Choosing appropriate statistical models for multicenter randomized controlled trials with continuous and binary endpoints

Abstract

Many randomized controlled trials (RCTs) recruit individuals to multiple clinical centers rather than a single center. This strategy may provide a larger sample size and, therefore, have greater power to detect potential differences among experimental treatments. After balanced randomization, analyses of multicenter studies still need to appropriately adjust for the center effects and possibly other covariates to ensure valid inference. However, for real-world studies, regardless of whether the outcome is continuous or binary, it is often challenging to properly account for them or decide whether to remove the interaction effects, especially when the treatment arm ratio is unequal or the total sample size is small. This work considered two projects. In the first project, (1) continuous outcomes were explored under a blocked randomization process, which can induce correlation among treatment groups and violate the statistical assumption that all individuals were independent. (2) The correct test statistics for the null hypothesis of no treatment effect under the mixed-effects models were derived under homogeneous and heterogeneous scenarios. (3) The method-of-moments based on Type III sum of squares and restricted maximum likelihood (REML) procedures with Kenward-Roger (KR) adjustment were examined for the impact on inference for center, treatment, and center-by-treatment interaction effects under mis-specified models in two simulations studies. One study considered only center effects, and the other considered center and block nested within the center (e.g., litter). In the second project, (1) the performance characteristics of Cochran-Mantel-Haenszel (CMH), generalized linear mixed model (GLMM), and generalized estimating equations (GEEs) for binary data were compared under both balanced and unbalanced designs via simulation under homogeneous scenarios. (2) Furthermore, these three primary methods were explored in various situations with and without accounting for the center or center-by-treatment interaction effects. In summary, for both continuous and binary outcomes, it is important to assess whether or not treatment effects are heterogeneous across centers. In particular for a continuous outcome when the number of centers is small, whether or not to exclude the center-by-treatment interaction term should be determined by p-values from the Type III sum of the squares analysis instead of REML. The simulation results showed that REML was too conservative even with KR adjustment. When center-by-treatment was statistically significant, the center-by-treatment interaction term should be included in the model as random rather than fixed, otherwise Type I error rates for testing treatment effects were inflated. However, when models were mis-specified (i.e., missing non-zero random effects), increasing the number of centers (e.g., 25) and considering the nested variable (e.g., litter) as fixed could improve model performance in terms of Type I error rate and power for inference on treatment effects. For a binary outcome, CMH is always recommended as the most preferable approach in homogeneous scenarios. When center-by-treatment effects were present in the data, GLMM incorporating center and center-by-treatment interaction as random could be used to provide precise and valid inference for treatment effect. When the number of centers was large (e.g., 25), GEE with robust standard errors (center as the subject for exchangeable working correlation structure) was shown to be the best option for both homogeneous and heterogeneous cases.