Marginal and conditional approaches to multivariate variables subject to limit of detection

A marginal approach and a variance-component mixed effect model approach (here called a conditional approach) are commonly used to analyze variables that are subject to limit of detection. We examine the theoretical relationship and investigate the numerical performance of these two approaches. We make some recommendations based on our results. The marginal approach is recommended for bivariate normal variables, and the variance-component mixed effect model is preferable for other multivariate analysis in most circumstances. Two approaches are illustrated through one case study from a preclinical experiment.