The receiver operating characteristic (ROC) regression-modeling technique was used to evaluate the influence of race on the diagnostic accuracies of the ONH, RNFL, and macular parameters with RTVue in glaucoma, with adjustment and evaluation of the possible confounding effects of age, disease severity, and size of the optic disc. This modeling approach was used previously by Medeiros et al.
20 for evaluation of the effect of covariates on the performance of diagnostic tests in glaucoma. The methodology allows the evaluation of the influence of covariates on the diagnostic performance of the test, so that ROC curves for specific values of the covariate of interest can be obtained. Also, it allows adjustment for the possible confounding effects of other covariates. Details of the modeling procedure have been described previously.
20 In brief, the ROC
X,XD(
q) is the probability that a diseased individual with disease-specific covariates
XD (that is, covariates specific to diseased subjects, such as disease severity) and common covariates
X (covariates common to both diseased and healthy subjects, such race and optic disc size) has test results
YD 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, Φ is the normal cumulative distribution function (cdf), and Φ
−1(
q) is the inverse normal cdf of the false-positive rate (FPR). If the coefficient for a specific variable
X (say β) is greater than 0, then the discrimination between diseased and nondiseased subjects increases with increasing values of this covariate. Similarly, if the coefficient for the disease-specific covariate
XD (say β
D) is greater than 0, then diseased subjects with higher values of this covariate are more distinct from nondiseased subjects than are diseased subjects with lower values of
XD. In the present study, the following ROC regression model was fit to assess the influence of race, age, 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 Visual Field Index (VFI). Interaction terms between the variables and Φ
−1(
q) can be included to allow the effects of the covariates to differ by various amounts, depending on the FPR
q (or specificity 1 −
q)—that is, to influence the shape of the curve.