Cluster Randomization Trials

Dr. Ranadip Chowdhury.

M.B.B.S., M.D.

M.I.P.H.A.

What Are Cluster Randomization Trials

Cluster randomization trials are experiments in which intact social units or clusters of individuals rather than independent individuals are randomly allocated to intervention groups.

Examples:• Medical practices selected as the

randomization unit.

• Communities selected as the randomization unit.

• Hospitals selected as the randomization unit in trials.

Reasons for Adopting Cluster Randomization

• Intervention naturally applied at the cluster level

• Administrative convenience

• To avoid treatment group contamination

• To obtain cooperation of investigators

• To enhance subject compliance

Challenges of CRTs

• Unit of Randomization vs. Unit of Analysis.

• Low power and a relatively high probability of chance imbalance b/w intervention arms.

• Post randomization recruitment bias

Design• 2 main approaches to randomization:

Unrestricted allocation

Restricted allocationMatchingStratificationMinimizationCovariate-constrained randomization

Choosing an allocation technique

Adv V/S Limitation of allocation techniquesTechnique Advantages Limitations

Simple randomization No need for baseline data Higher risk for imbalance

Matching •Improves Face validity•Balance effectively for covariates.

•Lost to follow-up is doubled•Challenges with analysis•Difficult to estimate ICC•Reduced degrees of freedom limits power.

Stratification May be used in combination with other allocation techniques.

Can balance for covariates on its own.

Minimization Can balance effectively for many covariates.

•Continuous covariates may need to be split into categories.•Potential for selection bias.

Covariate-constrained randomization

•Balances most effectively for many covariates.•Limits risk of selection bias.

•Access to baseline data.•Additional statistical support.•Allocation must occur after recruitment.

Cohort versus cross-sectional designs

• Possible instability in cohorts of large size, with the resulting likelihood of subject loss to follow-up.

• Representativeness of the target population, which is invariably hampered by the ageing of the cohort over time

If the primary questions of interest focus on change at the community level rather than at the level of the individual, cohort samples are the less natural choice.

Methodological Considerations in CRT• Observations on participants in the same cluster

tend to be correlated (non-independent).

• Degree of correlation within clusters is known as intracluster correlation coefficient (ρ).

• Intracluster correlation coefficient is the proportion of the total variance of the outcome that can be explained by the variation between clusters.

Sample size • 2 important components of variation:

• Within cluster (Intracluster correlation coefficient)

• Between cluster(A useful rule of thumb is that the power does not increase

appreciably once the number subjects per cluster exceeds 1/ ρ)

• No simple relation exist between k and ρ for continuous outcomes but a relation exists for binary outcome.

• For the same statistical power the overall sample size needs to be larger in CRT than in an individually randomized trial.

Standard sample size formulae for CRT

• where nI is the required sample size per arm using a trial with individual randomization to detect a difference d, and VIF(Design Effect) can be modified to allow for variation in cluster sizes. This is the standard result, that the required sample size for a CRCT is that required under individual randomisation, inflated by the variance inflation factor.

• The trial will randomize the intervention over k clusters per arm each of size m, to provide a total of nc = mk individuals per arm.

• The number of clusters required per arm : assuming equal cluster sizes.

CRTs with a fixed number of clusters: sample size per cluster

• For a trial with a fixed number of equal sized clusters (k) the required sample size per arm for a trial with pre-specified power 1 - b, to detect a difference of d, is nc.

• Where nI is the sample size required under individual randomisation.

• The corresponding number of individuals in each of the k equally sized clusters.

CRTs with a fixed number of clusters: a practical advice

• Determine the required number of individuals per arm in a trial using individual randomisation (nI).

• Determine whether a sufficient number of clusters are available. For equal sized clusters, this will occur when: k > nI ρ

• Where the design is still not feasible• Either: the power must be reset at a value lower than the maximum

available power• the detectable difference must be set greater than the minimum

detectable difference• both power and detectable difference are adjusted in combination.

Statistical model for intracluster correlation

• where yik is the value of the response variable for unit i in cluster k, and is the overall mean. The remaining two terms represent the two levels of variation in the data, with ik representing the “within-cluster variation between observations from the same cluster, and bk the “between cluster” variation.

Analysis• Reducing clusters to independent observation

or summary statistics.

• Fixed effect regression/ ANOVA

• Methods that explicitly account for clustering

SUMMARY STATISTICS:– Un-weighted method of analysis in unequal

numbers of observations per cluster.– Taking the average of the observation in each

cluster, information regarding the individual observations is lost.

Fixed effects regression/ANOVA approaches– If a fixed effect is used, then the results of the

analysis are strictly only applicable to the particular set of clusters in the study.

– If the data are normal or can be transformed to normality, then a normal regression (ANOVA) approach with a fixed effect for cluster and an effect for group can be used.

• Methods that explicitly account for clustering:– Methods that adjust existing tests to account

clustering• Depends on data distribution

– Modeling approaches • Linear Mixed model (LMM)• Generalized Linear Mixed model (GEE)

Cluster Specific (CS) Model• The clusters are sampled from a

larger population and the effect of any particular cluster i is to add a random effect Zi to all the outcomes. For a cluster randomized we could set X =1 for intervention and X =0 for control. A CS model measures the effect on Y of changing X, while Z is held constant. This is a common model for longitudinal data, where it is possible to imagine, say in a cross-over trial, a treatment value changing over time. However, in a cluster randomized, everyone in a cluster receives the same treatment, and although a CS model can be fitted, the result can be interpreted theoretically.

Marginal Model

• Fitting this model is equivalent to fitting a Marginal model, that is we estimate the effect of X on Y as averaged over all the clusters Z.

• CS models would seem to be most suitable for testing effect of cluster level covariates, while Marginal models are conceptually preferable for estimating the effect of cluster level covariate.

• Difference between two approaches disappear as the ICC approaches zero.

• CS provides direct estimates of variance components while those are treated as nuisance parameters when the population average approached is adopted.

Reporting CRTs

Pitfalls and Controversies

• Ethical Issues

• Unit of reference

• Over matching

• Sample size and study power

• Assessing value of ICC from small studies.

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