Estimating pregnancy outcome probabilities based on observational cohorts has to account for both left-truncation, because the time scale is gestational age, and for competing risks, because, for example, an induced abortion may be precluded by a spontaneous abortion. The applied aim of this work was to investigate the impact of statins on pregnancy outcomes using data from Teratology Information Services. Using the standard Aalen–Johansen estimator of the cumulative event probabilities suggested the medically unexpected finding that statin exposure decreased the probability of induced abortion and led to more live births. The reason was an early induced abortion in a very small risk set in the control group, leading to unstable estimation which propagated over the whole time span. We suggest a stabilized Aalen–Johansen estimator which discards contributions from overly small risk sets. The decision whether a risk set is considered overly small is controlled by tuning parameters which we choose using a cross-validated Brier Score. We show that the new estimator enjoys the same asymptotic properties as the original Aalen–Johansen estimator. Small sample properties are investigated in extensive simulations. We also discuss extensions to more general multistate models.
"Nonparametric estimation of pregnancy outcome probabilities." Ann. Appl. Stat. 11 (2) 840 - 867, June 2017. https://doi.org/10.1214/17-AOAS1020