A comparison of categorical models for right-censored data.

Abstract

The purpose of this research was to assess the performance of dichotomous response regression models for right-censored data in various settings. Discrete models have the advantage over the usual parametric models that almost any particular distribution can be approximated quite well. Although a separate parameter for each discrete interval is usually recommended, fitting the hazard function using polynomials may increase efficiency when hazard function estimation is of interest. An extensive simulation study was performed to investigate the performance of discrete regression models in both proportional hazards (p.h.) and non-p.h. settings. Factors investigated include logistic vs. log vs. complementary log(-log) (cloglog) regression, discretizing time using equal length intervals vs. equal numbers of events per interval, modeling the discrete hazard function with indicator variables vs. polynomial functions of time or log(time), and others. Estimators for discrete models were compared with those for the Cox model (continuous and discrete) and also the correct parametric model. In general, fixed event intervals and small width intervals worked best. For p.h., cloglog is the best link function, and polynomial functions of time or log(time) provided excellent approximations to the true hazard functions. For non-p.h., covariate-time interactions provided good estimators of risk ratios and conditional hazard functions with large sample sizes, but such complex models performed poorly with small sample sizes. No link function was uniformly better in all situations.