Analyzing method comparison data with skew-normal measurement error models: incorporating generalized scale mixtures and varying degrees of freedom

Abstract

Comparing two measurement methods is vital in various fields, such as medical research, epidemiology, economics, and environmental studies, to determine whether a new measurement method can be used interchangeably with an existing one. Measurement error models (MEMs) are commonly used for this purpose, where the methods have different measuring scales. However, these models often assume normality, which can be problematic when dealing with skewed and heavy-tailed data. To address this issue, we propose the replicated measurement error model (RMEM) under scale mixtures of skew-normal (SMSN) distributions with different levels of skewness and heavy tails of the true covariate and error distributions. Our primary aim is to assess the extent of similarity and agreement between two measurement methods using this model. The expectation conditional maximization (ECM) approach is applied to fit the model. A simulation study is conducted to evaluate the effectiveness and robustness of the proposed methodology and is illustrated by analyzing systolic blood pressure data. The probability of agreement is used further to assess the agreement between the two measurement methods. The findings indicate that the proposed model effectively analyses replicated method comparison data with measurement errors, even when there are outliers, skewness, and heavy-tailedness.

Keywords:

• ECM algorithm
• Method comparison data
• Probability of agreement
• Replicated measurement error models
• Scale mixtures of skew-normal distributions

Disclosure statement

The authors report there are no competing interests to declare.

Data availability

The systolic blood pressure dataset used in this study has already been published in the article by Carrasco and Jover (2003) and can be accessed at https://personal.utdallas.edu/∼pankaj/agreement_book/datasets/blood_pressure.txt.

Additional information

Funding

This work was supported by the University of Peradeniya under Grant URG/2022/59/S.