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Addititional file 1. Figure 1 Study flow-chart. AVA, aortic valve area; AS, aortic stenosis; F/U, follow up. Figure 2 Survival of patients with moderate aortic stenosis who were without severe morbidities or left ventricular dysfunction, with survival times censored at aortic valve replacement (N = 461). (A) Observed survival in comparison to the expected survival based on the age- and sex-matched total Minnesota population. (B) Observed survival according to New York Heart Association (NYHA) functional class. Figure 3. Survival of patients with moderate aortic stenosis according to stroke volume index (SVi) 0.3 m/s/y vs. ≤ 0.3 m/s/y) in patients with available echocardiographic follow-up (N = 505). (A) Observed survival free of death. (B) Observed survival free of death or heart failure (HF) hospitalization.

Table S2. Additional data collected during the study period. (DOC 43 kb)

Standard Protocol Items: Recommendations for Interventional Trials (SPIRIT) 2013 Checklist: recommended items to address in a clinical trial protocol and related documents. (DOC 120 kb)

Table S1. Baseline characteristics and secondary outcomes of the Seattle-PAP trial [40â 45]. (DOCX 21 kb)

Image analysis frequently deals with shape estimation and image reconstruction. The ob jects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a definition of set expectation using oriented distance functions and study the properties of the associated empirical set. Conditions are given such that the empirical average is consistent, and a method to calculate a confidence region for the expected set is introduced. The proposed method is applied to both real and simulated data examples., Comment: 26 pages, 10 figures