Estimating a preference-based index from the Clinical Outcomes in Routine Evaluation - Outcome Measure (CORE-OM): valuation of CORE-6D

Background: The Clinical Outcomes in Routine Evaluation - Outcome Measure (CORE-OM) is used to evaluate the effectiveness of psychological therapies in people with common mental disorders. The objective of this study was to estimate a preference-based index for this population using CORE-6D, a health state classification system derived from CORE-OM consisting of a 5-item emotional component and a physical item, and to demonstrate a novel method for generating states that are not orthogonal. Methods: Rasch analysis was used to identify 11 plausible ‘emotional’ health states from CORE-6D (rather than conventional statistical design that would generate implausible states). By combining these with the 3 response levels of the physical item of CORE-6D, 33 plausible health states can be described, of which 18 were selected for valuation. An interview valuation survey of 220 members of public in South Yorkshire, UK, was undertaken using the time-trade-off method to value the 18 health states; regression analysis was subsequently used to predict values for all possible states described by CORE-6D. Results: A number of multivariate regression models were built to predict values for the 33 plausible health states of CORE-6D, using the Rasch logit value of the emotional health state and the response level of the physical item as independent variables. A cubic model with high predictive value (adjusted R squared 0.990) was finally selected, which can be used to predict utility values for all 927 states described by CORE-6D. Conclusion: The CORE-6D preference-based index will enable the assessment of cost-effectiveness of interventions for people with common mental disorders using existing and prospective CORE-OM datasets. The new method for generating states may be useful for other instruments with highly correlated dimensions

Estimating a preference-based index from the clinical outcomes in routine evaluation-outcome measure (CORE-OM): Valuation of CORE-6D

Background. The Clinical Outcomes in Routine Evaluation–Outcome Measure (CORE-OM) is used to evaluate the effectiveness of psychological therapies in people with common mental disorders. The objective of this study was to estimate a preference-based index for this population using CORE-6D, a health state classification system derived from the CORE-OM consisting of a 5-item emotional component and a physical item, and to demonstrate a novel method for generating states that are not orthogonal. Methods. Rasch analysis was used to identify 11 emotional health states from CORE-6D that were frequently observed in the study population and are, thus, plausible (in contrast, conventional statistical design might generate implausible states). Combined with the 3 response levels of the physical item of CORE-6D, they generate 33 plausible health states, 18 of which were selected for valuation. A valuation survey of 220 members of the public in South Yorkshire, United Kingdom, was undertaken using the time tradeoff (TTO) method. Regression analysis was subsequently used to predict values for all possible states described by CORE-6D. Results. A number of multivariate regression models were built to predict values for the 33 health states of CORE-6D, using the Rasch logit value of the emotional state and the response level of the physical item as independent variables. A cubic model with high predictive value (adjusted R2 = 0.990) was selected to predict TTO values for all 729 CORE-6D health states. Conclusion. The CORE-6D preference-based index will enable the assessment of cost-effectiveness of interventions for people with common mental disorders using existing and prospective CORE-OM data sets. The new method for generating states may be useful for other instruments with highly correlated dimensions

On subgroups in division rings of type 22

Let $D$ be a division ring with center $F$. We say that $D$ is a {\em division ring of type $2$} if for every two elements $x, y\in D,$ the division subring $F(x, y)$ is a finite dimensional vector space over $F$. In this paper we investigate multiplicative subgroups in such a ring.Comment: 10 pages, 0 figure

A local-global principle for linear dependence of noncommutative polynomials

A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the proof yields generalizations to directional local linear dependence and evaluations in general algebras over fields of arbitrary characteristic. A main feature of the proof is that it makes it possible to deduce bounds on the size of the matrices where the (directional) local linear dependence needs to be tested in order to establish linear dependence.Comment: 8 page

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

Regular Moebius transformations of the space of quaternions

Let H be the real algebra of quaternions. The notion of regular function of a quaternionic variable recently presented by G. Gentili and D. C. Struppa developed into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the quaternionic setting introduces new phenomena. This paper studies regular quaternionic transformations. We first find a quaternionic analog to the Casorati-Weierstrass theorem and prove that all regular injective functions from H to itself are affine. In particular, the group Aut(H) of biregular functions on H coincides with the group of regular affine transformations. Inspired by the classical quaternionic linear fractional transformations, we define the regular fractional transformations. We then show that each regular injective function from the Alexandroff compactification of H to itself is a regular fractional transformation. Finally, we study regular Moebius transformations, which map the unit ball B onto itself. All regular bijections from B to itself prove to be regular Moebius transformations.Comment: 12 page

Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential

We present a detailed numerical study of the effect of a disordered potential on a confined one-dimensional Bose-Einstein condensate, in the framework of a mean-field description. For repulsive interactions, we consider the Thomas-Fermi and Gaussian limits and for attractive interactions the behavior of soliton solutions. We find that the disorder average spatial extension of the stationary density profile decreases with an increasing strength of the disordered potential both for repulsive and attractive interactions among bosons. In the Thomas Fermi limit, the suppression of transport is accompanied by a strong localization of the bosons around the state k=0 in momentum space. The time dependent density profiles differ considerably in the cases we have considered. For attractive Bose-Einstein condensates, a bright soliton exists with an overall unchanged shape, but a disorder dependent width. For weak disorder, the soliton moves on and for a stronger disorder, it bounces back and forth between high potential barriers.Comment: 13 pages, 13 figures, few typos correcte