Some statistical theory for interpreting reference distributions

Reference distributions quantify the extremeness of clinical test results, typically relative to those of a healthy population. Intervals of these distributions are used in medical decision-making, but while there is much guidance for constructing them, the statistics of interpreting them for diagnosis have been less explored. Here we work directly in terms of the reference distribution, defining it as the likelihood in a posterior calculation of the probability of disease. We thereby identify assumptions of the conventional interpretation of reference distributions, criteria for combining tests, and considerations for personalizing interpretation of results from reference data. Theoretical reasoning supports that non-healthy variation be taken into account when possible, and that combining and personalizing tests call for careful statistical modeling.