Optimal decision criterion for detecting change in bone mineral density during serial monitoring: a Bayesian approach.

Abstract

Interpretation of change in serial bone densitometry using least significant change (LSC) may not lead to optimal decision making. Using the principles of Bayesian statistics and decision sciences, we developed the Optimal Decision Criterion (ODC) which resulted in 11-12.5% higher rate of correct classification compared with the LSC method. The interpretation of change in serial bone densitometry emphasizes using least significant change (LSC) to distinguish between true changes and measurement error. Using the principles of Bayesian statistics and decision sciences, we developed the optimal decision criterion (ODC) based on maximizing a 'utility' function that rewards the correct and penalizes the incorrect classification of change. The relationship between LSC and ODC is demonstrated using a clinical sample from the Manitoba Bone Density Program. Under certain conditions, it can be shown that using LSC at the 95% confidence level implicitly equates the benefit of 39 true positive diagnoses with the harm of one false positive classification of BMD change. ODC resulted in an 11% higher rate of correct classification for lumbar spine BMD change and a 12.5% better performance for classifying total hip BMD change compared with LSC with this method. ODC has the same clinical interpretation as LSC but with two major advantages: it can incorporate prior knowledge of the likely values of the true change and it can be fine-tuned based on the relative value placed on the correct and incorrect classifications. Bayesian statistics and decision sciences could potentially increase the yield of a BMD monitoring program.