Assessing the agreement between two quantitative assays with repeated measurements

We propose a statistical test in evaluating the equivalence (or agreement) between assay values x and y obtained using two methods in assay or instrument validation, where both x and y are measurements of an unobserved analyte z. Our method builds on the availability of repeated measurements from each sampled subject, which enables us to assess the agreement in terms of the conditional mean of the difference x - y given z as well as the conditional variance of x - y given z. With the help of repeated measurements and a large number of sampled subjects, our method does not require any distributional assumption on (x, y, z) or any model assumption on the conditional mean (or variance) of x - y. Furthermore, our test is designed so that when the null hypothesis is rejected, we can conclude that the two assay methods do not have practically meaningful difference with a high statistical assurance, which is an approach adopted in the assessment of bioequivalence between two drug products.