Journal
BAYESIAN ANALYSIS
Volume 7, Issue 4, Pages 771-799Publisher
INT SOC BAYESIAN ANALYSIS
DOI: 10.1214/12-BA726
Keywords
Conception; Fecundity; Generalized t-distribution; Generalized nonlinear model; Markov chain Monte Carlo; Menstrual Cycle; Posterior distribution
Funding
- National Institutes of Health, Eunice Kennedy Shriver National Institute of Child Health and Human Development
- U.K. National Health Service Executive Primary Care Career Scientist and Service Research and Development Awards
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Human fecundity is an issue of considerable interest for both epidemiological and clinical audiences, and is dependent upon a couple's biologic capacity for reproduction coupled with behaviors that place a couple at risk for pregnancy. Bayesian hierarchical models have been proposed to better model the conception probabilities by accounting for the acts of intercourse around the day of ovulation, i.e., during the fertile window. These models can be viewed in the framework of a generalized nonlinear model with an exponential link. However, a fixed choice of link function may not always provide the best fit, leading to potentially biased estimates for probability of conception. Motivated by this, we propose a general class of models for fecundity by relaxing the choice of the link function under the generalized nonlinear model framework. We use a sample from the Oxford Conception Study (OCS) to illustrate the utility and fit of this general class of models for estimating human conception. Our findings reinforce the need for attention to be paid to the choice of link function in modeling conception, as it may bias the estimation of conception probabilities. Various properties of the proposed models are examined and a Markov chain Monte Carlo sampling algorithm was developed for implementing the Bayesian computations. The deviance information criterion measure and logarithm of pseudo marginal likelihood are used for guiding the choice of links. The supplemental material section contains technical details of the proof of the theorem stated in the paper, and contains further simulation results and analysis.
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