Hierarchical models for the probabilities of conception.

Area of Science:

• Reproductive Health
• Biostatistics
• Epidemiology

Background:

• Interest in accurate conception probability models has grown over 30 years.
• Previous models by Barrett and Marshall (1969) and Schwartz et al. (1980) have been extended with covariates.
• Complex models pose challenges for frequentist methods, making Bayesian approaches via Markov chain Monte Carlo (MCMC) more feasible.

Purpose of the Study:

• To analyze conception probabilities using a Bayesian model incorporating protected intercourse.
• To assess the effects of water contaminants and hormones on fecundability using data from the California Women's Reproductive Health Study.
• To propose novel methods for modeling protected intercourse and applying Bayesian analysis with a unimodality assumption.

Main Methods:

• Developed a Bayesian model to analyze conception probabilities.
• Modeled the ratio of conception probabilities for protected versus unprotected intercourse.
• Employed Bayesian analysis with a unimodality assumption (conception probability increases before ovulation and decreases after).
• Utilized Gibbs sampling for Bayesian estimation and Markov chain Monte Carlo (MCMC) for computation.

Main Results:

• The Bayesian model successfully analyzed conception probabilities from the California Women's Reproductive Health Study.
• Evidence suggests that water contaminants and hormones (covariates) impact fecundability.
• The proposed modeling approach for protected intercourse was applied.

Conclusions:

• Bayesian methods, particularly with Gibbs sampling, are effective for analyzing complex reproductive health models.
• The study provides insights into factors affecting fecundability, including protected intercourse, water contaminants, and hormones.
• The unimodality assumption in Bayesian analysis aids in understanding conception probability patterns around ovulation.