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Abstract:
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It is well-known that the sample correlation coefficient (R_xy) is the maximum likelihood estimator (MLE) of the Pearson correlation (?_xy) for 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 MLE of ?_xy 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 estimation of rank correlation for clustered data by (a) converting ranks of both X and Y to the probit scale, (b) estimating the Pearson correlation between probit scores for X and Y, and (c) using the relationship between Pearson and rank correlation for normally distributed data. The validity of the methods in finite-sized samples is supported by simulation studies. Finally, 2 examples from ophthalmology & analgesic abuse are used to illustrate the methods.
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