Both delayed study entry (left‐truncation) and competing risks are common phenomena in observational time‐to‐event studies. For example, in studies conducted by Teratology Information Services (TIS) on adverse drug reactions during pregnancy, the natural time scale is gestational age, but women enter the study after time origin and upon contact with the service. Competing risks are present, because an elective termination may be precluded by a spontaneous abortion. If left‐truncation is entirely random, the Aalen‐Johansen estimator is the canonical estimator of the cumulative incidence functions of the competing events. If the assumption of random left‐truncation is in doubt, we propose a new semiparametric estimator of the cumulative incidence function. The dependence between entry time and time‐to‐event is modeled using a cause‐specific Cox proportional hazards model and the marginal (unconditional) estimates are derived via inverse probability weighting arguments. We apply the new estimator to data about coumarin usage during pregnancy. Here, the concern is that the cause‐specific hazard of experiencing an induced abortion may depend on the time when seeking advice by a TIS, which also is the time of left‐truncation or study entry. While the aims of counseling by a TIS are to reduce the rate of elective terminations based on irrational overestimation of drug risks and to lead to better and safer medical treatment of maternal disease, it is conceivable that women considering an induced abortion are more likely to seek counseling. The new estimator is also evaluated in extensive simulation studies and found preferable compared to the Aalen‐Johansen estimator in non–misspecified scenarios and to at least provide for a sensitivity analysis otherwise.