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