Effect of uncertainty in calibration on the correlation structure of the rheumatoid factor immunoassay calibration function

Clinical laboratory measurements are vital to the medical decision-making process, and specifically, measurement of rheumatoid factor antibodies is part of the disease criteria for various autoimmune conditions. Uncertainty estimates describe the quality of the measurement process, and uncertainty in calibration of the instrument used in the measurement can be an important contributor to the net measurement uncertainty. In this paper, we develop a physics-based mathematical model of the rheumatoid factor measurement process, or assay, and then use the Monte Carlo method to investigate the effect of uncertainty in the calibration process on the correlation structure of the parameters of the calibration function. We demonstrate numerically that a change in uncertainty of the calibration process can be quantified by one of two metrics: (1) the 1-norm condition number of the correlation matrix, or (2) the sum of the absolute values of the correlation coefficients between the parameters of the calibration function.