Aspects of matching and power in group randomized trials
A group randomized trial is an experiment in which groups, such as communities, schools or workplaces, are randomized to receive treatment or act as controls. Frequently, the number of groups is small. Because it is the groups that are randomized, the statistical analysis may often be conducted using summary statistics for each group.A key issue in the design of group randomized trials is whether a matched or unmatched design should be used. Because the number of groups is often small, any imbalance between the treatment and control groups with respect to some important characteristic is more apparent, and can lead to the suggestion that an observed treatment effect is due to imbalance rather than to the treatment. Matching can deflect that suggestion.Matching has countervailing effects on the power of the trial. It potentially increases power by reducing variability, but reduces power because of the loss of degrees of freedom when the number of groups is small. The question therefore arises as to whether a matched design mandates a matched analysis, or whether the matching may be ignored in the analysis, and the power lost through loss of degrees of freedom recovered.This dissertation examines the consequences of ignoring the matching in the analysis. Group summary statistics in a matched trial may be modeled by a correlated bivariate normal distribution, the correlation representing the effectiveness of the matching. We show that when the matching induces a negative correlation, ignoring the matching leads to an anti-conservative test, and thus under such circumstances may not be ignored. When the matching induces a positive correlation, the matching may be ignored.If the matching induces a positive correlation, ignoring the matching increases power when the correlation is small; retaining the effect of matching in the analysis increases power when the correlation is large.We advance a theorem that, when the matching is ignored, the power of the experiment increases with the correlation when the correlation is positive and the power is more than 50%.We derive and evaluate certain adaptive tests that adjust for the estimated correlation.
- Biostatistics