On design considerations and randomization-based inference for community intervention trials

This paper discusses design considerations and the role of randomization-based inference in randomized community intervention trials. We stress that longitudinal follow-up of cohorts within communities often yields useful information on the effects of intervention on individuals, whereas cross-sectional surveys can usefully assess the impact of intervention on group indices of health. We also discuss briefly special design considerations, such as sampling cohorts from targeted subpopulations (for example, heavy smokers), matching the communities, calculating sample size, and other practical issues. We present randomization tests for matched and unmatched cohort designs. As is well known, these tests necessarily have proper size under the strong null hypothesis that treatment has no effect on any community response. It is less well known, however, that the size of randomization tests can exceed nominal levels under the 'weak' null hypothesis that intervention does not affect the average community response. Because this weak null hypothesis is of interest in community intervention trials, we study the size of randomization tests by simulation under conditions in which the weak null hypothesis holds but the strong null hypothesis does not. In unmatched studies, size may exceed nominal levels under the weak null hypothesis if there are more intervention than control communities and if the variance among community responses is larger among control communities than among intervention communities; size may also exceed nominal levels if there are more control than intervention communities and if the variance among community responses is larger among intervention communities. Otherwise, size is likely near nominal levels. To avoid such problems, we recommend use of the same numbers of control and intervention communities in unmatched designs. Pair-matched designs usually have size near nominal levels, even under the weak null hypothesis. We have identified some extreme cases, unlikely to arise in practice, in which even the size of pair-matched studies can exceed nominal levels. These simulations, however, tend to confirm the robustness of randomization tests for matched and unmatched community intervention trials, particularly if the latter designs have equal numbers of intervention and control communities. We also describe adaptations of randomization tests to allow for covariate adjustment, missing data, and application to cross-sectional surveys. We show that covariate adjustment can increase power, but such power gains diminish as the random component of variation among communities increases, which corresponds to increasing intraclass correlation of responses within communities. We briefly relate our results to model-based methods of inference for community intervention trials that include hierarchical models such as an analysis of variance model with random community effects and fixed intervention effects. Although we have tailored this paper to the design of community intervention trials, many of the ideas apply to other experiments in which one allocates groups or clusters of subjects at random to intervention or control treatments.