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On optimal transport maps between d1-concave densities
In this paper we extend the scope of Caffarelli’s contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probability densities in Rd. Our focus is on a broader category of densities, specifically those that are d1-concave and can be represented as V−d, where V is convex. By setting appropriate conditions, we derive linear or sublinear limitations for the optimal transport map. This leads us to a comprehensive Lipschitz estimate that aligns with the principles established in Caffarelli’s theorem.
Journal Article
Sample-Level and Individual-Level Risk-Tolerance Estimates from a DCE and a TT Exercise
Background Quantitative-estimates of risk tolerance can be useful for both regulatory and individualized clinical decision-making. However, little is known about how sample-level and individual-level measures of risk tolerance compare across preference-elicitation methods. Using a survey instrument designed for this purpose, we evaluated the convergent validity of sample-level estimates of maximum- acceptable risk (MAR) from a discrete-choice experiment (DCE) and a threshold technique (TT) exercise. Methods Patients with lower-limb intermittent claudication (IC) completed an online survey designed to elicit benefit risk tradeoffs between devices with varying risks of a repeat revascularization procedure and risks of death, both at 2 and 5 years. A 292 factorial design randomized patients to complete the DCE or TT first and to risk levels shown with or without icon arrays. The fixed level of benefit offered in the TT exercise was a reduction in the risk of a repeat procedure from 30% to 10% by 2 years, and from 40% to 30% by 5 years. Risk of death by 5 years with both decide options began at 8%, and increased by 2 percentage points (up to 20%) for the more effective device until the patient chose the less effective device. The TT directly provided lower bound risk-tolerance values. Interval regression also was applied to TT data to estimate sample-level MARs. MARs from the DCE were calculated with a random-parameters logit (RPL) model using the sample level distributions from benefits and risks of devices from which individual-level estimates were derived and truncated at 8% and 20%. Results Seven US medical centres recruited 272 patients with IC to complete the survey. Mean age was 70 years (SD = 10.1), 68% were male, and 92% were White. Sample-level MARs from the TT were 12.9% (95% CI 12.413.04) using direct responses and 14.1% (95% CI 13.514.6) with interval regression compared to 12.7% (95%CI 11.913.6) from the DCE. Individual-level MARs different between the ITT and DCE by less than 2 percentage-points for 53% of patients. The mean absolute difference between patients DCE and TT MARs was 2.5 (SD = 2.4). Results were consistent across versions with or without icon arrays. Conclusions Group-level mean MARs from the DCE and TT (direct response) were very similar. At the individual level, however, differences in MARs between the DCE and TT were observed. Uncertainty associated with individual-level estimates from the RPL mat contribute to individual-level differences.
Journal Article
Risk pricing strategies for public-private partnership projects
\"This book sets out the key principle strategies involved in risk pricing of PPP projects in a clear and accessible way and provides the reader with fundamental principles of risk pricing theories and enveloping processes\"-- Provided by publisher.
Book
COMPARING SELF-REPORTED MEASURES OF SUBJECTIVE COGNITIVE DECLINE
Abstract
Symptoms of subjective cognitive decline (SCD) can be early indicators of possible future dementia. Estimates of self-reported SCD prevalence are available from various data sources including the Behavioral Risk Factor Surveillance System’s (BRFSS) current Cognitive Decline Optional Module. Recent revisions to the Module were proposed based on input from subject matter experts, including reducing introductory phrasing and refining question and response options. It is unknown how these changes may impact estimates of SCD prevalence. To assess whether prevalence of SCD differs based on Module phrasing and conceptualizations of SCD-related questions, this analysis used data (n=3526) from the 2022 FallStyles survey. Respondents were randomly assigned to one of two groups receiving different sets of Module questions: group A received questions mirroring the former language and group B received the revised phrasing. Estimates were weighted to match the 2021 US Current Population Survey. SCD prevalence among respondents aged ≥18 years was 8.9% in group A versus 16.9% in group B. Among adults aged ≥45 years, SCD prevalence in group A (9.3%) was similar to the 2019-2020 BRFSS estimate (9.8%), while it was nearly double (17.6%) in group B. Within both groups, SCD prevalence was higher among those earning less than $25,000, with lower educational attainment, and who identified as female than their counterparts. Simplified prompts and refined questions may provide higher estimates of SCD prevalence. Given the subjective interpretation of respondents’ own memory changes involved in measuring SCD, understanding the impact of question phrasing and language is critical when interpreting resulting data.
Journal Article
Universal potential estimates for 1
We extend the so-called universal potential estimates of Kuusi-Mingione type (J. Funct. Anal. 262: 4205–4269, 2012) to the singular case 1
Journal Article