This article deals with
correlating two variables that have values that fall below the known limit of
detection (LOD) of the measuring device; these values are known as non-detects
(NDs). We use simulation to compare several methods for estimating the
association between two such variables. The most commonly used method, simple
substitution, consists of replacing each ND with some representative value such
as LOD/2. Spearman’s correlation, in which all NDs are assumed to be tied at
some value just smaller than the LOD, is also used. We evaluate each method
under several scenarios, including small to moderate sample size, moderate to
large censoring proportions, extreme
imbalance in censoring proportions, and non-bivariate normal (BVN) data.
In this article, we focus on the coverage probability of 95% confidence
intervals obtained using each method. Confidence intervals using a maximum
likelihood approach based on the assumption of BVN data have acceptable
performance under most scenarios, even with non-BVN data. Intervals based on
Spearman’s coefficient also perform well under many conditions. The methods are
illustrated using real data taken from the biomarker literature.
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