Estimating Association Between Paired Outcomes in Clustered Data with Informative Subgroup Size
Informative cluster size (ICS) and informative subgroup size (ISS) can distort marginal association estimates when the number of observed units, or their distribution across outcome-defined categories, is related to the outcomes under study. This issue is especially relevant for paired outcomes, where the observed association can depend on cluster size, paired-category composition, and the process by which units become available for analysis. We propose three weighted estimating approaches for marginal association between paired outcomes in clustered data. The weights are derived from within-cluster resampling arguments and extend inverse cluster-size and subgroup-size weighting to paired outcome categories. We also modify an existing ISS testing procedure by utilizing Stouffer's method to reduce computational burden. To evaluate the methods, we develop a simulator for clustered paired outcomes that separates unit-level association, latent cluster-level association, and outcome-dependent retention. Simulations show that pair-based weighting can reduce bias when association arises through unit-level dependence and subgroup composition is informative, but can attenuate association carried by latent cluster-level structure. Typical inverse-cluster weighting remains more stable when the association is primarily cluster-level. Application to NHANES oral-health data shows small positive periodontal and caries associations overall, with filled-surface outcomes showing stronger ISS evidence and greater sensitivity to pair-based weighting than decayed-surface outcomes. These results indicate that marginal association under ICS and ISS should be interpreted in relation to the source of association, observed-unit structure, and assumptions used to choose the weighting scheme.