A comparison between copula-based, mixed model, and estimating equation methods for regression of bivariate correlated data

TL;DR

This study compares copula-based GJRM, GLMM, and GEE methods for bivariate longitudinal data, showing GJRM's advantages in accuracy, flexibility, and fit, especially with non-normal distributions.

Contribution

It demonstrates that GJRM provides unbiased, accurate estimates across various distributions and outperforms GLMMs and GEE in many scenarios, highlighting its advantages for bivariate data analysis.

Findings

GJRM yields unbiased estimates with correct standard errors when the copula is specified.

GLMMs can produce biased estimates and poor fit with non-normal or skewed data.

GJRM offers more flexible modeling of marginal distributions and correlation structures.

Abstract

This paper presents a simulation study comparing the performance of generalized joint regression models (GJRM) with generalized linear mixed models (GLMM) and generalized estimating equations (GEE) for regression of longitudinal data with two measurements per observational unit. We compare models on the basis of overall fit, coefficient accuracy and computational complexity. We find that for the normal model with identity link, all models provide accurate estimates of regression coefficients with comparable fit. However, for non-normal marginal distributions and when a non-identity link function is used, we highlight a major pitfall in the use of GLMMs: without significant adjustment they provide highly biased estimates of marginal coefficients and often provide extreme fits. GLMM coefficient bias and relative lack of fit is more pronounced when the marginal distributions are more skewed or highly correlated. In addition, we find major discrepancies between the estimates from different GLMM software implementations. In contrast, we find that GJRM provides unbiased estimates across all distributions with accurate standard errors when the copula is correctly specified; and the GJRM provides a model fit favourable or comparable to GLMMs and GEEs in almost all cases. We also compare the approaches for a real-world longitudinal study of doctor visits. We conclude that for non-normal bivariate data, the GJRM provides a superior model with more consistently accurate and interpretable coefficients than the GLMM, and better or comparable fit than both the GLMM and GEE, while providing more flexibility in choice of marginal distributions, and control over correlation structure.