Abstract
BackgroundIn a multicenter trial, responses for subjects belonging to a common center are correlated. Such a clustering is usually assessed through the design effect, defined as a ratio of two variances. The aim of this work was to describe and understand situations where the design effect involves a gain or a loss of power.MethodsWe developed a design effect formula for a multicenter study aimed at testing the effect of a binary factor (which thus defines two groups) on a continuous outcome, and explored this design effect for several designs (from individually stratified randomized trials to cluster randomized trials, and for other designs such as matched pair designs or observational multicenter studies).ResultsThe design effect depends on the intraclass correlation coefficient (ICC) (which assesses the correlation between data for two subjects from the same center) but also on a statistic S, which quantifies the heterogeneity of the group distributions among centers (thus the level of association between the binary factor and the center) and on the degree of global imbalance (the number of subjects are then different) between the two groups. This design effect may induce either a loss or a gain in power, depending on whether the S statistic is respectively higher or lower than 1.ConclusionWe provided a global design effect formula applying for any multicenter study and allowing identifying factors – the ICC and the distribution of the group proportions among centers – that are associated with a gain or a loss of power in such studies.
Highlights
In a multicenter trial, responses for subjects belonging to a common center are correlated
The design effect (Deff) is defined as the ratio of two variances: the variance of the estimator when the center effect is taken into account over the variance of the estimator under the hypothesis of a simple random sample [2,3]
To illustrate the impact of heterogeneity between the global group sizes on the design effect, we considered hypothetical situations, less likely to occur, where 10 centers recruit 20 subjects each, for balanced designs (i.e., n1 = n2, Table S4a in Additional file 1) and imbalanced designs (i.e., n1 ≠ n2, Table S4b in Additional file 1), and for different levels of heterogeneity of group distributions among centers and two intraclass correlation coefficient (ICC) values
Summary
Responses for subjects belonging to a common center are correlated. Such a clustering is usually assessed through the design effect, defined as a ratio of two variances. Multicenter studies involve correlation in data because subjects from the same center are more similar than are those from different centers [1]. Such a correlation potentially affects the power of standard statistical tests, and conclusions made under the assumption that data are independent can be invalidated.
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