Log-linear analysis of censored survival data with partially observed covariates

Abstract Log-linear models provide a flexible means of extending life table techniques for the analysis of censored survival data with categorical covariates, as discussed by Holford (1980) and Laird and Olivier (1981). We extend this methodology to incorporate cases in which one or more of the categorical covariates are sometimes missing. Maximum likelihood estimates of the parameters are calculated using data from all cases. This can result in large gains in efficiency over standard methods that require the exclusion of cases with incomplete data. With this approach, we assume that the hazard function, conditional on the covariates, is a stepwise function over disjoint intervals of time. The model has two parts: a log-linear model describing the hazard parameters, and a multinomial model describing the probabilities in the contingency table defined by the covariates. The main interest is in the model for the hazard parameters. We show how to calculate maximum likelihood estimates of parameters of the mo...

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