Flexible modelling of discrete failure time including time-varying smooth effects

Discrete survival models have been extended in several ways. More flexible models are obtained by including time-varying coefficients and covariates which determine the hazard rate in an additive but not further specified form. In this paper, a general model is considered which comprises both types of covariate effects. An additional extension is the incorporation of smooth interaction between time and covariates. Thus, in the linear predictor smooth effects of covariates which may vary across time are allowed. It is shown how simple duration models produce artefacts which may be avoided by flexible models. For the general model which includes parametric terms, time-varying coefficients in parametric terms and time-varying smooth effects estimation procedures are derived which are based on the regularized expansion of smooth effects in basis functions. The approach is used to model the sojourn time in a psychiatric hospital. It is demonstrated how initial conditions which have non-linear influence are damped over time.