Interpreting two test results of one analyte from the same individual using bivariate reference values

Often a measurement of an analyte is repeated in the same patient. Then the physician must interpret a pair of test results of the same analyte (x1, x2), measured in specimens collected hours to weeks apart. Physicians compare both test results against the univariate reference limits (RLs) and perhaps the difference x2 - x1 against reference change values (RCVs). We believe that it would be rational to compare a specific pair of (x1, x2) values against percentiles in the bivariate distribution of (x1, x2) from reference individuals. That has never been done, so we simulated (x1, x2) reference values using data on RLs, intraindividual biological variation in healthy individuals, and analytical variation. The bivariate percentiles corresponding to (x1, x2) observations were estimated from the Mahalanobis distances (MDs) in the bivariate distribution of (x1, x2) reference values. With a very few exceptions, the combination of 95% RLs and 95% RCVs did not enclose any (x1, x2) reference value with a bivariate percentile above 95. However, the combination enclosed only 92-93% of the (x1, x2) reference values below the bivariate 95 percentile. In conclusion, bivariate percentiles in the distribution of (x1, x2) reference values from a healthy reference population can be derived from available data, and used for reporting and interpreting the finding of a specific (x1, x2) observation in a patient.