Aging functions and multivariate notions of NBU and IFR

For d≥2, let X=(X1, …, Xd) be a vector of exchangeable continuous lifetimes with joint survival function $\overline{F}$. For such models, we study some properties of multivariate aging of $\overline{F}$ that are described by means of the multivariate aging function $B_{\overline{F}}$, which is a useful tool for describing the level curves of $\overline{F}$. Specifically, the attention is devoted to notions that generalize the univariate concepts of New Better than Used and Increasing Failure Rate. These multivariate notions are satisfied by random vectors whose components are conditionally independent and identically distributed having univariate conditional survival function that is New Better than Used (respectively, Increasing Failure Rate). Furthermore, they also have an interpretation in terms of comparisons among conditional survival functions of residual lifetimes, given a same history of observed survivals

A characterization of the multivariate excess wealth ordering

In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate right-spread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the excess wealth ordering by Shaked and Shanthikumar (1998) and Fernández-Ponce et al. (1998). The multivariate excess wealth function enable us to define a new stochastic comparison which is weaker than the multivariate dispersion orderings. Also, some properties relating the multivariate excess wealth order with stochastic dependence are describe

Types of dependence and time-dependent association between two lifetimes in single parameter copula models

Most publications on modeling insurance contracts on two lives, assuming dependence of the two lifetimes involved, focus on the time of inception of the contract. The dependence between the lifetimes is usually modeled through a copula and the effect of this dependence on the pricing of a joint life policy is measured. This paper investigates the effect of association at the outset on the mortality in the future. The conditional law of mortality of an individual, given his survival and given the life status of the partner is derived. The conditional joint survival distribution of a couple at any duration, given that the two lives are then alive, is also derived. We analyze how the degree of dependence between the two members of a couple varies throughout the duration of a contract. We will do that for (mainly Archimedean) copula models, with one parameter for the degree of dependence. The conditional distributions hence derived provide the basis for the calculation of prospective provisions

Dementia and Primary-Care Health Measures:Hearing, Gait, and Markers of Inflammation

Dementia is a syndrome associated with declining cognitive function that has a variety of types and causes, and is encountered frequently in general medical practice. Researchers are actively exploring possible risk factors for dementia. The St. Louis University Mental Status (SLUMS) exam is a dementia-screening exam used in primary care visits to detect cognitive impairment that may be a sign of dementia. This study compared scores on the SLUMS exam to other measures recorded in a typical primary care visit in 86 patients of age 65 and older to look for correlations between indicators of health, such as physical examination measures and complete blood count panels, and cognitive impairment, as measured by score on the SLUMS exam. Abnormal gait was associated with a lower score on the SLUMS exam compared to normal (p=.006), failure of the hearing test in both ears was associated with a lower score on the SLUMS exam compared to patients passing the hearing test in one or both ears (p=.046), red blood cell count was positively correlated with SLUMS exam score (p=.020), white blood cell count was negatively correlated with SLUMS exam score (p=.003), and serum albumin levels were negatively correlated with SLUMS exam score (p=.002). These data support the view that both physical impairments and markers of an inflammatory response are related to dementia

Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

Genetic analysis of cortical thickness and fractional anisotropy of water diffusion in the brain

Objectives: The thickness of the brain’s cortical gray matter (GM) and the fractional anisotropy (FA) of the cerebral white matter (WM) each follow an inverted U-shape trajectory with age. The two measures are positively correlated and may be modulated by common biological mechanisms. We employed four types of genetic analyses to localize individual genes acting pleiotropically upon these phenotypes. Methods: Whole-brain and regional GM thickness and FA values were measured from high-resolution anatomical and diffusion tensor MR images collected from 712, Mexican American participants (438 females, age=47.9±13.2 years) recruited from 73 (9.7±9.3 individuals/family) large families. The significance of the correlation between two traits was estimated using a bivariate genetic correlation analysis. Localization of chromosomal regions that jointly influenced both traits was performed using whole-genome quantitative trait loci (QTL) analysis. Gene localization was performed using SNP genotyping on Illumina 1M chip and correlation with leukocyte-based gene-expression analyses. The gene-expressions were measured using the Illumina BeadChip. These data were available for 371 subjects. Results: Significant genetic correlationwas observed amongGMthickness and FA values. Significant logarithm of odds (LOD≥3.0) QTLs were localized within chromosome 15q22–23. More detailed localization reported no significant association (p <5·10−5) for 1565 SNPs located within the QTLs. Post hoc analysis indicated that 40% of the potentially significant (p ≤10−3) SNPs were localized to the related orphan receptor alpha (RORA) and NARG2 genes. A potentially significant association was observed for the rs2456930 polymorphism reported as a significant GWAS finding in Alzheimer’s disease neuroimaging initiative subjects. The expression levels for RORA and ADAM10 genes were significantly (p <0.05) correlated with both FA and GM thickness. NARG2 expressions were significantly correlated with GM thickness (p <0.05) but failed to show a significant correlation (p =0.09) with FA. Discussion: This study identified a novel, significant QTL at 15q22–23. SNP correlation with gene-expression analyses indicated that RORA, NARG2, and ADAM10 jointly influenceGM thickness and WM–FA values

Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach

In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing