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This paper uses a non-parametric test, based on consistently estimated discrimination accuracy defined as concordance probability between quantitative predictor and outcome, to compare paired biomarkers in predicting a health outcome, possibly subject to random censoring. Comparing with the Wilcoxon test for paired predictors based on Harrell's C-index, we found that the proposed test is better in presence of random censoring, although the two unbiased tests are equivalent for outcome either uncensored or censored by a constant. A simulation study also demonstrates that the bias in estimated difference in concordance probability, due to ignoring random censoring, results in overestimated power, especially when random censoring is heavy. The method was applied in two studies, where the biomarkers measured from the same study subjects are correlated. The first study on 299 school children in Bangladesh found the associations that higher blood arsenic and manganese were related to lower intellectual test scores, while the differences between the biomarkers in predicting the intellectual test scores were not statistically significant. The second study on 418 patients with primary biliary cirrhosis found that the baseline serum bilirubin had greater discrimination accuracy than the baseline serum albumin in predicting survival time.

Comparing paired biomarkers in predicting quantitative health outcome subject to random censoring