A Bayesian Parametric and Nonparametric Approach for the Imputation of Multivariate Left-Censored Data Due to Limit of Detection

Left-censored observations due to limits of detection and/or quantification are common in clinical and epidemiologic research when continuous predictors are assessed from human specimens. In these settings, values below a certain threshold are not detectable in laboratory analysis and are reported as missing in the dataset. Classical imputation approaches have mostly relied on imputing the same number for all non-detected samples, thus compromising the continuous nature of the censored variables and affecting their variability and potential inclusion in regression modeling. Continuous imputations have been presented, but generally focusing on a single variable at the time. It is common, moreover, for the same human specimen to be used for the quantification of several biomarkers or exposures simultaneously, thus resulting in a complex set of multivariate and possibly correlated left-censored observations. To the best of our knowledge, there is no established framework that flexibly accounts for the real-world complexity of these data. We propose a Bayesian multiple imputation (MI) approach that relies on the introduction of multivariate latent variables to handle multivariate left-censored data. We present a general framework, accommodating both a parametric approach, assuming multivariate normality of the data, and a nonparametric approach, modeling observations by means of a location Dirichlet process mixture of multivariate normal kernels. Both approaches are implemented through a Gibbs sampling scheme. The performances of our approach are investigated with a simulation study based on environmental exposures, and illustrated by analyzing a real dataset on cardiovascular biomarkers.