A comparison of different prediction models in glaucoma screening

Abstract

Purpose: This study analyses the possibility of risk-assessment the risk of developing glaucoma over the period of 1 year based on the "Number" (provided by the Nerve Fiber Analyzer) by using a multitude of parameters that are gathered by several different eye examination techniques at the initial investigation. Methods: Within the above-mentioned study, a total of 336 patients with an increased risk of having glaucoma were analyzed. The complete ophthalmological examination included biomicroscopy of the optic nerve head, achromatic automated perimetry (Humphrey Field Analyzer), quantitative disc (Topographic Scanning Systems, TopSS®) and nerve fiber layer measurements (Nerve Fiber Layer Analyzer, GDx®) at the beginning of the study and 1 year thereafter. Three visual field parameters (mean deviation, corrected pattern standard deviation, glaucoma hemifield test), 7 topographic and 19 polarimetric parameters were used for these statistical analyses. The problem was considered as a regression problem (RP) as well as a classification problem (CP): the simplest predictor, that is the "Number" at the initial investigation (CP), linear discriminant analyses without and with a forward stepwise variable selection algorithm (CP), four different classification tree analyses (CP) and different types of neural networks: regression networks (RP), linear networks (CP) and three layer perceptron networks (CP) with various variable selection algorithms and network architectures were applied in order to build models with sufficient prediction power. All models, except the simple predictor were tested with independent test set data, to ensure first a generalization for new patients and secondly that the results are not artifacts of the training process. The performance of the models was measured by sensitivity and specificity rates for CPs, multiple correlation coefficients between predicted and actual outcome for regression networks in each of the samples. Due to the large amount of computations, the models were computed for right eyes only. Results: The simple predictor showed a specificity rate of 73% (95% CI: 65-80%) based on all observations. The following specificity rates could be found in the test samples: the linear discriminant analysis (LDA) without variable selection algorithm could not be applied, LDA plus variable selection algorithm: 85% (95% CI: 75-93%), four different models based on classification tree analyses: 87% (95% CI: 70-96%), 90% (95% CI: 74-98%), %), 87% (95% CI: 70-96%) and 71% (95% CI: 52-86%); linear neural networks (not all eyes were classified due to the doubt option) 95% (95% CI: 75-100%) and three layer perceptron network (also with doubt option): 100% (95% CI: 81-100%). The simple predictor showed a sensitivity rate of 76% (95% CI: 69-83%) based on all observations. The following sensitivity rates were observed in the test samples: the LDA without variable selection algorithm could not be applied, LDA plus variable selection algorithm: 61% (95% CI: 49-72%), four different models based on classification tree analyses: 63% (95% CI: 47-77%), 58% (95% CI: 42-72%), 63% (95% CI: 47-77%) and 61% (95% CI: 44-75%); linear neural networks (not all eyes were classified due to the doubt option): 78% (95% CI: 56-100%) and three layer perceptron network (also with doubt option): 88% (95% CI: 47-100%). The regression network showed a correlation of 0.63 (95% CI: 0.49-0.76). Conclusion: This study yielded a negative result as to the initial exam, since in spite of different approaches none of the eight considered, quite elaborate models showed a considerably better performance than the simple predictor. Since the mean of the "Number" did not change considerably and the correlation of the "Number" (initial exam vs findings at 1 year) was moderate at best, we suggest to extend the prediction periods to 2 or even 5 years. During a longer prediction period, more changes of the "Number" may occur and further attempts can be made to find prediction models that can serve as an early warning system for the clinician.