Abstract
Hazard models that link covariates to hazard function of survival distribution are roughly classified into multiplicative and additive ones. The well-known proportional hazard model used widely in survival study, is a specia1 one of the multiplicative models. In this paper, we examine the adequacy to evaluate the effect of covariates on survival time by means of the multip1icative models (or especia11y, the proportional hazard model), based on the fitting of a comprehensive model, i.e. data adaptive hazard model, which includes additive and multip1icative models as special cases. Further, we examine the goodness of fit of a model, i.e. genera1ized additive proportional hazard model which extends linear predictor into additive one, in order to diagnose the adequacy of the proportional hazard model within the frame of the multiplicative models. Comparing the results from the fittings of the generalized additive and the proportional hazard models, we evaluate the adequacy to express the effect of covariates on survival by the proportional hazard model uti11zing a few practical examples. As a result, it is seen that the data adaptive model is useful to diagnose the goodness of fit of the multip1icative models, especially the proportional hazard model. It is also seen that the fitting of the generalized additive proportional hazard mode1 is useful to examine "linearity" assumption in the proportional hazard model
