10 A Review of Statistical Analyses for Competing Risks

Abstract

Abstract This paper reviews the statistical analyses of competing risks data. There is an extensive history of this topic; however, the literature is often confusing partially because it evolved over time. The available data for competing risks is in the form of time until event occurrence where T is the time from some suitable starting point until some cause of failure for each individual who fails, and δi is an indicator variable equal to 1 if failure is due to the ith cause, 0 otherwise. In the latent failure time approach, one assumes that there are k potential failure times, X1, X2, …, Xk, associated with each risk. T is then the min (X1, X2, …, Xk) and δi is an indicator variable equal to 1 if failure is due to the ith cause, 0 otherwise. References for the latent failure time model prior to the 1970s may be found in David and Moeschberger (1978), and more recently in Klein and Moeschberger (2003). The direction of the statistical analyses of competing risks studies changed dramatically after the identifiability problem for marginal distributions of the latent failure time model was pointed out by Tsiatis (1975), Prentice et al. (1978), and many others. At that time, interest centered on estimating identifiable competing risk probabilities. Most of the references cited in this paper deal with the more recent attempts to analyze competing risks data.