Estimating an adjusted risk difference in a cluster randomized trial with individual-level analyses.

In cluster randomized trials (CRTs) with a binary outcome, intervention effects are usually reported as odds ratios, but the CONSORT statement advocates reporting both a relative and an absolute intervention effect. With a simulation study, we assessed several methods to estimate a risk difference (RD) in the framework of a CRT with adjustment on both individual- and cluster-level covariates. We considered both a conditional approach (with the generalized linear mixed model [GLMM]) and a marginal approach (with the generalized estimating equation [GEE]). For both approaches, we considered the Gaussian, binomial, and Poisson distributions. When considering the binomial or Poisson distribution, we used the g-computation method to estimate the RD. Convergence problems were observed with the GEE approach, especially with low intra-cluster coefficient correlation values, small number of clusters, small mean cluster size, high number of covariates, and prevalences close to 0. All methods reported no bias. The Gaussian distribution with both approaches and binomial and Poisson distributions with the GEE approach had satisfactory results in estimating the standard error. Results for type I error and coverage rates were better with the GEE than GLMM approach. We recommend using the Gaussian distribution because of its ease of use (the RD is estimated in one step only). The GEE approach should be preferred and replaced with the GLMM approach in cases of convergence problems.