Correlation coefficient estimation involving a left censored laboratory assay variable

When assessing a correlation between two exposure or biological marker variables, one sometimes encounters the problem of indeterminate values for one of the variables due to an assay detection limit. In this event, investigators often report correlation coefficients computed after removing the pairs involving non-detectable values, or after substituting some small constant for those values. These ad hoc practices can lead to bias in both point and confidence interval estimates of the true correlation coefficient. To address this issue, we consider two parametric techniques for estimating the correlation in the presence of left censoring for one of the variables. The first is a maximum likelihood approach, and the second is an adaptation of multiple imputation motivated primarily by potential benefits in confidence interval coverage. Both of the estimators studied reduce to the standard Pearson's correlation coefficient in the event of no censoring, and hence are valid in cases where this measure would be appropriate for the complete data. We assess these approaches empirically and contrast them with ad hoc methods for estimating the correlation between cervicovaginal human immunodeficiency virus (HIV) viral load measurements and CD4+ lymphocyte counts from HIV positive women enrolled in a clinical trial conducted in Bangkok, Thailand.