A NUMERICAL STUDY ON BOOTSTRAP CONFIDENCE INTERVALS OF REGRESSION COEFFICIENTS IN THE COX MODEL FOR COMPETING RISKS WITH MISSING FAILURE TYPES(Theory and Applications)

The Cox regression model is often used to evaluate effects of covariates on failure time distributions for competing risks survival data. We consider a situation where failure times are observed but failure types cannot be observed for some individuals, assuming that the probability of missing the type of a failure is identical for all failure types. Hemmi (1995) has proposed a maximum pseudo-partial likelihood estimator (MPPLE) of regression coefficients in the Cox model in order to improve the maximum partial likelihood estimator (MPLE). The MPPLE has consistency, but its distribution, which is required for interval estimation, has not analytically been obtained so far. This paper applies bootstrap methods such as the percentile and BCa methods to construct confidence intervals for the regression coefficients based on the MPPLE, and evaluates them numerically in terms of coverage probability and interval length. Simulation studies show that the bootstrap methods enable us to construct appropriate confidence intervals, and that the bootstrap confidence intervals based on the MPPLE are shorter than the confidence intervals given by the normal approximation based on the MPLE.