Optimal design of cluster randomised trials with continuous recruitment and prospective baseline period

Abstract

Background: Cluster randomised trials, like individually randomised trials, may benefit from a baseline period of data collection. We consider trials in which clusters prospectively recruit or identify participants as a continuous process over a given calendar period, and ask whether and for how long investigators should collect baseline data as part of the trial, in order to maximise precision.

Methods: We show how to calculate and plot the variance of the treatment effect estimator for different lengths of baseline period in a range of scenarios, and offer general advice.

Results: In some circumstances it is optimal not to include a baseline, while in others there is an optimal duration for the baseline. All other things being equal, the circumstances where it is preferable not to include a baseline period are those with a smaller recruitment rate, smaller intracluster correlation, greater decay in the intracluster correlation over time, or wider transition period between recruitment under control and intervention conditions.

Conclusion: The variance of the treatment effect estimator can be calculated numerically, and plotted against the duration of baseline to inform design. It would be of interest to extend these investigations to cluster randomised trial designs with more than two randomised sequences of control and intervention condition, including stepped wedge designs.

Keywords: Efficient design; group randomised trials; power; sample size.

Figure 1.

Designs for two-arm, cluster randomised trials with continuous recruitment and a prospective baseline. (a) No transition period; (b) recruitment/identification suspended in both arms during a transition period; (c) recruitment/identification suspended in the intervention arm, but not the control arm, during a transition period; (d)–(f) as for (a)–(c), but the intervention arm begins the trial in the intervention condition, rather than beginning in the control condition and crossing over to the intervention.

Figure 2.

Variance of the treatment effect estimator according to the number of participants recruited in each cluster (m), the timing of cross-over in the intervention arm, the intracluster correlation for two participants sampled from the same cluster at the same time (ρ), and the factor by which this intracluster correlation is reduced for two participants sampled from the same cluster at opposite ends of the trial period (τ). There is no transition period, and the time effect is assumed to be a discontinuous at the cross-over. The variance in a given application is the value shown on the axis multiplied by ${\sigma }^2/J$, where ${\sigma }^2$ is the variance of the outcome and $J$ is the number of clusters in each arm.

Figure 3.

As Figure 2, but the time effect is assumed to be cubic polynomial.

Figure 4.

Results in the case $m=100,\rho =0.05,\tau =0.5$, with no transition period, according to the degree of the polynomial assumed for the time effect. At the bottom are the results when the time effect is discontinuous at the cross-over.

Figure 5.

Effect of a transition period on the variance of the treatment effect estimator. Cross-over is the time at which recruitment/identification under the intervention condition begins in the intervention arm. The time effect is assumed to be discontinuous at the cross-over. (a) and (b) $m=100,\rho =0.05$ with recruitment/identification in the control arm (a) suspended or (b) continued during the transition period; (c) the example of Project Masihambisane, running for 24 months with a 9-month transition period (or a 3-month transition period if the intervention is implemented straight away, with no baseline).

Figure 6.

As Figure 5, but the time effect is assumed to be a cubic polynomial. (a) and (b) $m=100,\rho =0.05$ with recruitment/identification in the control arm (a) suspended or (b) continued during the transition period.