Small-sample performance of the robust score test and its modifications in generalized estimating equations

Area of Science:

• Biostatistics
• Statistical Inference
• Longitudinal Data Analysis

Background:

• The sandwich variance estimator in generalized estimating equations (GEE) exhibits poor performance with few independent clusters.
• This can compromise the robust Wald test's validity, leading to inflated Type I errors and reduced confidence interval coverage.

Purpose of the Study:

• To investigate the small-sample performance of the robust score test for correlated data.
• To propose and evaluate modifications to enhance the robust score test's accuracy in small samples.

Main Methods:

• Comparative simulation study of robust score and robust Wald tests for correlated Bernoulli and Poisson data.
• Analysis of one-sample and two-sample comparisons to understand test behavior.
• Modification of the robust score statistic using a J/(J-1) adjustment factor, where J is the number of clusters.

Main Results:

• Robust Wald tests are overly liberal, while robust score tests are too conservative with small sample sizes.
• The proposed modification to the robust score test reduces conservativeness.
• Modified score tests demonstrated improved small-sample performance, with test sizes closer to nominal levels in simulations.

Conclusions:

• The modified robust score test offers a more reliable alternative to the Wald test for small clustered sample sizes.
• This approach is particularly relevant for analyzing data from group-randomized clinical trials.
• The proposed method was successfully applied to the TACOS group-randomized trial.