Heterogeneity in fecundability studies: issues and modelling

Modelization of fecundability stepped recently from demography and population-based contexts to reproductive biology and treatment of infertility. This created a strong call for flexibility and robustness. Indeed, explained and unexplained heterogeneities are non-negligible sources of bias that result in false conclusions as to the determinants of fertility or to the success rates of reproductive techniques, among other examples. There are two main sources of heterogeneity: biological heterogeneity and heterogeneity of sexual behaviour. A uniform presentation of time-to-pregnancy and Barrett-Marshall models is proposed to enlighten their similarities and differences in modelling heterogeneity of fecundability. Mixed models for fecundability studies are presented as tools to allow for unexplained heterogeneity and to quantify heterogeneity of the effect of observed factors and variability of size of this unexplained heterogeneity between subpopulations. Some criteria for the modelling strategy in fecundability studies are suggested with emphasis on the unit-treatment additivity criterion. The strong and complex selection process resulting from heterogeneity is described as well as the selection and cross-selection processes of observed and unobserved fecundability factors. Consequences regarding data collection and statistical inference are discussed. In the current context, a consensus setting general rules for data collection and statistical analysis would be useful to compare the results and increase the reliability of these results in medical practice.