Software for fitting nonstandard proportional subdistribution hazards models.

Fine and Gray (1999) suggested a Cox model for the subdistribution hazard, which is the hazard attached to the cumulative incidence function of interest in a competing risks setting. They also noted that standard Cox software may be used to fit the model provided that the potential censoring times are known for individuals observed to experience a competing event (‘censoring complete data’) and that otherwise an inverse probability of censoring weighting method can be used. Beyersmann and Schumacher (2008) extended the methods of Fine and Gray (1999) to allow for random time-dependent covariates. Shortly after the paper by Beyersmann and Schumacher, Ruan and Gray (2008) suggested a multiple imputation approach for fitting a subdistribution hazards model. The aim of the imputation is to recover the potential censoring times for individuals with an observed competing event. Then standard Cox software may again be used for the analysis, which allows for including time-dependent covariates. We note that the MI approach also allows the fitting of stratified models and frailty models using standard software. We have written an R-package kmi that both implements the multiple imputation procedure and contains a random sample of the censoring complete data used by Beyersmann and Schumacher. The package can be downloaded from the Comprehensive R Archive Network at http://cran.r-project.org. Table 1 reports the analyses either using multiple imputation, with 10 multiple imputations, or using the original censoring complete information for both the random subsample and the whole data set.