New ideas for method comparison: a Monte Carlo power analysis

TL;DR

This paper introduces new robust regression methods and a graphical validation technique, evaluated through Monte Carlo simulations, demonstrating higher power and reliability in method comparison tasks.

Contribution

It presents two novel robust regressions, M-Deming and MM-Deming, and a unified graphical statistical test for method validation, improving accuracy and reducing sample size requirements.

Findings

M-Deming regression outperforms Passing-Bablok in biased data scenarios.

The graphical validation method provides a more interpretable assessment.

Unified test shows higher power and lower sample size needs.

Abstract

In this paper some new proposals for method comparison are presented. On the one hand, two new robust regressions, the M-Deming and the MM-Deming, have been developed by modifying Linnet's method of the weighted Deming regression. The M-Deming regression shows superior qualities to the Passing-Bablok regression; it does not suffer from bias when the data to be validated have a reduced precision, and therefore turns out to be much more reliable. On the other hand, a graphical method (box and ellipses) for validations has been developed which is also equipped with a unified statistical test. In this test the intercept and slope pairs obtained from a bootstrap process are combined into a multinomial distribution by robust determination of the covariance matrix. The Mahalanobis distance from the point representing the null hypothesis is evaluated using the $\chi^{2}$ distribution. It is emphasized that the interpretation of the graph is more important than the probability obtained from the test. The unified test has been evaluated through Monte Carlo simulations, comparing the theoretical $\alpha$ levels with the empirical rate of rejections (type-I errors). In addition, a power comparison of the various (new and old) methods was conducted using the same techniques. This unified method, regardless of the regression chosen, shows much higher power and allows a significant reduction in the sample size required for validations.