Stabilizing cumulative incidence estimation of pregnancy outcome with delayed entries

A pregnancy may end up with (at least) three possible events: live birth, spontaneous abortion, or elective termination, yielding a competing risks issue when studying an association between a risk factor and a pregnancy outcome. Cumulative incidences (probabilities to end up with the different outcomes depending on gestational age) can be estimated via the Aalen-Johansen estimate. Another issue is that women are usually not entering such an observational study from the first day of pregnancy, resulting in delayed entries. As in traditional survival analysis, this can be solved by considering "at risk" at a given gestational age only for those women who entered the study before that age. However, the number of women at risk at an early gestational age might be extremely low, such that the estimates of cumulative incidence may increase exaggeratedly at that age because of a single event. One solution to reduce the problem has been recently proposed in the literature, which is to ignore simply those early events, creating a small mean bias but enhancing stability of estimates. In the present paper, we propose an alternative computationally simple approach to tackle this problem that consists to postpone to later gestational ages (rather than to ignore) those early events. The two approaches are compared with respect to bias, stability, and sensitivity on the smoothing parameter via simulations reproducing realistic pregnancy scenarios, and are illustrated with data from a study on the effects of statins on pregnancy outcomes. We also outline that all three approaches are asymptotically equivalent.