Semiparametric analysis of a generalized linear model with multiple covariates subject to detection limits

Studies on the health effects of environmental mixtures face the challenge of limit of detection (LOD) in multiple correlated exposure measurements. Conventional approaches to deal with covariates subject to LOD, including complete-case analysis, substitution methods, and parametric modeling of covariate distribution, are feasible but may result in efficiency loss or bias. With a single covariate subject to LOD, a flexible semiparametric accelerated failure time (AFT) model to accommodate censored measurements has been proposed. We generalize this approach by considering a multivariate AFT model for the multiple correlated covariates subject to LOD and a generalized linear model for the outcome. A two-stage procedure based on semiparametric pseudo-likelihood is proposed for estimating the effects of these covariates on health outcome. Consistency and asymptotic normality of the estimators are derived for an arbitrary fixed dimension of covariates. Simulations studies demonstrate good large sample performance of the proposed methods vs conventional methods in realistic scenarios. We illustrate the practical utility of the proposed method with the LIFECODES birth cohort data, where we compare our approach to existing approaches in an analysis of multiple urinary trace metals in association with oxidative stress in pregnant women.