Parametric and penalized generalized survival models

We describe generalized survival models, where g(S(t|z)), for link function g, survival S, time t, and covariates z, is modeled by a linear predictor in terms of covariate effects and smooth time effects. These models include proportional hazards and proportional odds models, and extend the parametric Royston-Parmar models. Estimation is described for both fully parametric linear predictors and combinations of penalized smoothers and parametric effects. The penalized smoothing parameters can be selected automatically using several information criteria. The link function may be selected based on prior assumptions or using an information criterion. We have implemented the models in R. All of the penalized smoothers from the mgcv package are available for smooth time effects and smooth covariate effects. The generalized survival models perform well in a simulation study, compared with some existing models. The estimation of smooth covariate effects and smooth time-dependent hazard or odds ratios is simplified, compared with many non-parametric models. Applying these models to three cancer survival datasets, we find that the proportional odds model is better than the proportional hazards model for two of the datasets.