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Estimation of rank correlation for clustered data
Author(s) -
Rosner Bernard,
Glynn Robert J.
Publication year - 2017
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7257
Subject(s) - pearson product moment correlation coefficient , statistics , intraclass correlation , bivariate analysis , estimator , mathematics , correlation , independent and identically distributed random variables , rank correlation , probit model , correlation coefficient , interclass correlation , partial correlation , rank (graph theory) , covariate , random variable , combinatorics , geometry , psychometrics
It is well known that the sample correlation coefficient ( R xy ) is the maximum likelihood estimator of the Pearson correlation ( ρ xy ) 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 ρ xy for 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.