Work

Estimation of rank correlation for clustered data

Year: 2017

Type: article

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 ρxy 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 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.

Source: Statistics in Medicine

DOI: 10.1002/sim.7257

Authors: Bernard Rosner, Robert J. Glynn

Institution: Harvard University

Language: English

Topic: Statistical Methods and Bayesian Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: green

Funder: National Eye Institute