title: Multiple imputation methods for handling missing data in cost-effectiveness analyses that use data from hierarchical studies: an application to cluster randomized trials.
abstract: Multiple imputation (MI) has been proposed for handling missing data in cost-effectiveness analyses (CEAs). In CEAs that use cluster randomized trials (CRTs), the imputation model, like the analysis model, should recognize the hierarchical structure of the data. This paper contrasts a multilevel MI approach that recognizes clustering, with single-level MI and complete case analysis (CCA) in CEAs that use CRTs.
  
  
  
  We consider a multilevel MI approach compatible with multilevel analytical models for CEAs that use CRTs. We took fully observed data from a CEA that evaluated an intervention to improve diagnosis of active labor in primiparous women using a CRT (2078 patients, 14 clusters). We generated scenarios with missing costs and outcomes that differed, for example, according to the proportion with missing data (10%-50%), the covariates that predicted missing data (individual, cluster-level), and the missingness mechanism: missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). We estimated incremental net benefits (INBs) for each approach and compared them with the estimates from the fully observed data, the "true" INBs.
  
  
  
  When costs and outcomes were assumed to be MCAR, the INBs for each approach were similar to the true estimates. When data were MAR, the point estimates from the CCA differed from the true estimates. Multilevel MI provided point estimates and standard errors closer to the true values than did single-level MI across all settings, including those in which a high proportion of observations had cost and outcome data MAR and when data were MNAR.
  
  
  
  Multilevel MI accommodates the multilevel structure of the data in CEAs that use cluster trials and provides accurate cost-effectiveness estimates across the range of circumstances considered.
authors.affiliation: Department of Health Services Research and Policy, London School of Hygiene and Tropical Medicine, London, UK (MG, KD, RG).
authors.forename: Manuel
authors.initials: M
authors.lastname: Gomes
authors.affiliation: Department of Health Services Research and Policy, London School of Hygiene and Tropical Medicine, London, UK (MG, KD, RG).
authors.forename: Karla
authors.initials: K
authors.lastname: Díaz-Ordaz
authors.affiliation: Department of Health Services Research and Policy, London School of Hygiene and Tropical Medicine, London, UK (MG, KD, RG).
authors.forename: Richard
authors.initials: R
authors.lastname: Grieve
authors.affiliation: Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK (MGK)
authors.forename: Michael G
authors.initials: MG
authors.lastname: Kenward
mesh_terms: D016000:Cluster Analysis; D003362:Cost-Benefit Analysis; D003627:Data Interpretation, Statistical; D016032:Randomized Controlled Trials as Topic
keywords: cluster randomized trials; cost-effectiveness analysis; hierarchical data; missing data; multiple imputation