To evaluate the effects of various clinical factors on the glaucoma diagnostic capability of each macular and RNFL thickness parameter, multivariate ROC regression analysis was performed as proposed by Alonzo and Pepe.
15 The ROC regression model (ROC generalized linear model)
15 with probit link can be written as
where α
1 and α
2 are the intercept and slope of the ROC curve, respectively. When
q is 1-specificity of the test, ROC(
q) represents sensitivity. The coefficient β for the covariate
X greater than zero, which represents the discrimination between those with disease and those without disease, increases with increasing values of
X. Discrimination increases with the increasing value of a certain covariate,
X, when the coefficient, β, is greater than zero. Interaction terms between the variables and Φ
−1(
q) were included to allow the effects of the covariates to differ by varying amounts, depending on the
FPRq (or specificity1 −
q)—that is, to influence the shape of the curve. However, we found no covariate had a significant effect on the interaction term. Thus, the interaction terms were omitted in the final models. Age and sex were adjusted using a linear model, with empirically estimated error distribution.
16,17 To obtain confidence intervals for regression parameters, a bootstrap resampling procedure was used (
n = 1000 resamples). Univariate analysis was performed using each variable of VF_mean deviation (MD), VF_PSD, visual field index (VFI), spherical equivalent (SE), disc_area determined by Cirrus HD-OCT optic disc cube mode, VA, SS, and CCT. Among those, a set of variables that met a significance level <0.2 was entered in a multivariate regression analysis.
P < 0.05 was considered significant. A final model with no significant factors for each parameter is not presented.