Time-to-event analysis of preterm birth accounting for gestational age uncertainties

A time-to-event analysis is advocated for examining associations between time-varying environmental exposures and preterm birth in cohort studies. While the identification of preterm birth entirely depends on gestational age, the true gestational age is rarely known in practice. Obstetric estimate (OE) and gestational age based on the date of last menstrual period (LMP) are two commonly used measurements, but both suffer from various sources of error. Uncertainties in gestational age result in both outcome misclassification and measurement error of time-varying exposures, which can potentially introduce serious bias in health effect estimates. Motivated by the lack of validation data in large population-based studies, we develop a hierarchical Bayesian model that utilizes the two error-prone gestational age estimates to examine time-varying exposures on the risk of preterm birth while accounting for uncertainties in the estimates. The proposed approach introduces two discrete-time hazard models for the latent true gestational ages that are preterm (<37 weeks) or term (≥37 weeks). Then two multinomial models are adopted for characterizing misclassifications resulting from using OE-based and LMP-based gestational age. The proposed modeling framework permits the joint estimation of preterm birth risk factors and parameters characterizing gestational age misclassifications without validation data. We apply the proposed method to a birth cohort based on birth records from Kansas in 2010. Our analysis finds robust positive associations between exposure to ozone during the third trimester of pregnancy and preterm birth, even after accounting for gestational age uncertainty.