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.