April 2011
Volume 52, Issue 14
Free
ARVO Annual Meeting Abstract  |   April 2011
Does Least-Squares Regression Give Misleading Results When Applied To Data From Structure-Function Studies In Glaucoma?
Author Affiliations & Notes
  • Ivan Marin-Franch
    School of Optometry, Indiana University, Bloomington, Indiana
    Optometry and Visual Science, City University London, London, United Kingdom
  • David P. Crabb
    Optometry and Visual Science, City University London, London, United Kingdom
  • William H. Swanson
    School of Optometry, Indiana University, Bloomington, Indiana
  • Rizwan Malik
    Glaucoma Research Unit, Moorfields Eye Hospital, London, United Kingdom
  • David F. Garway-Heath
    Glaucoma Research Unit, Moorfields Eye Hospital, London, United Kingdom
  • Footnotes
    Commercial Relationships  Ivan Marin-Franch, None; David P. Crabb, None; William H. Swanson, Zeiss-Meditec (C); Rizwan Malik, None; David F. Garway-Heath, Carl Zeiss Meditec (F, C, R), Heidelberg Engineering (F, R), OptoVue (F)
  • Footnotes
    Support  NIH R01EY007716, NEI EY08208, and NEI EY11008
Investigative Ophthalmology & Visual Science April 2011, Vol.52, 4146. doi:
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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)

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Abstract
 
Purpose:
 

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.

 
Methods:
 

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.

 
Results:
 

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. 

 

 
Conclusions:
 

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.

 
Keywords: clinical (human) or epidemiologic studies: biostatistics/epidemiology methodology • perimetry • nerve fiber layer 
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