Retrospective ascertainment of recurrent events: An application to time topregnancy

Retrospectively ascertained data are common in many areas, including demogr aphy, epidemiology, and actuarial science. The main objective of this artic le is to study the effect of retrospective ascertainment on inference regar ding recurrent events of time to pregnancy (TTP) data. For the particular T TP 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 even ts 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 cens ored. We furthermore consider two different approaches to modeling the depe ndencies of the recurrent events. A traditional frailty model, where the fr ailty enters the model as an unobserved covariate, and a marginal frailty m odel are applied. We find that efficiency is gained from including the seco nd TTPs, with the full model being the most efficient. Further, the margina l frailty model is preferred over the traditional frailty model because est imates of covariate effects are easier to interpret and are ore robust to c hanges in the frailty distribution.