COMPARATIVE CALIBRATION WITHOUT A GOLD STANDARD

Comparative calibration is the broad statistical methodology used to a ssess the calibration of a set of p instruments, each designed to meas ure the same characteristic, on a common group of individuals. Differe nt from the usual calibration problem, the true underlying quantity me asured is unobservable. Many authors have shown that this problem, in general, does not have a unique solution. Most commonly used assumptio ns to obtain a unique solution are (i) one instrument is the gold stan dard (that is, unbiased) and (ii) the measurement errors of the p inst ruments are independent. Such constraints, however, may not be valid f or many clinical applications, for example, the universal standardizat ion project for dual X-ray absorptiometry (DXA) scanners. In this pape r, we propose a new approach to resolve the comparative calibration pr oblem when a gold standard is unavailable. Instead of the usual assump tions, we use external information in addition to data from the p inst ruments, to solve the problem. We address statistical estimation, hypo thesis testing and missing data problems. We apply the new method spec ifically to the universal standardization project data where a group o f individuals have been measured for bone mineral density (BMD) by thr ee DXA scanners. We compare the results of the new method to currently used methods and show that they have better statistical properties. ( C) 1997 by John Wiley & Sons, Ltd.