Details of the modeling procedure have been described previously.
18–22 In brief, the ROC
X, XD (
q) is the probability that a diseased individual with disease-specific covariates X
D (that is, covariates specific to diseased subjects, such as disease severity) and common covariates X (covariates common to both diseased and healthy subjects, such as optic disc size) has test results Y
D that are greater than or equal to the
qth quantile of the distribution of test results from nondiseased individuals. That is, when the specificity of the test is 1 −
q, the sensitivity is ROC
X, XD (
q). The general ROC regression model can be written as
where the coefficients α
1 and α
2 are the intercept and slope of the ROC curve, respectively, and Φ is the normal cumulative distribution function (cdf) and Φ
−1(
q) is the inverse normal cdf of the false positive rate. If the coefficient for a specific variable X (say, β) is greater than zero, then the discrimination between diseased and nondiseased subjects increases with increasing values of this covariate. Similarly, if the coefficient for the disease-specific covariate X
D (say, β
D) is greater than zero, then diseased subjects with larger values of this covariate are more distinct from nondiseased subjects than are diseased subjects with smaller values of X
D. In the present study, the following ROC regression model was fitted to assess the influence of the disease severity and optic disc size on the diagnostic performance of the ONH, RNFL, and macular parameters of the RTVue:
where severity is a continuous variable as determined by the VFI, and disc size is a continuous variable as determined by the HRT disc area. An interaction term between disc size and severity was included to assess whether the effect of disease severity was similar or different across different disc sizes. The effects of age, race, and optic disc area on the RTVue parameters are still unknown but have been reported with other imaging instruments.
1–8,23–26 Therefore, to avoid any potential bias due to group selection, all ROC analyses were adjusted for differences between glaucoma and control eyes for these variables. The model adjusts for the differences in variables between normal and glaucoma groups by fitting a linear regression of the marker distribution on the adjustment variables among controls. Standardized residuals based on this fitted linear model are used in place of the marker values for cases and controls.