Accounting for unreported and missing intercourse in human fertility studies
In prospective studies of human fertility that attempt to identify days of ovulation, couples record each day whether they had intercourse. Depending on the design of the study, couples either (I) mark the dates of intercourse on a chart or (II) mark 'yes' or 'no' for each day of the menstrual cycle. If protocol I is used, intercourse dates that couples fail to record are indistinguishable from dates of no intercourse. Consequently, estimates of day-specific fecundability are biased upwards. If protocol II is used, data from menstrual cycles with missing intercourse information must be discarded in order to fit current fertility models. We propose methods to account for unreported and missing intercourse under the assumption that the missingness mechanism is independent of time conditional on the unobservable true intercourse status. We use probit mixture models to allow for heterogeneity among couples, both in fecundability and in the missingness and non-reporting mechanisms. Markov chain Monte Carlo (MCMC) techniques are used for Bayesian estimation. The methods are generally applicable to the analysis of aggregated Bernoulli outcomes when there is uncertainty in whether a given trial, out of a series of trials, was completed. We illustrate the methods by application to two prospective fertility studies.
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