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.