title: Imputation strategies for missing binary outcomes in cluster randomized trials.
abstract: BACKGROUND
  Attrition, which leads to missing data, is a common problem in cluster randomized trials (CRTs), where groups of patients rather than individuals are randomized. Standard multiple imputation (MI) strategies may not be appropriate to impute missing data from CRTs since they assume independent data. In this paper, under the assumption of missing completely at random and covariate dependent missing, we compared six MI strategies which account for the intra-cluster correlation for missing binary outcomes in CRTs with the standard imputation strategies and complete case analysis approach using a simulation study.
  
  
  METHODS
  We considered three within-cluster and three across-cluster MI strategies for missing binary outcomes in CRTs. The three within-cluster MI strategies are logistic regression method, propensity score method, and Markov chain Monte Carlo (MCMC) method, which apply standard MI strategies within each cluster. The three across-cluster MI strategies are propensity score method, random-effects (RE) logistic regression approach, and logistic regression with cluster as a fixed effect. Based on the community hypertension assessment trial (CHAT) which has complete data, we designed a simulation study to investigate the performance of above MI strategies.
  
  
  RESULTS
  The estimated treatment effect and its 95% confidence interval (CI) from generalized estimating equations (GEE) model based on the CHAT complete dataset are 1.14 (0.76 1.70). When 30% of binary outcome are missing completely at random, a simulation study shows that the estimated treatment effects and the corresponding 95% CIs from GEE model are 1.15 (0.76 1.75) if complete case analysis is used, 1.12 (0.72 1.73) if within-cluster MCMC method is used, 1.21 (0.80 1.81) if across-cluster RE logistic regression is used, and 1.16 (0.82 1.64) if standard logistic regression which does not account for clustering is used.
  
  
  CONCLUSIONS
  When the percentage of missing data is low or intra-cluster correlation coefficient is small, different approaches for handling missing binary outcome data generate quite similar results. When the percentage of missing data is large, standard MI strategies, which do not take into account the intra-cluster correlation, underestimate the variance of the treatment effect. Within-cluster and across-cluster MI strategies (except for random-effects logistic regression MI strategy), which take the intra-cluster correlation into account, seem to be more appropriate to handle the missing outcome from CRTs. Under the same imputation strategy and percentage of missingness, the estimates of the treatment effect from GEE and RE logistic regression models are similar.
authors.affiliation: Department of Clinical Epidemiology & Biostatistics, McMaster University, Hamilton, ON, Canada.
authors.forename: Jinhui
authors.initials: J
authors.lastname: Ma
authors.forename: Noori
authors.initials: N
authors.lastname: Akhtar-Danesh
authors.forename: Lisa
authors.initials: L
authors.lastname: Dolovich
authors.forename: Lehana
authors.initials: L
authors.lastname: Thabane
mesh_terms: D016000:Cluster Analysis; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016015:Logistic Models; D008390:Markov Chains; D009010:Monte Carlo Method; D057216:Propensity Score; D016032:Randomized Controlled Trials as Topic / Q000379:methods / Q000706:statistics & numerical data*; D016896:Treatment Outcome