Pitfalls inherent in retrospective time-to-event studies: the example of time to pregnancy

Retrospective studies of time from initiation of risk (for example, transfusion of HIV-infected blood) to the occurrence of an endpoint of interest are useful in epidemiology. One example is studies of time to pregnancy, which have evaluated exposures that may affect human fertility. One can reconstruct the non-contracepting interval required for each woman's most recent pregnancy and then treat the data as if the couples had been studied prospectively. As we illustrate, however, failure-time models can be dangerously misleading when there have been trends over calendar time in exposures under study. We propose an ad hoc method for evaluating possible effects on fertility despite this bias, by making use of external data on trends in the exposure over time. This approach applies a prospective model and generates an empirical p-value, based on comparing the data-based estimated exposure coefficient with its null distribution estimated by simulation. A second method maximizes a conditional likelihood, and we show that this is equivalent to logistically modelling the relative odds for the subject's exposure as related to the reported time she required to achieve pregnancy.