Using the likelihood ratio to evaluate allowable total error – an example with glycated hemoglobin (HbA1c)

Abstract

Allowable total error is derived in many ways, often from data on biological variation in normal individuals. We present a new principle for evaluating allowable total error: What are the diagnostic consequences of allowable total errors in terms of errors in likelihood ratio (LR)? Glycated hemoglobin A1c in blood (HbA1c) in diagnosing diabetes mellitus is used as an example. Allowable total error for HbA1c is 3.0% derived from data on biological variation compared to 6.0% as defined by National Glycohemoglobin Standardization Program (NGSP). We estimated a function for LR of HbA1c in diagnosing diabetes mellitus using logistic regression with a clinical database (n=572) where diabetes status was defined by WHO criteria. Then we estimated errors in LR that correspond to errors in the measurement of HbA1c. Measuring HbA1c 3% too low at HbA1c of 6.5 percentage points (the suggested diagnostic limit) gives a LR of 0.36 times the correct LR, while measuring HbA1c 3% too high gives a LR of 2.77 times the correct LR. The corresponding errors in LR for allowable total error of 6% are 0.13 and 7.69 times the correct LR, respectively. These principles of evaluating allowable total error can be applied to any diagnostically used analyte where the distribution of the analyte's concentration is known in patients with and without the disease in a clinically relevant population. In the example used, the allowable total error of 6% leads to very erroneous LRs, suggesting that the NGSP limits of ±6% are too liberal.