Abstract
Missing observations are common in cluster randomised trials. The problem is exacerbated when modelling bivariate outcomes jointly, as the proportion of complete cases is often considerably smaller than the proportion having either of the outcomes fully observed. Approaches taken to handling such missing data include the following: complete case analysis, single‐level multiple imputation that ignores the clustering, multiple imputation with a fixed effect for each cluster and multilevel multiple imputation.We contrasted the alternative approaches to handling missing data in a cost‐effectiveness analysis that uses data from a cluster randomised trial to evaluate an exercise intervention for care home residents.We then conducted a simulation study to assess the performance of these approaches on bivariate continuous outcomes, in terms of confidence interval coverage and empirical bias in the estimated treatment effects. Missing‐at‐random clustered data scenarios were simulated following a full‐factorial design.Across all the missing data mechanisms considered, the multiple imputation methods provided estimators with negligible bias, while complete case analysis resulted in biased treatment effect estimates in scenarios where the randomised treatment arm was associated with missingness. Confidence interval coverage was generally in excess of nominal levels (up to 99.8%) following fixed‐effects multiple imputation and too low following single‐level multiple imputation. Multilevel multiple imputation led to coverage levels of approximately 95% throughout. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
Highlights
In cluster randomised trials (CRTs), the unit of random allocation is a group of individuals rather than the individual subjects
This represents a situation where there is an interaction between treatment and the covariate driving the missingness, i.e. the treatment modifies strength of association between the covariate and non-response, which may arise in clinical trials, because for example of side-effects or lack of perceived efficacy in the intervention arm, or disillusionment amongst those assigned to the control arm
The full-factorial nature of our simulation study enabled us to establish which characteristics have the greatest influence on the performance of the alternative methods for handling missing data considered here
Summary
In cluster randomised trials (CRTs), the unit of random allocation is a group of individuals (e.g. a school or a hospital) rather than the individual subjects. An advantage of MI is that unlike conventional likelihood analyses, it can incorporate so-called auxiliary variables that are not included in the analysis model, but which are related to both the missing values and to the probability of observations being missing Incorporating such auxiliary variables makes the underlying MAR assumption more plausible. The aim of this paper is to investigate and compare the performance of these different MI strategies for handling missing bivariate outcome data in CRTs, over a wide range of missingness mechanisms that are dependent on individual and cluster-level variables. We do this by first applying the methods to a cost-effectiveness study that used data from a published CRT (Section 3).
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