Wei, Lin and Weissfeld's marginal analysis of multivariate failure time data

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Abstract
Wei, Lin and Weissfeld (WLW) have applied an elaboration of Cox's proportional hazards regression to the analysis of recurrent events data. This application is controversial and has attracted criticism in a piecemeal fashion over 15 years. A frequently raised concern is the method's `risk set': each individual is considered to be at risk of all recurrent events from the start of the observation period. The WLW method often gives estimates that exceed those provided by alternative approaches. This paper investigates whether the estimates are a consequence of biased estimation, or reflect a particular aspect of the treatment effect. Simulation studies show that the WLW method infringes the proportional hazards assumption when applied to recurrent events data, but that the bias this may cause is not behind the distinctive effect estimates. Instead, the method's risk set is demonstrated to be responsible, leading to discussion of the interpretation of the treatment effect being estimated. Analyses of medical data indicate that the infringement of the proportional hazards assumption is not necessarily greater than that experienced with other applications of proportional hazards regression and need not prohibit the application of WLW's method to recurrent events data.