Bayesian Change Point Models and Missing Data Analysis for Menstrual Diary Data at the Approach of Menopause

As women approach menopause, the patterns of their menstruation segment lengths change. In order to study when changes in menstrual length happen, we use Bayesian change point models to jointly model both the mean variability of the segment length. The model incorporates separate mean and variance change points for each woman and a hierarchical model to link them together, along with regression components to include predictors of menopausal onset such as age at menarche and parity. Data are from TREMIN, an ongoing 70-year old longitudinal study that has obtained menstrual calendar data of women throughout their life course. Our study cohort includes nearly 1000 women, many of whom have missingness due to hormone use, surgery, random missingness and loss of contact. We integrate multiple imputation in our Bayesian estimation procedure to deal with different forms of the missingness. Posterior predictive model checks are applied to evaluate the model fit.