Missing outcome data are common in cluster randomized trials (CRTs) which can complicate inference. Further, the missingness can occur due to dropout of individuals, termed “sporadically” missing data, or dropout of clusters, termed “systematically” missing data, and these two types of missingness could have potentially different missing data mechanisms. We aimed to develop a well-performing and practical approach to handle inference in CRTs when outcome data may be both sporadically and systematically missing. To this end, we first examined the performance of four multilevel multiple imputation (MI) methods to handle sporadically and systematically missing CRT outcome data via a simulation study. Our findings showed that one multilevel MI method which uses the maximum likelihood estimates obtained from a linear mixed model to draw missing values outperformed the others under various scenarios. Using the best performing MI method, we developed methods for conducting sensitivity analysis to test the robustness of inferences under different missing at random (MAR) and missing not at random (MNAR) assumptions. The methods allow for different MNAR assumptions for cluster dropout and individual dropout to reflect that they may arise from different missing data mechanisms. We developed graphical displays to visualize sensitivity analysis results. Our methods are illustrated using a real data application.

Cluster randomized trials (CRTs) are increasingly used in many fields including public health and medicine. We consider two-arm CRTs with binary outcomes with possibly unequal intraclass correlations coefficients (ICCs) in the two arms. The efficacy of the intervention may be measured in terms of the risk difference (RD), relative risk (RR) or odds ratio (OR). We define cost efficiency (CE) as the ratio of the precision of the efficacy measure to the study cost and develop optimal allocations to the two arms for maximizing CE. The optimal design, which is based on the optimal allocation, could be different for different measures. We define relative cost efficiency (RCE) of a design as the ratio of its CE to CE of the optimal design and use RCE to compare different designs. Because the optimal allocation can be highly sensitive to the unknown ICCs and anticipated success rates, we propose a Bayesian method and a maximin method to construct an efficient and robust design. We show that the RCE of the designs based on the Bayesian method or the maximin method is generally larger than the balanced design. Based on the optimal allocation, we derive optimal sample size formulas which satisfy the power requirement and minimize the total study cost. All the results above are based on the assumption of constant cluster size. When there is extreme variation in cluster size, the usually used sample size formula assuming a constant cluster size may result in a design with low power. Assuming a balanced design, we develop a sample size formula for a two-arm CRT which obtains the desired power even though the cluster sizes are very different. This formula can be modified to incorporate optimal allocation consideration, hence it minimizes the study cost while satisfying the power requirement for a CRT with varying cluster sizes. Simulation is used to verify that our formulas can obtain the desired power.