Modelling digit preference in fecundability studies

Retrospective studies of fecundability, in which women are asked how many cycles they required to become pregnant, are often affected by problems of digit preference. A probability model for such digit preference is proposed in which misreporting favours 6 or 12 (and possibly also 3) cycles. It is assumed that in the absence of misreporting the number of cycles follows a beta-geometric distribution. The model is applied to two data sets, with clear-cut results: The inclusion of additional parameters to model the misreporting can lead to substantial improvements in fit, but causes little change to the estimated parameters of the underlying beta-geometric distribution. In some cases misreporting parameters may be regarded as nuisance parameters, while in others they may be of interest. We have found estimates of these parameters to vary between different categories of women in an interpretable manner. The models may also be used to estimate the percentage of couples in any study that misreport their conception waiting time.