The primary purpose of the study was to determine whether the baseline GPS is predictive of progression. Other variables analyzed as potential risk factors were age, baseline IOP, CCT, and the baseline SAP visual field index PSD. Hazard ratios (HRs) for the association between GPS parameters and the development of a documented progression were obtained by Cox proportional hazards models. We report HRs from univariate models, which do not adjust for the presence of other factors, as well as adjusted HRs from multivariate Cox proportional hazards models. For the multivariate models, we report hazard ratios after adjustment for age, baseline IOP, CCT, and SAP PSD. These variables have been reported to be significantly associated with the risk of development of glaucomatous visual field loss or optic disc deterioration among patients with ocular hypertension or suspected glaucoma.
14 15 16
We also evaluated the ability of subjective stereophotograph evaluation (grading and vertical cup/disc ratio) in predicting the development of progression. Univariate hazard ratios were reported for stereophotograph grading (glaucoma versus normal) as well as for vertical CDR. Adjusted HRs were also reported for these variables after adjustment for age, baseline IOP, CCT, and SAP PSD.
As the magnitude of a hazard ratio for a particular variable depends on its unit of measurement, a direct comparison of HRs would be an inappropriate way of comparing the predictive abilities of GPS and stereophotograph assessment. For this purpose, we used the
c-index, as suggested by Harrell.
17 The
c-index is similar to the area under the receiver operating characteristic (ROC) curve and is frequently used to evaluate the discriminating ability of predictive models in survival data. It is calculated as the proportion of all usable subject pairs in which the predictions and outcomes are concordant. If the predicted survival time is larger for the subject who actually survived longer, the predictions of the pair are concordant with the outcomes. In predicting the time to an event,
c is calculated by including all possible pairs of subjects, at least one of whom has experienced the event (viz., progression). Two subjects’ survival times cannot be ordered if both subjects are censored or if one has failed and the follow-up time of the other is less than the failure time of the first.
18 A
c-index of 0.5 indicates random predictions, whereas 1.0 indicates perfect prediction. The
c-index was calculated for multivariate models, including GPS, and adjusting for age, baseline IOP, CCT, and SAP PSD, as well as for multivariate models including stereophotograph parameters and adjusting for the same variables. Therefore, each multivariate model contained the combination of an optic disc parameter (objective versus subjective) plus other variables previously identified as significantly associated with the risk of the development of glaucoma. To test for the significance of the difference in discrimination between two models, we used the rcorrp.cens function from Harrell’s Hmisc/Design library.
17 This computes U statistics for testing whether the predictions of one model are more concordant with actual observations than those of another model.
To adjust for potentially confounding effects of treatment, these analyses were also performed incorporating treatment as a time-dependent covariate.
Statistical analyses were performed with commercial software packages (SPSS, ver. 15.0; SPSS, Chicago, IL; Stata, ver. 9.0; StataCorp, College Station, TX; and S-PLUS ver. 6.0; Insightful Corp., Seattle, WA). The α level (type I error) was set at 0.05.