title: Inferring marginal association with paired and unpaired clustered data.
abstract: 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.
authors.affiliation: 1 Department of Bioinformatics and Biostatistics, School of Public Health and Information Science, University of Louisville, USA.
authors.forename: Douglas J
authors.initials: DJ
authors.lastname: Lorenz
authors.affiliation: 2 Department of Preventive and Community Dentistry, College of Dentistry and Dental Clinics, Department of Epidemiology, College of Public Health, University of Iowa, USA.
authors.forename: Steven
authors.initials: S
authors.lastname: Levy
authors.affiliation: 3 Department of Biostatistics, College of Public Health and Health Professions College of Medicine, University of Florida, USA.
authors.forename: Somnath
authors.initials: S
authors.lastname: Datta
mesh_terms: D000293:Adolescent; D000465:Algorithms; D002648:Child; D016000:Cluster Analysis; D003627:Data Interpretation, Statistical; D016208:Databases, Factual; D003731:Dental Caries / Q000150:complications* / Q000453:epidemiology; D009050:Fluorosis, Dental / Q000209:etiology*; D006801:Humans; D064887:Observational Studies as Topic; D014481:United States / Q000453:epidemiology
keywords: Measures of association; clustered data; correlation; informative cluster size; marginal analysis