Allowing for imprecision of the intracluster correlation coefficient in the design of cluster randomized trials

Abstract

The sample size required for a cluster randomized trial depends on the magnitude of the intracluster correlation coefficient (ICC). The usual sample size calculation makes no allowance for the fact that the ICC is not known precisely in advance. We develop methods which allow for the uncertainty in a previously observed ICC, using a variety of distributional assumptions. Distributions for the power are derived, reflecting this uncertainty. Further, the observed ICC in a future study will not equal its true value, and we consider the impact of this on power. We implement calculations within a Bayesian simulation approach, and provide one simplification that can be performed using simple simulation within spreadsheet software. In our examples, recognizing the uncertainty in a previous ICC estimate decreases expected power, especially when the power calculated naively from the ICC estimate is high. To protect against the possibility of low power, sample sizes may need to be very substantially increased. Recognizing the variability in the future observed ICC has little effect if prior uncertainty has already been taken into account. We show how our method can be extended to the case in which multiple prior ICC estimates are available. The methods presented in this paper can be used by applied researchers to protect against loss of power, or to choose a design which reduces the impact of uncertainty in the ICC.

Developments in cluster randomized trials and Statistics in Medicine

“…Turner et al [12] state that imprecision in the estimate of is not accounted for in this application, but their own method could easily be extended to do so. More experience on the application of internal pilot studies to such trials is clearly needed.…”

“…However, it is difficult to know how to use these for planning purposes. As Turner et al [12] have pointed out, for planning purposes it may be better to select a design on the basis of power averaged across uncertainty rather than calculate power from an informally assessed ICC value. Moreover, substitution of a conservative ICC such as the upper value from a 95 per cent confidence interval usually reduces the power for a fixed sample size estimate much more than a method which allows for the imprecision of the ICC.…”

“…This Bayesian approach towards the determination of sample size could then be followed by a statistical analysis within the traditional frequentist framework. Turner et al [12] showed that increasing the number of clusters enables the total sample size to be reduced for a given power. With a given number of subjects estimated from an unclustered design, increasing the number of clusters also considerably reduces the lower limit of the posterior distribution of power.…”

Bayesian statistics in medicine: a 25 year review

“…Binary data from cluster randomized trials could be analysed directly on the risk scale [452] and adjusting for baseline imbalances in repeated cross-sectional cluster randomized trials could account for baseline heterogeneity [453]. Imprecision of the intracluster correlation coefficient was allowed for in design of cluster randomized trials [454], and interval estimates obtained from modelling [455]. Bayesian methods provided a way of analysing rate-ratios of repeated events in cluster-randomized trials against trachoma [456].…”

Sample size considerations when groups are the appropriate unit of analysis

“…Step 2: Determine the intracluster correlation coefficient (ICC) In contrast, when data are clustered, finding the sample size required to produce statistically significant results involves more sophisticated calculations (Hayes & Bennett 1999;Turner, Prevost, & Thompson, 2004;Campbell, Thomson, Ramsay, MacLennan, & Grimshaw, 2004). Determining the optimal sample size where groups or clusters are involved requires calculations involving the number of groups or clusters, number of individuals in the groups, in addition to the power, significance level, and effect size the investigator seeks to achieve (Donner, Piaggio, & Villar, 2003).…”