A Multiple Imputation Approach for Estimating Rank Correlation With Left-Censored Data

Frequently the correlation between two different measures of viral load obtained from each of a sample of patients is assessed in HIV studies. Kendall’s tau and Spearman’s rank correlations are often used for this assessment instead of Pearson’s correlation coefficient as they are not affected by outliers and nonnormality. However, such viral load data may be subject to left censoring due to values below assay detection limits. In this situation the usual estimators for the rank correlations (based on assigning ties to the values below the detection limits) may be severely biased. We propose a multiple imputation approach using a truncated bivariate normal model for imputation. Simulation results indicate that the imputation estimates are apparently unbiased for bivariate normally distributed data and still perform well if the data are misspecified.