Inclusion of time-varying covariates in cure survival models with an application in fertility studies

Cure survival models are used when we desire to acknowledge explicitly that an unknown proportion of the population studied will never experience the event of interest. An extension of the promotion time cure model enabling the inclusion of time-varying covariates as regressors when modelling (simultaneously) the probability and the timing of the monitored event is presented. Our proposal enables us to handle non-monotone population hazard functions without a specific parametric assumption on the baseline hazard. This extension is motivated by and illustrated on data from the German Socio-Economic Panel by studying the transition to second and third births in West Germany.