Statistical evaluation of measurement precision in linear dose-response relationships via interlaboratory studies

TL;DR

This paper introduces a statistical framework for evaluating measurement precision in dose-response relationships from interlaboratory studies, using linear mixed-effects models and ANOVA for detailed variance analysis.

Contribution

It develops a method to quantify and analyze between-laboratory variances in dose-response studies, enabling discrimination between baseline shifts and sensitivity differences.

Findings

Exact ANOVA decomposition of variance components

Three F-tests for dose-response trend and homogeneity of intercepts and slopes

Application to nanomaterials study data

Abstract

This paper proposes a framework for evaluating the statistical precision of measurement methods from interlaboratory studies where the outcome is a dose-response relationship summarized by a regression line. For such measurement methods, where a linear mixed-effects model is applied that allows laboratories to differ in both baseline level and dose-response slope, we define precision evaluation metrics specified in ISO 5725, repeatability and between-laboratory variances. These are method-level precision metrics, and the latter are constructed as design-averaged dose-specific between-laboratory variances over the dose levels and the participating laboratories. For fully balanced designs with common dose levels and equal replication, we obtain an exact decomposition of the total sum of squares, closed-form analysis of variance (ANOVA) estimators of the precision variances, and three associated $F$-tests targeting (i) the overall dose-response trend, (ii) homogeneity of intercepts, and (iii) homogeneity of slopes across laboratories. This formulation enables precision to be quantified and estimated directly and supports an evaluation of whether between-laboratory discrepancies are caused primarily by baseline shifts or by differences in sensitivity, in contrast to fixed-effect comparisons that only detect the presence of differences. Furthermore, we analyze data obtained from an interlaboratory study on observations in bronchoalveolar lavage fluid from experiments involving the intratracheal administration of nanomaterials to rats, using the proposed method as a case study.