Dynamic model for multivariate markers of fecundability

Dynamic latent class models provide a flexible framework for studying biologic processes that evolve over time. Motivated by studies of markers of the fertile days of the menstrual cycle, we propose a discrete-time dynamic latent class framework, allowing change points to depend on time, fixed predictors, and random effects. Observed data consist of multivariate categorical indicators, which change dynamically in a flexible manner according to latent class status. Given the flexibility of the framework, which incorporates semi-parametric components using mixtures of betas, identifiability constraints are needed to define the latent classes. Such constraints are most appropriately based on the known biology of the process. The Bayesian method is developed particularly for analyzing mucus symptom data from a study of women using natural family planning.