Multivariate parametric random effect regression models for fecundability studies

Delay until conception is generally described by a mixture of geometric dis tributions. Weinberg and Gladen (1986, Biometrics 42, 547-560) proposed a r egression generalization of the beta-geometric mixture model where covariat es effects were expressed in terms of contrasts of marginal hazards. Scheik e and Jensen (1997, Biometrics 53, 318-329) developed a frailty model for d iscrete event times data based on discrete-time analogues of Hougaard's res ults (1984, Biometrika 71, 75-83). This paper is on a generalization to a t hree-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 f rom a flexible family of random effect distributions. This makes it possibl e, in the context of medically assisted conception, to include data sources with multiple pregnancies (or attempts at pregnancy) per couple.