Methods for Comparing Correlations Involving Left-Censored Laboratory Data

1. Introduction In biomedical research, left-censored laboratory data is common. In infectious disease studies, for example, assays for quantification of viral concentration, e.g. human immunodeficiency virus type 1 (HIV-1), hepatitis C (HCV), cytomegalovirus, or human papilloma virus, are subject to lower limits of detection and quantification. Over the past several years, it has become increasingly recognized that using standard analysis methods for this type of data without accounting for censoring will result in biased parameter estimates [1]. While methods for the analysis of data with censoring limits incorporated as part of the model, with multiple imputation, or with inflated zero values have been available for a number of years, methods that adapt these techniques for censored laboratory data have only recently been described [1-3]. The particular problem of interest in this manuscript is the estimation of the correlation between variables subject to left-censoring. In the context of infectious disease studies, this correlation might reflect the association of the concentrations of different viral infections, e.g. HIV-1 and HCV, or might reflect the degree that viral levels in different body compartments are correlated, e.g. HIV-1 RNA levels in plasma, saliva, or cervical-vaginal lavage fluid (CVL). Furthermore, it might be of interest to see if the correlation between different subgroups is the same. For example, we might want to evaluate whether some individuals are able to control multiple viral infections differently, or show discordance in the association between compartments. Recent papers have described methods for incorporating censoring in this context. Lynn [2] and Lyles et al [4] described how the likelihood