The purpose of this paper is to review methods to be applied for analyses of categorized surbibal data on the theoretical basis of the log0linear models and compare log-linear models with Cox´s models.
The theoretical basis which log-linear models can apply to the categorical survival data relys on the two simple relationships; (1) when there exist a piecewise-exponential survival distrbution and categorical covariates, log-linear models foe the cell means of contigency tables with poisson data are equivalent to log-linear hazard models for survival data, and (2) the likeligoods for these two cases are also equivalent. Owing to these relationships, we can concisely express maximum likelihood estimates and significance testing of parameters of log-linear survival models.
An example reasing Veteran Lung Cancer data of Prentice (1973) is given to comparison of cox´s model with log-linear models. Consequently, when we assume that the time axis can be partitioned into mutually exclusive, exhaustive intervals, log-linear survival models are more appropriate than Cox´s model in order to find the effects of covariates, and reduce the informations of survival times.
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