Nonparametric methods for clustered data in pre-post intervention design

Abstract

In pre-post factorial designs involving clustered units, parametric methods such as generalized linear mixed effects models are used to handle within subject correlations. However, the distributional and parametric model assumptions in these methods are not always satisfied, especially so with modern data sets, and are often difficult to verify in practice. Often times, the assumptions may not even be realistic when data are measured in a non-metric scale as commonly happens, for example, in Quality-of-Life outcomes. In this article, nonparametric effect-size measures for clustered data in factorial designs with pre-post measurements will be introduced. In our setup, the pre and post occasions may also be viewed as two treatment conditions. Arbitrary dependence among observations within a cluster and across treatment groups is allowed. The effect-size estimators along with their asymptotic properties for computing confidence intervals and performing hypotheses tests are investigated. The proposed methods handle within-cluster as well as between-cluster treatment assignments seamlessly. The methods are shown to be effective in finite samples using simulation studies and they have high powers, especially in situations with multiple forms of clustering. Applications are illustrated with data from a three-arm Randomized Trial of Indoor Wood Smoke reduction.