Estimating marginal association between paired outcomes in clustered data with an application to analyzing caries and periodontal disease data from the National Health and Nutrition Examination Survey

Abstract

The within-cluster subgroup composition of units can inform on the marginal distribution of those units outcomes, denoted informative subgroup size (ISS). Moreover, within-cluster subgroup composition of paired outcomes can allow one outcome to inform upon the marginal distribution of the other. If this type of ISS ignored, it can bias marginal association estimates by allowing subgroup composition to influence how clusters contribute to the analysis. We develop two weighting approaches for estimating marginal association between paired outcomes in this setting. The weights are derived using within-cluster resampling arguments and extend conventional cluster weighting to paired response subgroups. We adapt an existing test of marginal dependence to assess ISS by examining this subgroup structure in both directions. In simulated data exhibiting this bidirectional ISS, pair-based weighting reduced bias when association was primarily carried through the paired observations. These weights also allow scientifically or clinically meaningful dichotomizations to enter directly into the weighting scheme, with the choice of subgroup definition further improving estimation in several simulated settings. Application to NHANES oral-health data showed strong evidence of ISS for filled-surface outcomes across subgroups defined by clinical attachment loss and pocket depth, with the corresponding periodontal--caries associations generally small and positive. These methods provide a practical approach for estimating marginal association when paired subgroup composition is informative.

19 pages, 4 tables, 5 figures in Main.tex 11 pages, 6 tables in Supplementary.tex