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Nonparametric double additive cure survival models: An application to the estimation of the non-linear effect of age at first parenthood on fertility progression

Abstract This article introduces double additive models to describe the effect of continuous covariates in cure survival models, thereby relaxing the traditional linearity assumption in the two regression parts. This class of models extends the classical event history models when an unknown proportion of the population under study will never experience the event of interest. They are used on data from the German Socio-Economic Panel (GSOEP) to examine how age at first birth relates to the timing and quantum of fertility for given education levels of the respondents. It is shown that the conditional probability of having further children decreases with the mother's age at first birth. While the effect of age at first birth in the third birth's probability model is fairly linear, this is not the case for the second child with an accelerating decline detected for women that had their first kid beyond age 30.