Evaluating Agreement Among Multiple Methods With Replicated Measurements Using Scale Mixtures of Skew‐Normal Measurement Error Models

This paper introduces a robust parametric approach for assessing the agreement among multiple measurement methods when dealing with replicated data from a continuous variable. Many existing methodologies in the literature rely heavily on the normality assumption and often employ mixed‐effects models. However, in practical scenarios, these assumptions may not hold true due to the presence of skewness and heavy‐tailed distributions. Additionally, inherent measurement errors can further complicate the use of mixed‐effects models. To overcome these issues, we propose a multivariate measurement error model that assumes scale mixtures of skew‐normal distributions for the unobserved true covariates and scale mixtures of normal distributions for the errors. This formulation flexibly accommodates both skewness and heavy‐tailed characteristics within the data, allowing for different degrees of freedom for the true covariate and error distributions. An expectation‐conditional‐maximization algorithm is developed to estimate the parameters of this novel model. Furthermore, we employ the concept of the probability of agreement to evaluate agreement among the various pairs of measurement methods. To validate the efficacy of our proposed model, we conducted extensive simulation studies involving various sample sizes (50, 100, and 200) and varying skewness parameters (1, 5, and 10). Moreover, we demonstrate the practical applicability of our methodology by applying it to real tumor data. Our findings conclusively demonstrate the effectiveness of the proposed model in the analysis of replicated method comparison data across multiple methods, particularly in situations involving measurement errors, skewness, and heavy‐tailed distributions.