title: Missing Data in Cluster Randomised Trials
Creators: name: Hossain, A
Publisher: name: London School of Hygiene & Tropical Medicine
Year: 2017

description: Missing outcomes are a commonly occurring problem in cluster randomised trials, which
can lead to biased and inefficient inference if ignored or handled inappropriately. Handling
missing data in CRTs is complicated due to the hierarchical structure of the
data. Two approaches for analysing such trials are cluster-level analysis and individual level
analysis. An assumption regarding missing outcomes in CRTs that is sometimes
plausible is that missingness depends on baseline covariates, but conditioning on these
baseline covariates, not on the outcome itself, which is known as a covariate dependent
missingness (CDM) mechanism. The aim of my thesis was to investigate the validity
of the approaches to the analysis of CRTs for the three most common outcome types:
continuous, binary and time-to-event, when outcomes are missing under the assumption
of CDM. Missing outcomes were handled using complete records analysis (CRA) and
multilevel multiple imputation (MMI).
We investigated analytically, and through simulations, the validity of the different combinations
of the analysis model and missing data handling approach for each of the three
outcome types. Simulations studies were performed considering scenarios depending on
whether the missingness mechanism is the same between the intervention groups and
whether the covariate effect is the same between the intervention groups in the outcome
model. Based on our analytical and simulations results, we give recommendations for
which methods to use when the CDM assumption is thought to be plausible for missing
outcomes. The key findings of this thesis are as follows.
Continuous outcomes:
  Cluster-level analyses using CRA are in general biased unless the intervention
groups have the same missingness mechanism and the same covariate effects on
outcome in the data generating model.
  In the case of individual-level analysis, the linear mixed model (LMM) using CRA
adjusted for covariates such that the CDM assumption holds gives unbiased estimates
of intervention effect regardless of whether the missingness mechanism is
the same or different between the intervention groups, and whether there is an
interaction between intervention and baseline covariates in the data generating
model for outcome, provided that such interaction is included in the model when
required.
  There is no gain in terms of bias or efficiency of the estimates using MMI over
CRA as long as both approaches use the same functional form of the same set of
baseline covariates.

Binary outcomes:
  The adjusted cluster-level estimator for estimating risk ratio (RR) using full data
is consistent if the true data generating model is a log link model, the functional
form of the baseline covariates is the same between the intervention groups, and
the random effects distribution is the same between the intervention groups.
  Cluster-level analyses using CRA for estimating risk difference (RD) are in general
biased. For estimating RR, cluster-level analyses using CRA are valid if the true
data generating model has log link and the intervention groups have the same
missingness mechanism and the same functional form of the covariates in the
outcome model.
  In contrast, MMI followed by cluster-level analyses gives valid inferences for estimating
RD and RR regardless of whether the missingness mechanism is the same
or different between the intervention groups, and whether there is an interaction
between intervention and baseline covariate in the outcome model, provided that
such interaction is included in the imputation model when required.
  In the case of individual-level analysis, both random effects logistic regression
(RELR) and generalised estimating equations (GEE) give valid inferences using
both CRA (adjusted for covariates such that the CDM assumption holds) and
MMI regardless of whether the missingness mechanism is the same or different
between the intervention groups, and whether there is an interaction between
intervention and baseline covariate in the outcome model, provided that such
interaction is included in both the imputation model and the analysis model when
required.
  Like continuous outcomes, in the absence of auxiliary variables, there is no benefit
in performing MMI rather than doing CRA in terms of bias or efficiency of the
estimates.
Time-to-Event outcomes:
  In the case of censored data, the unadjusted cluster-level analysis for estimating
rate ratio (RaR) is consistent when the event rates are small and the covariate
effects are the same between the intervention groups. In contrast, the adjusted
cluster-level analysis for estimating RaR is consistent for any event rates when the
the covariate effects are the same between the intervention groups.
  The gamma shared frailty model as an individual-level analysis underestimates
the standard errors (SEs) of the estimates when each intervention group has small
number of clusters.
