Reference Range Estimation: Accounting for Measurement System Errors

Reference range is a statistic that is used in health related fields to represent the range of the most likely values for a variable of interest. Based on this range, individuals are classified as being healthy or unhealthy. In biostatistics, the reference range is calculated as the (1 − α)% prediction interval, where this prediction interval is based on the estimated population variance from the data. Such estimation of population variance is not precise, because obtained test results do usually have errors associated with them. These errors are due to the imprecise test procedure or gauge used. In this paper, the total variability in the data is decomposed into two categories. The first is the patient‐to‐patient variability and the other is the variability due to the measurement system used. Estimation of the two kinds is performed through a gauge repeatability and reproducibility study, then the reference range is calculated, taking into account only the patient‐to‐patient variability. The revised reference range procedure is illustrated through a case study of vitamin B12 test results. A closed form formula is given to calculate the probability of a given test result being within the revised reference range.