Table 1.

Summary of details of ten regression models evaluated in the simulation study

Model	SEs	95% CI or posterior interval	Other assumptions
GLM-Bin	Model-based, unadjusted for center correlation	Wald
GEE binomial	Robust sandwich	t-based	Exchangeable working correlation
GEE binomial KC-correcteda	Robust sandwich with small-sample correction	t-based	Exchangeable working correlation
GEE Poisson	Robust sandwich	t-based	Exchangeable working correlation
GEE Poisson KC-correcteda	Robust sandwich with small-sample correction	t-based	Exchangeable working correlation
GLMM binomial	Model-based	Wald	Adaptive quadrature with 10 points
GLMM binomial bootstrapa	Parametric bootstrap	Parametric bootstrap, quantile-based	Laplace for fitting bootstrap samples
GLMM Poisson	Model-based	Wald	Adaptive quadrature with 10 points
GLMM Poisson bootstrapa	Parametric bootstrap	Parametric bootstrap, quantile-based	Laplace for fitting bootstrap samples
Bayesian binomial GLMM	Posterior SD	Quantile-based posterior interval	Priors β0 ~ Normal(0,102); β1, β2 ~ Normal(0,1); σ ~ half-Normal(0,1)

Abbreviations: GEE Generalized estimating equation, GLM-Bin Log-binomial regression model, GLMM Generalized linear mixed model, KC Kauermann and Carroll

^aThe small sample KC correction or bootstrap samples correct only the SEs and 95% CIs and do not affect the point estimates of the risk ratio