A joint mixed effects dispersion model for menstrual cycle length and time-to-pregnancy

Menstrual cycle patterns are often used as indicators of female fecundity and are associated with hormonally dependent diseases such as breast cancer. A question of considerable interest is in identifying menstrual cycle patterns, and their association with fecundity. A source of data for addressing this question is prospective pregnancy studies that collect detailed information on reproductive aged women. However, methodological challenges exist in ascertaining the association between these two processes as the number of longitudinally measured menstrual cycles is relatively small and informatively censored by time to pregnancy (TTP), as well as the cycle length distribution being highly skewed. We propose a joint modeling approach with a mixed effects dispersion model for the menstrual cycle lengths and a discrete survival model for TTP to address this question. This allows us to assess the effect of important characteristics of menstrual cycle that are associated with fecundity. We are also able to assess the effect of fecundity predictors such as age at menarche, age, and parity on both these processes. An advantage of the proposed approach is the prediction of the TTP, thus allowing us to study the efficacy of menstrual cycle characteristics in predicting fecundity. We analyze two prospective pregnancy studies to illustrate our proposed method by building a model based on the Oxford Conception Study, and predicting for the New York State Angler Cohort Prospective Pregnancy Study. Our analysis has relevant findings for assessing fecundity.