analyses. We investigate both fully parametric (Weibull) and semiparametric models, the latter based not on the Cox model but on an extension of an idea by Gelfand and Mallick (1995, Biometrics 51, 843-852), which models the integrated baseline hazar d as a mixture of monotone functions. We illustrate the methods using data from a recent multicenter AIDS clinical trial, comparing their ease of use, interpretation, and degree of robustness with respect to estimates of both the unit-specific baseline hazards and the treatment effect.