Assessing the agreement of biomarker data in the presence of left-censoring

In many clinical biomarker studies, Lin's concordance correlation coefficient (CCC) is commonly used to assess the level of agreement of a biomarker measured under two different conditions. However, measurement of a specific biomarker typically cannot provide accurate numerical values below the lower limit of detection (LLD) of the assay, which results in left-censored data. Most researchers discard the data below the LLD or apply simple data imputation methods in the presence of left-censored data, such as replacing values below the LLD with a fixed number less than or equal to the LLD. This is not statistically optimal, because it often leads to biased estimates and overestimates the precision.

We describe a simple method using a bivariate normal distribution in this situation and apply SAS statistical software to arrive at the maximum likelihood (ML) estimate of the parameters and construct the estimate of the CCC. We conduct a computer simulation study to investigate the statistical properties of the ML method versus the data deletion and simple data imputation method. We also contrast the methods with real data using two urine biomarkers, Interleukin 18 and Cystatin C.

The computer simulation studies confirm that the ML procedure is superior to the data deletion and simple data imputation procedures. In all of the simulated scenarios, the ML method yields the smallest relative bias and the highest percentage of the 95% confidence intervals that include the true value of the CCC. In the first simulation scenario (sample size of 100 paired data points, 25% left-censoring for both members of the pair, true CCC of 0.238), the relative bias is -1.43% for the ML method, -40.97% for the data deletion method, and it ranges between -12.94% and -21.72% for the simple data imputation methods. Similarly, when the left-censoring for one of the members of the data pairs increases from 25% to 40%, the relative bias displays the same pattern for all methods.

When estimating the CCC from paired biomarker data in the presence of left-censored values, the ML method works better than data deletion and simple data imputation methods.