Missing continuous outcomes under covariate dependent missingness in cluster randomised trials.

Anower Hossain,Jonathan W Bartlett,Karla Diaz-Ordaz

doi:10.1177/0962280216648357

Abstract

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group.

Highlights

In cluster randomised trials (CRTs), identifiable clusters of individuals such as villages, schools, medical practices – rather than individuals – are randomly allocated to each of intervention and control groups, while individual-level outcomes of interest are observed within each cluster
We study the validity of three analysis methods – unadjusted cluster-level analysis, adjusted cluster-level analysis and linear mixed model (LMM) – when there is missingness in the continuous outcome, and this missingness depends on baseline covariates, and conditional on these baseline covariates, not on the outcomes itself
When the missingness mechanism is the same between the intervention groups and there is no interaction between intervention and baseline covariate in the outcome model, both the unadjusted and adjusted cluster-level analyses gave unbiased estimates of intervention effect with coverage probabilities very close to the nominal level

Summary

Introduction

In cluster randomised trials (CRTs), identifiable clusters of individuals such as villages, schools, medical practices – rather than individuals – are randomly allocated to each of intervention and control groups, while individual-level outcomes of interest are observed within each cluster. The value of ICC typically ranges from 0.001 to 0.05 and it is rare for clinical outcomes to have ICC above 0.1.1 Small values of ICC can lead to substantial variance inflation factors and should not be ignored.[2,3] CRTs are being increasingly used in the fields of health promotion and health service research Reasons for such popularity include the nature of intervention that itself may dictate its application at the cluster level, less risk of intervention contamination and administrative convenience.[4] It is well known that the power and precision of CRTs are lower relative to trials that individually randomise the same number of individuals.[2] In spite of this, the advantages associated with CRTs are perceived by researchers to outweigh the potential loss of statistical power and precision in some situations

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