A nonparametric multiplicative hazard model for event history analysis

A major issue in exploring and analysing complex life history data with multiple states and recurrent events is the development and availability of flexible models and methods that allow the exploration of unknown dynamics of underlying transition intensities, the modelling and estimation of nonlinear functional forms of covariates and time-varying effects, the inclusion of time-dependent covariates and the handling of multivariate time scales. In this paper we propose and develop a nonparametric multiplicative hazard model that takes into account these requirements. Embedded in the counting process framework, estimation is based on penalised likelihoods and splines. We illustrate our approach by an application to sleep-electroencephalography data with multiple recurrent states of human sleep.