Abstract
Cluster randomization results in an increase in sample size compared to individual randomization, referred to as an efficiency loss. This efficiency loss is typically presented under an assumption of no contamination in the individually randomized trial. An alternative comparator is the sample size needed under individual randomization to detect the attenuated treatment effect due to contamination. A general framework is provided for determining the extent of contamination that can be tolerated in an individually randomized trial before a cluster randomized design yields a larger sample size. Results are presented for a variety of cluster trial designs including parallel arm, stepped-wedge and cluster crossover trials. Results reinforce what is expected: individually randomized trials can tolerate a surprisingly large amount of contamination before they become less efficient than cluster designs. We determine the point at which the contamination means an individual randomized design to detect an attenuated effect requires a larger sample size than cluster randomization under a nonattenuated effect. This critical rate is a simple function of the design effect for clustering and the design effect for multiple periods as well as design effects for stratification or repeated measures under individual randomization. These findings are important for pragmatic comparisons between a novel treatment and usual care as any bias due to contamination will only attenuate the true treatment effect. This is a bias that operates in a predictable direction. Yet, cluster randomized designs with post-randomization recruitment without blinding, are at high risk of bias due to the differential recruitment across treatment arms. This sort of bias operates in an unpredictable direction. Thus, with knowledge that cluster randomized trials are generally at a greater risk of biases that can operate in a nonpredictable direction, results presented here suggest that even in situations where there is a risk of contamination, individual randomization might still be the design of choice.
Highlights
Cluster randomization is a commonly used trial design for evaluating interventions that can only be delivered at the cluster-level, it is often used to evaluate individual-level interventions.[1,2,3] One of the reasons individual-level interventions are evaluated using cluster randomization is the concern over contamination such that those allocated to the control inadvertently receive the intervention, perhaps because of geographical or social proximity
When contamination operates in one direction only, and all other biases being absent, individual randomization will provide a lower bound for the effect that would be realized under the real-world situation of everyone being offered the intervention
In this paper we provide a general framework for determining the amount of contamination that can be tolerated in an individually randomized design before a larger sample size is required than a multiple period cluster randomized design
Summary
Cluster randomization is a commonly used trial design for evaluating interventions that can only be delivered at the cluster-level, it is often used to evaluate individual-level interventions.[1,2,3] One of the reasons individual-level interventions are evaluated using cluster randomization is the concern over contamination such that those allocated to the control inadvertently receive the intervention, perhaps because of geographical or social proximity. When contamination operates in one direction only (eg, when comparing a novel intervention to usual care), and all other biases being absent, individual randomization will provide a lower bound for the effect that would be realized under the real-world situation of everyone being offered the intervention. We outline previously published formulae for the sample size required for a variety of different designs under individual and cluster randomization. For both individual and cluster randomization, we outline these formulae by considering any inflation or deflation required over a parallel individually randomized design using simple randomization. We use the term design effect to denote the inflation (or deflation) in sample size needed over that of simple individual randomization; and outline all these formulae in terms of these design effects. For reasons which become evident later, we define all formulae in terms of the total number of measurements as opposed to the total number of participants (on whom multiple measurements might be taken)
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