Retrospective ascertainment of recurrent events: An application to time to pregnancy

Retrospectively ascertained data are common in many areas, including demography, epidemiology, and actuarial science. The main objective of this article is to study the effect of retrospective ascertainment on inference regarding recurrent events of time to pregnancy (TTP) data. For the particular TTP dataset that we consider, couples are included retrospectively based on their first pregnancy and then followed prospectively to a second pregnancy or to end of study. We consider a conditional model for the recurrent events data where the second TTP is included only if it is observed and a full model where the nonobserved second TTPs are included as suitably right censored. We furthermore consider two different approaches to modeling the dependencies of the recurrent events. A traditional frailty model, where the frailty enters the model as an unobserved covariate, and a marginal frailty model are applied. We find that efficiency is gained from including the second TTPs, with the full model being the most efficient. Further, the marginal frailty model is preferred over the traditional frailty model because estimates of covariate effects are easier to interpret and are ore robust to changes in the frailty distribution.