Modelling the type and timing of consecutive events: application to predicting preterm birth in repeated pregnancies

Summary Predicting the occurrence and timing of adverse pregnancy events such as preterm birth is an important analytical challenge in obstetrical practice. Developing statistical approaches that can be used to assess the risk and timing of these adverse events will provide clinicians with tools for individualized risk assessment that account for a woman's prior pregnancy history. Often adverse pregnancy outcomes are subject to competing events; for example, interest may focus on the occurrence of pre‐eclampsia‐related preterm birth, where preterm birth for other reasons may serve as a competing event. We propose modelling the type and timing of adverse outcomes in repeated pregnancies. We formulate a joint model, where types of adverse outcomes across repeated pregnancies are modelled by using a polychotomous logistic regression model with random effects, and gestational ages at delivery are modelled conditionally on the types of adverse outcome. The correlation between gestational ages conditional on the adverse pregnancies is modelled by the semiparametric normal copula function. We present a two‐stage estimation method and develop the asymptotic theory for the estimators proposed. The model and estimation procedure proposed are applied to the National Institute of Child Health and Human Development consecutive pregnancies study data and evaluated by simulations.