A Comparison of Methods for Correlating Two Variables in the Presence of Nondetects

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Stephen Looney* and Courtney E. McCracken
• Companies: Georgia Regents University and Emory University
• Keywords: limit of detection ; Pearson correlation ; Spearman correlation ; Kendall coefficient ; substitution methods ; maximum likelihood estimation

Abstract

This presentation 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 smaller than the LOD, has also been 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. The methods are compared in terms of estimation bias, median absolute deviation, 95% confidence interval width, etc., but our primary focus is on coverage probability. A maximum likelihood approach based on the assumption of BVN data has acceptable performance under most scenarios, even with non-BVN data. Spearman's rho also performs well under many conditions. The methods are illustrated using real data taken from the biomarker literature.