Approaches for Assessing Effects of Exposures on Human Fertility

Fecundability (conception rate per menstrual cycle) varies among non-contracepting couples. Time-to-pregnancy studies can identify exposures contributing to that variability, using three designs: incident cohort, prevalent cohort, and retrospective. Typically, researchers then apply semi-parametric, generalized linear time-to-pregnancy models to data, with either a log or a logit "link," to estimate either a fecundability ratio (FR) or a fecundability odds ratio (FOR). The ongoing-attempt study design can also be informative.

We consider a different generalized linear model, based on an inverse link. It models the heterogeneity as beta distributed and enables estimation of both the FR and FOR, defined based on population mean fecundabilities, without requiring constancy across attempt time. Under an ongoing-attempt design, the parameter associated with a dichotomous exposure has no clear meaning with a log or a logit link, but under the proposed approach estimates the ratio of the two average times to pregnancy. Basing simulations on conception rates from a large study, we compare the three analytic approaches for confidence interval coverage and power. We also assess the performance of a commonly used method for verifying the constancy of FOR or FR across time.

The inverse-link approach had slightly less power than the others, but its estimates maintained nominal confidence interval coverage under nonconstancy. A popular method for testing constancy across time for the FR and FOR had poor power.

The inverse-link analysis offers a useful alternative to the usual methods, with estimation performance that generalizes to the ongoing-attempt design and does not require hard-to-verify constancy assumptions.