A multivariate measurement error model for method comparison data under skewed and heavy-tailed distributions

Abstract

Agreement evaluation among multiple measurement methods is vital in healthcare and related disciplines. The main objective is to evaluate the extent of agreement based on a parametric approach through multiple comparisons of method pairs. In literature, existing approaches often depend on the normality assumption and typically employ mixed-effects models. However, in reality, the assumptions are breached depending on skewness and heavy-tailedness. Also, the presence of inherent measurement errors denies the usage of mixed-effect models. To overcome these challenges, this article introduces a novel multivariate measurement error model (MEM) that assumes scale mixtures of skew-normal distributions, including skew-𝑡, skew generalized-𝑡, and skew-normal for true unobserved covariates and scale mixtures of normal distributions for errors. A key feature of this model is that it can accommodate different degrees of freedom for the true covariate and errors. Further, the normally distributed replicated MEM is considered for comparative analysis. The maximum likelihood estimates are derived through the expectation conditional maximum algorithm. To assess the performance of these estimates, we conducted a simulation study, considering metrics such as bias and root mean square error. The tumour dataset is utilized to illustrate the practical application of the proposed model effectively, and using the probability of agreement metric, we have assessed agreement among the possible method pairs. The results reveal that our proposed model is well-suited for modelling method comparison data between multiple methods across small, modest, and large samples, particularly when data exhibit skewness and heavy tails.