Tests for informative cluster size using a novel balanced bootstrap scheme.

Clustered data are often encountered in biomedical studies, and to date, a number of approaches have been proposed to analyze such data. However, the phenomenon of informative cluster size (ICS) is a challenging problem, and its presence has an impact on the choice of a correct analysis methodology. For example, Dutta and Datta (2015, Biometrics) presented a number of marginal distributions that could be tested. Depending on the nature and degree of informativeness of the cluster size, these marginal distributions may differ, as do the choices of the appropriate test. In particular, they applied their new test to a periodontal data set where the plausibility of the informativeness was mentioned, but no formal test for the same was conducted. We propose bootstrap tests for testing the presence of ICS. A balanced bootstrap method is developed to successfully estimate the null distribution by merging the re-sampled observations with closely matching counterparts. Relying on the assumption of exchangeability within clusters, the proposed procedure performs well in simulations even with a small number of clusters, at different distributions and against different alternative hypotheses, thus making it an omnibus test. We also explain how to extend the ICS test to a regression setting and thereby enhancing its practical utility. The methodologies are illustrated using the periodontal data set mentioned earlier.