Table 1.

Summary of simulation study.

Analysis methods were evaluated using the results from 1000 simulated data sets, each of which was analyzed using the analysis methods applied to the simulated number of episodes^a for each of the villages in the two treatment conditions. Simulation details and model code are given in the supplementary material. Any abbreviations that have been used for ease of readability in all following tables and figures have been defined here.

Scenarios simulated
Treatment effect		Rate ratio: eβ1 = 1.0, 0.9, 0.8, 0.7, 0.6, $\frac{0.619}{1.088}$
Number of clusters		6, 10, 14, 18
Effect of year		α: Year 1 = e0.0843–0.1054 year 2 = e 0.0843 – 0.1054
One rainy season		Separate analyses of the first- and second-year results
Two rainy seasons (parallel)		Analysis of combined Year 1 and Year 2 data
Two rainy seasons (crossover)		Analysis of data from a crossover design
Metrics evaluated
Bias		Difference between the estimated and true value for β1
Coverage		Proportion of 95% confidence interval that includes β1
Power		Probability of rejecting the null hypothesis: eβ1 = 1.0
Summary of models compared
Category	Name	Method of model fitting
MM	Mixed models	PL: Pseudo-likelihood
		PLKR: Pseudo-likelihood, Kenward-Roger correction
		ML: Laplace: Laplace approximation to the likelihood
		ML: AGQ-10: Adaptive Gaussian quadrature
GEEs	Generalized estimating equations
		Using model-based standard error
		Using empirical standard error
		Using MBN correction, proposed by Morel, Bokossa, and Neerchal
		Using FG correction, proposed by Fay and Graubard
	Cluster-level analyses
		Unweighted t-test
		Size weighted
		Variance weighted
		Adjusted residual

^aThe number of episodes was simulated to follow a Poisson distribution with mean rate λ_ijk denoting the rate with treatment i = (0,1) in village j = 1 ,…, 7 and subject k = 1 ,…, N_ij; X₁ = 0 satisfying log(λ_ijk) = α + β₁X_i + β₂X_ijk + u_ij, where X_i = 0 (control) or X_i = 1 (Ivermectin), and X_ijk = 0 (female) or X_ijk = 1 (male) and α = intercept; β₁ = log of the rate ratio treatment versus control; β₂ = log of the rate ratio male versus females; and u_ij = random village effect: u_ij ∼ N(0, 0.05 or 0.10).