Rethinking calibration as a statistical estimation problem to improve measurement accuracy

Calibration in analytical chemistry is crucial for ensuring the accuracy and reliability of measurements. Proper calibration strategies minimize errors, enhance reproducibility, and maintain compliance with regulatory requirements. Without it, data integrity could be compromised, leading to incorrect conclusions and potentially flawed decisions in both research and industrial applications. Calibration strategies can be affected by the type of analytical instrumentation utilized as well as the time and resources available to the analyst. In this work, we reevaluated the commonly used calibration method as a statistical estimation problem to highlight the long history of improving calibration uncertainty and proposed a Bayesian hierarchical modeling (BHM) approach, which offers enhanced accuracy and consistency for calibration-based methods without changing the current experimental settings. Using data from three types of calibration problems, we showed that (1) the notable variability of a typical calibration-based method is due largely to the relatively limited sample size used for fitting the calibration curve, (2) the BHM approach effectively mitigated this uncertainty by pooling relevant information from multiple data points within a test and combining information from calibration curve coefficients across similar calibration curves, and (3) replications can enhance the estimation of measurement uncertainty. Our findings demonstrate that the accuracy and consistency of all calibration-based measurement methods can be significantly enhanced by replacing the conventional regression method with the more robust BHM modeling approach.