The Fitting of Exponential, Weibull and Extreme Value Distributions to Complex Censored Survival Data Using GLIM

Abstract

SUMMARY Regression models may be fitted to censored survival data by the use of exponential, Weibull and extreme value distributions in GLIM. Standard probability plotting procedures for uncensored data may be modified to allow for censoring. A simultaneous test procedure may be used to determine a minimal adequate regression model. The procedure is briefly illustrated on two sets of published cancer survival data. A RECENT paper by Kay (1977) surveys methods for the analysis of censored survival data. Kay considers the fitting of exponential and Weibull models, and Cox's distribution-free model, the assessment of the form of the survival distribution through residual plots, and the determination of relevant variables in the regression of the hazard function on explanatory variables. The purpose of the present paper is to describe the use of GLIM (Baker and Nelder, 1978) to fit exponential, Weibull or extreme value distributions, by expressing the likelihood in each case as a Poisson likelihood, with a log-linear model for the Poisson mean corresponding to the log- linear model for the hazard function. A simultaneous test procedure developed for complex cross-classifications may be applied to the reduction of the complex regression model to a parsimonious form. The procedure is illustrated on two-sample data published by Gehan (1965), and on complex data published by Prentice (1973).