Analyzing censored data in the analysis of multiplicative repeatability and reproducibility studies

Abstract

Measurements from instruments are sometimes censored at or below the instrument’s lower or upper limit of detection because the instruments have a calibrated response only over a certain data range. Near the ends of the range, the system reports a censored value such as “measurand value is less than threshold,” or “measurand value is more than threshold.” How should one analyze data that includes such “less than” and/or “more than” results and what is the impact of such censoring on estimation of variance components? To answer these two questions, this article makes three contributions: (1) It illustrates a straightforward numerical Bayesian analysis of such censored data based on the likelihood function, (2) it provides a simulation study to show the impact of increased amounts of censoring, and (3) it shows that if the true likelihood has an unknown form for measurand values near the threshold and another known form away from the threshold, then it is prudent for the measurement system to report censored values rather than actual values. Open source software to analyze censored data is provided as supplementary material.