Correlating two viral load assays with known detection limits

A timely objective common to many HIV studies involves assessing the correlation between two different measures of viral load obtained from each of a sample of patients. This correlation has scientific utility in a number of contexts, including those aimed at a comparison of competing assays for quantifying virus and those aimed at determining the level of association between viral loads in two different reservoirs using the same assay. A complication for the analyst seeking valid point and interval estimates of such a correlation is the fact that both variables may be subject to left censoring due to values below assay detection limits. We address this problem using a bivariate normal likelihood that accounts for left censoring of two variables that may have different detection limits. We provide simulation results to evaluate sampling properties of the resulting correlation estimator and compare it with ad hoc estimators in the presence of nondetects. In an effort to obtain improved confidence interval properties relative to the Wald approach, we evaluate and compare profile likelihood-based intervals. We apply the methods to HIV viral load data on women and infants from a trial in Bangkok, Thailand, and we discuss an extension of the original model to accommodate interval censoring arising due to the study design.