Human exposure to persistent environmental pollutants often results in concentrations with a range of values below the laboratory detection limits. Growing evidence suggests that inadequate handling of concentrations below the limit of detection (LOD) may bias assessment of health effects in relation to environmental exposures. We seek to quantify such bias in models focusing on the day-specific probability of pregnancy during the fertile window and propose a model-based approach to reduce such bias. A multivariate skewed generalized t-distribution constrained by the LOD is assumed for the chemical concentrations, which realistically represents the underlying distribution. A latent variable-based framework is used to model fecundibility, which nonlinearly relates conception probability to chemical concentrations, daily intercourses, and other important covariates. The advantages of the proposed approach include the use of multiple chemical concentrations to aid the estimation of left censored chemical exposures, as well as the model-based feedback mechanism for fecundibility outcome to inform the estimations, and an adequate handling of model uncertainty through a joint modeling framework. A Markov chain Monte Carlo sampling algorithm is developed for implementing the Bayesian computations and the logarithm of pseudo-marginal likelihood measure is used for model choices. We conduct simulation studies to demonstrate the performance of the proposed approach and apply the framework to the Longitudinal Investigation of Fertility and the Environment study which evaluates the effects of exposures to environmental pollutants on the probability of pregnancy. We found that p,p'-DDT is negatively associated with the day-specific probability of pregnancy.
Keywords: Fecundity; Generalized t-distribution; Markov chain Monte Carlo; Menstrual cycle; Posterior distribution; Pregnancy.