Bayesian modeling of retrospective time-to-pregnancy data with digit preference bias

The study of factors affecting human fertility is an important problem affording interesting statistical and computational challenges. Analyses of human fertility rates must cope with extra variability in fecundability parameters as well as a host of covariates ranging from the obvious, such as coital frequency, to the subtle, like the smoking habits of the female's mother. In retrospective human fecundity studies, researchers ask couples the time required to conceive. This time-to-pregnancy data often exhibits digit preference bias, among other problems. We introduce computationally intensive models with sufficient flexibility to represent such bias and other causes yielding a similar lack of monotonicity in conception probabilities.