Multivariate parametric random effect regression models for fecundability studies

Delay until conception is generally described by a mixture of geometric distributions. Weinberg and Gladen (1986, Biometrics 42, 547-560) proposed a regression generalization of the beta-geometric mixture model where covariates effects were expressed in terms of contrasts of marginal hazards. Scheike and Jensen (1997, Biometrics 53, 318-329) developed a frailty model for discrete event times data based on discrete-time analogues of Hougaard's results (1984, Biometrika 71, 75-83). This paper is on a generalization to a three-parameter family distribution and an extension to multivariate cases. The model allows the introduction of explanatory variables, including time-dependent variables at the subject-specific level, together with a choice from a flexible family of random effect distributions. This makes it possible, in the context of medically assisted conception, to include data sources with multiple pregnancies (or attempts at pregnancy) per couple.