title: Estimation of rank correlation for clustered data.
abstract: It is well known that the sample correlation coefficient (Rxy) is the maximum likelihood estimator of the Pearson correlation (ρxy) for independent and identically distributed (i.i.d.) bivariate normal data. However, this is not true for ophthalmologic data where X (e.g., visual acuity) and Y (e.g., visual field) are available for each eye and there is positive intraclass correlation for both X and Y in fellow eyes. In this paper, we provide a regression-based approach for obtaining the maximum likelihood estimator of ρxyfor clustered data, which can be implemented using standard mixed effects model software. This method is also extended to allow for estimation of partial correlation by controlling both X and Y for a vector U_ of other covariates. In addition, these methods can be extended to allow for estimation of rank correlation for clustered data by (i) converting ranks of both X and Y to the probit scale, (ii) estimating the Pearson correlation between probit scores for X and Y, and (iii) using the relationship between Pearson and rank correlation for bivariate normally distributed data. The validity of the methods in finite-sized samples is supported by simulation studies. Finally, two examples from ophthalmology and analgesic abuse are used to illustrate the methods. Copyright © 2017 John Wiley & Sons, Ltd.
authors.affiliation: Channing Division of Network Medicine, Harvard Medical School, 181 Longwood Avenue, Boston, MA, 02115, U.S.A.
authors.forename: Bernard
authors.identifier: 0000-0001-6907-0056
authors.initials: B
authors.lastname: Rosner
authors.affiliation: Department of Medicine, Division of Preventive Medicine, Harvard Medical School, 900 Commonwealth Avenue, Boston, MA, 02115, U.S.A.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Glynn
mesh_terms: D000700:Analgesics / Q000652:urine; D056808:Biostatistics; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009885:Ophthalmology / Q000706:statistics & numerical data; D012044:Regression Analysis; D012174:Retinitis Pigmentosa / Q000503:physiopathology; D018401:Sample Size; D012984:Software; D019966:Substance-Related Disorders / Q000652:urine; D014792:Visual Acuity; D014794:Visual Fields
chemical_list: D000700:Analgesics
keywords: Pearson correlation; clustered data; partial correlation; rank correlation