Comparative calibration without a gold standard

Comparative calibration is the broad statistical methodology used to assess the calibration of a set of p instruments, each designed to measure the same characteristic, on a common group of individuals. Different from the usual calibration problem, the true underlying quantity measured is unobservable. Many authors have shown that this problem, in general, does not have a unique solution. Most commonly used assumptions to obtain a unique solution are (i) one instrument is the gold standard (that is, unbiased) and (ii) the measurement errors of the p instruments are independent. Such constraints, however, may not be valid for many clinical applications, for example, the universal standardization project for dual X-ray absorptiometry (DXA) scanners. In this paper, we propose a new approach to resolve the comparative calibration problem when a gold standard is unavailable. Instead of the usual assumptions, we use external information in addition to data from the p instruments, to solve the problem. We address statistical estimation, hypothesis testing and missing data problems. We apply the new method specifically to the universal standardization project data where a group of individuals have been measured for bone mineral density (BMD) by three DXA scanners. We compare the results of the new method to currently used methods and show that they have better statistical properties.