Marginal association measures for clustered data

The use of correlation coefficients in measuring the association between two continuous variables is common, but regular methods of calculating correlations have not been extended to the clustered data framework. For clustered data in which observations within a cluster may be correlated, regular inferential procedures for calculating marginal association between two variables can be biased. This is particularly true for data in which the number of observations in a given cluster is informative for the association being measured. In this paper, we apply the principle of inverse cluster size reweighting to develop estimators of marginal correlation that remain valid in the clustered data framework when cluster size is informative for the correlation being measured. These correlations are derived as analogs to regular correlation estimators for continuous, independent data, namely, Pearson's ρ and Kendall's τ. We present the results of a simple simulation study demonstrating the appropriateness of our proposed estimators and the inherent bias of other inferential procedures for clustered data. We illustrate their use through an application to data from patients with incomplete spinal cord injury in the U.S.A.