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PURPOSE: To investigate the diagnostic capacity of spectral-domain optical coherence tomography (SD-OCT) combined with air-puff tonometry using artificial intelligence (AI) in differentiating between normal and keratoconic eyes. METHODS: Patients who had either undergone uneventful laser vision correction with at least 3 years of stable follow-up or those who had forme fruste keratoconus (FFKC), early keratoconus (EKC), or advanced keratoconus (AKC) were included. SD-OCT and biomechanical information from air-puff tonometry was divided into training and validation sets. AI models based on random forest or neural networks were trained to distinguish eyes with FFKC from normal eyes. Model accuracy was independently tested in eyes with FFKC and normal eyes. Receiver operating characteristic (ROC) curves were generated to determine area under the curve (AUC), sensitivity, and specificity values. RESULTS: A total of 223 normal eyes from 223 patients, 69 FFKC eyes from 69 patients, 72 EKC eyes from 72 patients, and 258 AKC eyes from 258 patients were included. The top AUC ROC values (normal eyes compared with AKC and EKC) were Pentacam Random Forest Index (AUC = 0.985 and 0.958), Tomographic and Biomechanical Index (AUC = 0.983 and 0.925), and Belin-Ambrósio Enhanced Ectasia Total Deviation Index (AUC = 0.981 and 0.922). When SD-OCT and air-puff tonometry data were combined, the random forest AI model provided the highest accuracy with 99% AUC for FFKC (75% sensitivity; 94.74% specificity). CONCLUSIONS: Currently, AI parameters accurately diagnose AKC and EKC, but have a limited ability to diagnose FFKC. AI-assisted diagnostic technology that uses both SD-OCT and air-puff tonometry may overcome this limitation, leading to improved treatment of patients with keratoconus. [ J Refract Surg . 2022;38(6):374–380.]

a b s t r a c tIt is well known that the literature on judgement aggregation inherits the impossibility results from the aggregation of preferences that it generalises. This is due to the fact that the typical judgement aggregation problem induces an ultrafilter on the set of individuals. We propose a model-theoretic framework for the analysis of judgement aggregation and show that the conditions typically imposed on aggregators induce an ultrafilter on the set of individuals, thus establishing a generalised version of the Kirman-Sondermann correspondence. In the finite case, dictatorship then immediately follows from the principality of an ultrafilter on a finite set. This is not the case for an infinite set of individuals, where there exist free ultrafilters, as Fishburn already stressed in 1970. Following Lauwers and Van Liedekerke's (1995) seminal paper, we investigate another source of impossibility results for free ultrafilters: the domain of an ultraproduct over a free ultrafilter extends the individual factor domains, such that the preservation of the truth value of some sentences by the aggregate model -if this is as usual to be restricted to the original domain -may again require the exclusion of free ultrafilters, leading to dictatorship once again.

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Abstract. It is well known that the literature on judgment aggregation inherits the impossibility results from the aggregation of preferences that it generalises. This is due to the fact that the typical judgment aggregation problem induces an ultralter on the the set of individuals, as was shown in a model theoretic framework by Herzberg and Eckert (2009), generalising the Kirman-Sondermann correspondence and extending the methodology of Lauwers and Van Liedekerke (1995). In the nite case, dictatorship then immediately follows from the principality of an ultralter on a nite set. This is not the case for an innite set of individuals, where there exist free ultralters, as Fishburn already stressed in 1970. The main problem associated with free ultralters in the literature on aggregation problems is however, the arbitrariness of their selection combined with the limited anonymity they guarantee (which already led Kirman and Sondermann (1972) to speak about invisible dictators). Following another line of Lauwers and Van Liedekerke's (1995) seminal paper, this note explores another source of impossibility results for free ultralters: The domain of an ultraproduct over a free ultralter extends the individual factor domains, such that the preservation of the truth value of some sentences by the aggregate model if this is as usual to be restricted to the original domain may again require the exclusion of free ultralters, leading to dictatorship once again.