Joint modeling of longitudinal binary data and time to an event: An application to human fecundity models

Time to pregnancy (TTP), the number of menstrual cycles needed to achieve pregnancy, is widely used as a measure of fecundability in epidemiologic studies. Until recently, these studies did not incorporate information on frequency and timing of intercourse with respect to the fertile days of the cycle. Dunson (2003) and Stanford and Dunson (2007) have shown that intercourse behavior can have a large impact on probability of conception. It is also known that intercourse behavior in couples varies greatly, as it is influenced by libido and other factors such as age and parity (Wilcox et al. 2004). We propose a joint model for intercourse behavior using association models for binary correlated data and a discrete survival model for TTP, incorporating unobserved libido via a latent variable. We use an EM algorithm approach for the estimation procedure. These methods are applied to the New York State Angler Cohort Prospective Pregnancy Study.