A Bayesian multiple imputation method for handling longitudinal pesticide data with values below the limit of detection

Abstract

Environmental and biomedical research often produces data below the limit of detection (LOD), or left-censored data. Imputing explicit values for values < LOD in a multivariate setting, such as with longitudinal data, is difficult using a likelihood-based approach. A Bayesian multiple imputation (MI) method is introduced to handle left-censored multivariate data. A Gibbs sampler, which uses an iterative process, is employed to simulate the target multivariate distribution within a Bayesian framework. Following convergence, multiple plausible data sets are generated for analysis by standard statistical methods outside of a Bayesian framework. With explicit imputed values available variables can be analyzed as outcomes or predictors. We illustrate a practical application using longitudinal data from the Community Participatory Approach to Measuring Farmworker Pesticide Exposure (PACE3) study to evaluate the association between urinary acephate concentrations (indicating pesticide exposure) and self-reported potential pesticide poisoning symptoms. Additionally, a simulation study is used to evaluate the sampling property of the estimators for distributional parameters as well as regression coefficients estimated with the generalized estimating equation (GEE) approach. Results demonstrated that the Bayesian MI estimates performed well in most settings, and we recommend the use of this valid and feasible approach to analyze multivariate data with values < LOD.