  The Williams approach performs better than the Greenwood approach for estimating
the SEs of Kaplan-Meier (KM) estimates unless the event rate is low and
the value of intraclass correlation coefficient is very small.Missing outcomes are a commonly occurring problem in cluster randomised trials, which
can lead to biased and inefficient inference if ignored or handled inappropriately. Handling
missing data in CRTs is complicated due to the hierarchical structure of the
data. Two approaches for analysing such trials are cluster-level analysis and individual-level
analysis. An assumption regarding missing outcomes in CRTs that is sometimes
plausible is that missingness depends on baseline covariates, but conditioning on these
baseline covariates, not on the outcome itself, which is known as a covariate dependent
missingness (CDM) mechanism. The aim of my thesis was to investigate the validity
of the approaches to the analysis of CRTs for the three most common outcome types:
continuous, binary and time-to-event, when outcomes are missing under the assumption
of CDM. Missing outcomes were handled using complete records analysis (CRA) and
multilevel multiple imputation (MMI).
We investigated analytically, and through simulations, the validity of the different combinations
of the analysis model and missing data handling approach for each of the three
outcome types. Simulations studies were performed considering scenarios depending on
whether the missingness mechanism is the same between the intervention groups and
whether the covariate effect is the same between the intervention groups in the outcome
model. Based on our analytical and simulations results, we give recommendations for
which methods to use when the CDM assumption is thought to be plausible for missing
outcomes. The key findings of this thesis are as follows.
Continuous outcomes:
  Cluster-level analyses using CRA are in general biased unless the intervention
groups have the same missingness mechanism and the same covariate effects on
outcome in the data generating model.
  In the case of individual-level analysis, the linear mixed model (LMM) using CRA
adjusted for covariates such that the CDM assumption holds gives unbiased estimates
of intervention effect regardless of whether the missingness mechanism is
the same or different between the intervention groups, and whether there is an
interaction between intervention and baseline covariates in the data generating
model for outcome, provided that such interaction is included in the model when
required.
  There is no gain in terms of bias or efficiency of the estimates using MMI over
CRA as long as both approaches use the same functional form of the same set of
baseline covariates.
Binary outcomes:
  The adjusted cluster-level estimator for estimating risk ratio (RR) using full data
is consistent if the true data generating model is a log link model, the functional
form of the baseline covariates is the same between the intervention groups, and
the random effects distribution is the same between the intervention groups.
  Cluster-level analyses using CRA for estimating risk difference (RD) are in general
biased. For estimating RR, cluster-level analyses using CRA are valid if the true
data generating model has log link and the intervention groups have the same
missingness mechanism and the same functional form of the covariates in the
outcome model.
  In contrast, MMI followed by cluster-level analyses gives valid inferences for estimating
RD and RR regardless of whether the missingness mechanism is the same
or different between the intervention groups, and whether there is an interaction
between intervention and baseline covariate in the outcome model, provided that
such interaction is included in the imputation model when required.
  In the case of individual-level analysis, both random effects logistic regression
(RELR) and generalised estimating equations (GEE) give valid inferences using
both CRA (adjusted for covariates such that the CDM assumption holds) and
MMI regardless of whether the missingness mechanism is the same or different
between the intervention groups, and whether there is an interaction between
intervention and baseline covariate in the outcome model, provided that such
interaction is included in both the imputation model and the analysis model when
required.
  Like continuous outcomes, in the absence of auxiliary variables, there is no benefit
in performing MMI rather than doing CRA in terms of bias or efficiency of the
estimates.
Time-to-Event outcomes:
  In the case of censored data, the unadjusted cluster-level analysis for estimating
rate ratio (RaR) is consistent when the event rates are small and the covariate
effects are the same between the intervention groups. In contrast, the adjusted
cluster-level analysis for estimating RaR is consistent for any event rates when the
the covariate effects are the same between the intervention groups.
  The gamma shared frailty model as an individual-level analysis underestimates
the standard errors (SEs) of the estimates when each intervention group has small
number of clusters.
  The Williams approach performs better than the Greenwood approach for estimating
the SEs of Kaplan-Meier (KM) estimates unless the event rate is low and
the value of intraclass correlation coefficient is very small.