Inferring marginal association with paired and unpaired clustered data

In the marginal analysis of clustered data, where the marginal distribution of interest is that of a typical observation within a typical cluster, analysis by reweighting has been introduced as a useful tool for estimating parameters of these marginal distributions. Such reweighting methods have foundation in within-cluster resampling schemes that marginalize potential informativeness due to cluster size or within-cluster covariate distribution, to which reweighting methods are asymptotically equivalent. In this paper, we introduce a reweighting scheme for the marginal analysis of clustered data that generalizes prior reweighting methods, with a particular application to measuring bivariate correlation in unpaired clustered data, in which observations of two random variables are not naturally paired at the within-cluster level. We develop unpaired clustered data analogs of well-known product moment correlation coefficients (Pearson, Spearman, phi), as well as the polyserial coefficient for measuring correlation between one discrete and one continuous variable. We evaluate the performance of these coefficients via a simulation study and demonstrate their use by finding no statistically significant association between dental caries at an early age and dental fluorosis at age 13 using a large dental dataset.