The estimation of calibration equations for variables with heteroscedastic measurement errors

In clinical chemistry and medical research, there is often a need to calibrate the values obtained from an old or discontinued laboratory procedure to the values obtained from a new or currently used laboratory method. The objective of the calibration study is to identify a transformation that can be used to convert the test values of one laboratory measurement procedure into the values that would be obtained using another measurement procedure. However, in the presence of heteroscedastic measurement error, there is no good statistical method available for estimating the transformation. In this paper, we propose a set of statistical methods for a calibration study when the magnitude of the measurement error is proportional to the underlying true level. The corresponding sample size estimation method for conducting a calibration study is discussed as well. The proposed new method is theoretically justified and evaluated for its finite sample properties via an extensive numerical study. Two examples based on real data are used to illustrate the procedure.