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Ivan Marin-Franch, David P. Crabb, William H. Swanson, Rizwan Malik, David F. Garway-Heath; Does Least-Squares Regression Give Misleading Results When Applied To Data From Structure-Function Studies In Glaucoma?. Invest. Ophthalmol. Vis. Sci. 2011;52(14):4146.
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© ARVO (1962-2015); The Authors (2016-present)
To validate linear least-squares regression methods, widelyused in studies of relationships between measures of functionaland structural glaucomatous damage. Four methods, with differentassumptions on measurement errors, were considered: ordinaryleast-squares (OLS), major-axis (MA), standardized major-axis(SMA), and Deming regression.
Simulated data on structural and functional damage were generatedusing the linear model due to Hood & Kardon [Prog Ret EyeRes 2007;26:688-710]. Test-retest variability (measurement error)was added to simulated data, and OLS, MA, SMA, and Deming linesfitted. For Deming regression, standard deviations of test-retestvariabilities must be estimated. Fits were assessed by a statisticaltest for slope. Fits were obtained also for real data on glaucomatousdamage.
Figure shows examples of different fits.
Table shows results for a test for slope.
In simulations, thetrue slope was identified most reliably with Deming regression,an unsurprising result as Deming regression generalizes theother 3 methods. Slopes from fits to real data were generallysignificantly different from each other.
Inferences from linear regression are model dependent. Testsof linear relations between structure and function in glaucomamay be improved by the use of Deming regression, although itsapplication requires knowledge about test-retest variabilityof measures of glaucomatous damage.
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