Estimating and modelling cumulative incidence functions using time-dependent weights

Competing risks occur in survival analysis when a subject is at risk of more than one type of event. A classic example is when there is consideration of different causes of death. Interest may lie in the cause-specific hazard rates, which can be estimated using standard survival techniques by censoring competing events. An alternative measure is the cumulative incidence function (CIF) which gives an estimate of absolute or crude risk of death accounting for the possibility that individuals may die of other causes. Geskus (2011 Biometrics, 67: 39–49) has recently proposed an alternative way for the estimation and modeling of the CIF that can use weighted versions of standard estimators. I will describe a Stata command, stcrprep, that restructures survival data and calculates weights based on the censoring distribution. The command is based on the R command crprep, but I will describe a number of extensions that enable the CIF to be modeled directly using parametric models on large datasets. After restructuring the data and incorporating the weights, one can use sts graph to plot the CIF and stcox can be used to fit a Fine and Gray model for the CIF. An advantage of fitting models in this way is that it is possible to use a number of the standard features of the Cox model, for example, using Schoenfeld residuals to visualize and test the proportional subhazards assumption. I will also describe some additional options that are useful for fitting parametric models and useful for large datasets. In particular, I will describe how the flexible parametric survival models estimated with stpm2 can be used to directly model the cumulative-incidence function. An important advantage is that all the predictions built into stpm2 can be used to directly predict the CIF, subdistribution hazards, etc.