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.

翻译：本文提出一个框架，用于从实验室间研究中评估测量方法的统计精度，其中结果是由回归线总结的剂量-反应关系。针对此类测量方法，应用允许实验室在基线水平和剂量-反应斜率存在差异的线性混合效应模型，我们定义了ISO 5725中规定的精度评估指标——重复性方差和实验室间方差。这些是方法层面的精度指标，后者被构建为剂量水平和参与实验室上设计平均的特定剂量实验室间方差。对于具有共同剂量水平和相等复制次数的完全平衡设计，我们获得了总平方和的精确分解、精度方差的闭合形式方差分析(ANOVA)估计量，以及三个相关的$F$检验，分别针对：(i)整体剂量-反应趋势，(ii)截距同质性，以及(iii)斜率在实验室间的同质性。该公式能够直接量化和估计精度，并支持评估实验室间差异主要是由基线偏移还是敏感性差异引起，这与仅检测差异存在的固定效应比较形成对比。此外，我们以涉及大鼠气管内给予纳米材料的实验中支气管肺泡灌洗液观测数据的实验室间研究为例，使用所提出方法对该数据进行分析。