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Semi-parametric methods are often used for the estimation of interventioneffects on correlated outcomes in cluster-randomized trials (CRTs). Whenoutcomes are missing at random (MAR), Inverse Probability Weighted (IPW)methods incorporating baseline covariates can be used to deal with informativemissingness. Also, augmented generalized estimating equations (AUG) correct forimbalance in baseline covariates but need to be extended for MAR outcomes.However, in the presence of interactions between treatment and baselinecovariates, neither method alone produces consistent estimates for the marginaltreatment effect if the model for interaction is not correctly specified. Wepropose an AUG-IPW estimator that weights by the inverse of the probability ofbeing a complete case and allows different outcome models in each interventionarm. This estimator is doubly robust (DR), it gives correct estimates whetherthe missing data process or the outcome model is correctly specified. Weconsider the problem of covariate interference which arises when the outcome ofan individual may depend on covariates of other individuals. When interferingcovariates are not modeled, the DR property prevents bias as long as covariateinterference is not present simultaneously for the outcome and the missingness.An R package is developed implementing the proposed method. An extensivesimulation study and an application to a CRT of HIV risk reduction-interventionin South Africa illustrate the method.

Accounting for interactions and complex inter-subject dependency in estimating treatment effect in cluster randomized trials with missing outcomes