December 2010
Volume 51, Issue 12
Free
Letters to the Editor  |   December 2010
Author Response: Model-Fitting Adequacy and Clinical Rationality in Multivariate Linear Regression Analysis
Author Affiliations & Notes
  • Laurence Shen Lim
    Singapore Eye Research Institute, Singapore National Eye Centre, Singapore;
  • Tien Yin Wong
    Singapore Eye Research Institute, Singapore National Eye Centre, Singapore;
    the Department of Ophthalmology, Yong Loo Lin School of Medicine, National University of Singapore, Singapore; and
    the Centre for Eye Research Australia, University of Melbourne, Victoria, Australia.
Investigative Ophthalmology & Visual Science December 2010, Vol.51, 6897. doi:10.1167/iovs.10-5894
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      Laurence Shen Lim, Tien Yin Wong; Author Response: Model-Fitting Adequacy and Clinical Rationality in Multivariate Linear Regression Analysis. Invest. Ophthalmol. Vis. Sci. 2010;51(12):6897. doi: 10.1167/iovs.10-5894.

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      © ARVO (1962-2015); The Authors (2016-present)

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We are grateful for the interest shown by Hsieh in our paper on the distribution and determinants of ocular biometric parameters in the Singapore Malay Eye Study (SIMES). 1 In his letter, he offers his interpretation of the statistical analyses and results of our paper, and we would like to take this opportunity to provide clarification of some of the points that he raises. 
His main concern is that the standardized beta (β) coefficients derived from the multivariate adjusted linear regression models of the predictors of different biometric parameters, presented in Table 5 of our original paper, may be erroneous. For example, the standardized β for “Height, cm” of 0.162 for axial length (AL) is interpreted as implying that “when body height increases 10 cm, AL … will increase 1.62 mm.” We fully agree that, were this example the case, the results would be implausible. However, we want to point out that such an interpretation is only appropriately applied to the unstandardized coefficient or regression estimate, typically annotated as B in statistical software. In linear regression, the relationship is described by the equation: dependent variable = (B × predictor) + constant + error term. The standardized β coefficients presented in our table are the surrogates of Pearson's correlation coefficient and give indications of the relative influences of each predictor on the dependent rather than quantifications of the absolute magnitude of each relationship. 
We want to assure Hsieh and all our readers that every effort was made to ensure the greatest validity of the multivariate regression models. As Hsieh has pointed out, overparameterization is unlikely, given the small number of parameters relative to the 2788 observations in our sample. Predictors in the multivariate models were chosen based on biological plausibility and the published literature and were verified with the results of age- and sex-adjusted models before inclusion. Multiple collinearity was determined from the scrutiny of individual Pearson correlation coefficients, residuals, and tolerance measures. 
References
Lim LS Saw SM Jeganathan VS . Distribution and determinants of ocular biometric parameters in an Asian population: the Singapore Malay eye study. Invest Ophthalmol Vis Sci. 2010;51:103–109. [CrossRef] [PubMed]
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