Comparing Generalized Estimating Equation and Linear Mixed Effects Model for Estimating Marginal Association with Bivariate Continuous Outcomes

ABSTRACT

Purpose

Both linear regression with generalized estimating equations (GEE) and linear mixed-effects models (LMEM) can be used to estimate the marginal association of an exposure with clustered continuous outcomes. This study compares their performance for bivariate continuous outcomes which are common in eye studies.

Methods

Parametric and non-parametric simulations were used to compare the GEE models including independent, exchangeable, and unstructured working correlation structures and LMEM including random intercept only and random intercept and slope models in R and SAS. Data generation referenced the data distributions from a real-world study for estimating ocular structure-visual function relationships in patients with retinitis pigmentosa.

Results

From both parametric and non-parametric simulations, comparing the random intercept LMEM and GEE exchangeable model, bias was similar; coverage probability of the 95% confidence interval (CI) from the random intercept LMEM was often closer to 95%, especially when the sample size was small; the power for testing the association of the exposure was higher from the GEE exchangeable model, but its type-I error rate might be inflated especially when the sample size was small. The type-I error rate from the random intercept LMEM was closer to 0.05, but it might be under 0.05 and coverage probability might be over 95%. The GEE independent model performed worst and the LMEM with both random intercept and slope might not converge.

Conclusion

To estimate marginal exposure-outcome association with bivariate continuous outcomes, the random intercept LMEM may be preferred. It has the best coverage probability of 95% CI and is the only model with correct type-I error rates in this study. However, it may have low power and overly wide CI in studies with small sample size or low inter-eye correlation.

KEYWORDS:

• structure-function
• correlated data analysis
• clinical trial design
• FIGHT-RP study
• retinitis pigmentosa

Acknowledgments

We appreciate Dr. Peter Campochiaro for his agreement to use the RP data. We thank Dr. Barbara S Hawkins for reviewing and editing an early version of the manuscript. We also thank Dr. Ann-Margret Ervin, and Dr. Ghassan B. Hamra for reviewing the thesis that the manuscript was derived from.

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/09286586.2022.2098984

Disclosure of interest

The authors report no conflict of interest.

Data availability statement

The FIGHT-RP data are available on request from the FIGHT-RP study contact author Dr. Peter Campochiaro. Information on the Fight-RP study can be found at https://pubmed.ncbi.nlm.nih.gov/31805012/.

Disclosure statement

None of the following authors have any proprietary interests or conflicts of interest related to this submission.

Additional information

Funding

This work was supported by the National Eye Institute grants (R34EY031429 and R21EY032955), and an unrestricted fund awarded to the Wilmer Eye Institute by Research to Prevent Blindness (RPB).