Cost Sharing under Uncertainty: An Algorithmic Approach to Cooperative Interval-Valued Games

Recently, Branzei, Dimitrov, and Tijs (2003) introduced cooperative interval-valued games. Among other insights, the notion of an interval core has been coined and proposed as a solution concept for interval-valued games. In this paper we will present a general mathematical programming algorithm which can be applied to find an element in the interval core. As an example, we discuss lot sizing with uncertain demand to provide an application for interval-valued games and to demonstrate how interval core elements can be computed. Also, we reveal that pitfalls exist if interval core elements are computed in a straightforward manner by considering the interval borders separately.

The bovine dilated cardiomyopathy locus maps to a 1.0-Mb interval on chromosome 18

Cardiomyopathies are myocardial diseases that lead to cardiac dysfunction, heart failure, arrhythmia, and sudden death. In human medicine, cardiomyopathies frequently warrant heart transplantation in children and adults. Bovine dilated cardiomyopathy (BDCMP) is a heart muscle disorder that has been observed during the last 30 years in cattle of Holstein-Friesian origin. In Switzerland BDCMP affects Swiss Fleckvieh and Red Holstein breeds. BDCMP is characterized by a cardiac enlargement with ventricular remodeling and chamber dilatation. The common symptoms in affected animals are subacute subcutaneous edema, congestion of the jugular veins, and tachycardia with gallop rhythm. A cardiomegaly with dilatation and hypertrophy of all heart chambers, myocardial degeneration, and fibrosis are typical postmortem findings. It was shown that all BDCMP cases reported worldwide traced back to a red factor-carrying Holstein-Friesian bull, ABC Reflection Sovereign. An autosomal recessive mode of inheritance was proposed for BDCMP. Recently, the disease locus was mapped to a 6.7-Mb interval MSBDCMP06-BMS2785 on bovine Chr 18 (BTA18). In the present study the BDCMP locus was fine mapped by using a combined strategy of homozygosity mapping and association study. A BAC contig of 2.9 Mb encompassing the crucial interval was constructed to establish the correct marker order on BTA18. We show that the disease locus is located in a gene-rich interval of 1.0 Mb and is flanked by the microsatellite markers DIK3006 and MSBDCMP51.

Zidovudine impairs immunological recovery on first-line antiretroviral therapy: collaborative analysis of cohort studies in southern Africa

OBJECTIVES Zidovudine (ZDV) is recommended for first-line antiretroviral therapy (ART) in resource-limited settings. ZDV may, however, lead to anemia and impaired immunological response. We compared CD4+ cell counts over 5 years between patients starting ART with and without ZDV in southern Africa. DESIGN Cohort study. METHODS Patients aged at least 16 years who started first-line ART in South Africa, Botswana, Zambia, or Lesotho were included. We used linear mixed-effect models to compare CD4+ cell count trajectories between patients on ZDV-containing regimens and patients on other regimens, censoring follow-up at first treatment change. Impaired immunological recovery, defined as a CD4+ cell count below 100 cells/μl at 1 year, was assessed in logistic regression. Analyses were adjusted for baseline CD4+ cell count and hemoglobin level, age, sex, type of regimen, viral load monitoring, and calendar year. RESULTS A total of 72,597 patients starting ART, including 19,758 (27.2%) on ZDV, were analyzed. Patients on ZDV had higher CD4+ cell counts (150 vs.128 cells/μl) and hemoglobin level (12.0 vs. 11.0 g/dl) at baseline, and were less likely to be women than those on other regimens. Adjusted differences in CD4+ cell counts between regimens containing and not containing ZDV were -16 cells/μl [95% confidence interval (CI) -18 to -14] at 1 year and -56 cells/μl (95% CI -59 to -52) at 5 years. Impaired immunological recovery was more likely with ZDV compared to other regimens (odds ratio 1.40, 95% CI 1.22-1.61). CONCLUSION In southern Africa, ZDV is associated with inferior immunological recovery compared to other backbones. Replacing ZDV with another nucleoside reverse transcriptase inhibitor could avoid unnecessary switches to second-line ART.

Electrocardiographic PR interval and adverse outcomes in older adults: the Health, Aging, and Body Composition study

BACKGROUND The electrocardiographic PR interval increases with aging, differs by race, and is associated with atrial fibrillation (AF), pacemaker implantation, and all-cause mortality. We sought to determine the associations between PR interval and heart failure, AF, and mortality in a biracial cohort of older adults. METHODS AND RESULTS The Health, Aging, and Body Composition (Health ABC) Study is a prospective, biracial cohort. We used multivariable Cox proportional hazards models to examine PR interval (hazard ratios expressed per SD increase) and 10-year risks of heart failure, AF, and all-cause mortality. Multivariable models included demographic, anthropometric, and clinical variables in addition to established cardiovascular risk factors. We examined 2722 Health ABC participants (aged 74±3 years, 51.9% women, and 41% black). We did not identify significant effect modification by race for the outcomes studied. After multivariable adjustment, every SD increase (29 ms) in PR interval was associated with a 13% greater 10-year risk of heart failure (95% confidence interval, 1.02-1.25) and a 13% increased risk of incident AF (95% confidence interval, 1.04-1.23). PR interval >200 ms was associated with a 46% increased risk of incident heart failure (95% confidence interval, 1.11-1.93). PR interval was not associated with increased all-cause mortality. CONCLUSIONS We identified significant relationships of PR interval to heart failure and AF in older adults. Our findings extend prior investigations by examining PR interval and associations with adverse outcomes in a biracial cohort of older men and women.

Effects of beta-alanine supplementation and interval training on physiological determinants of severe exercise performance.

INTRODUCTION We aimed to manipulate physiological determinants of severe exercise performance. We hypothesized that (1) beta-alanine supplementation would increase intramuscular carnosine and buffering capacity and dampen acidosis during severe cycling, (2) that high-intensity interval training (HIT) would enhance aerobic energy contribution during severe cycling, and (3) that HIT preceded by beta-alanine supplementation would have greater benefits. METHODS Sixteen active men performed incremental cycling tests and 90-s severe (110 % peak power) cycling tests at three time points: before and after oral supplementation with either beta-alanine or placebo, and after an 11-days HIT block (9 sessions, 4 × 4 min), which followed supplementation. Carnosine was assessed via MR spectroscopy. Energy contribution during 90-s severe cycling was estimated from the O2 deficit. Biopsies from m. vastus lateralis were taken before and after the test. RESULTS Beta-alanine increased leg muscle carnosine (32 ± 13 %, d = 3.1). Buffering capacity and incremental cycling were unaffected, but during 90-s severe cycling, beta-alanine increased aerobic energy contribution (1.4 ± 1.3 %, d = 0.5), concurrent with reduced O2 deficit (-5.0 ± 5.0 %, d = 0.6) and muscle lactate accumulation (-23 ± 30 %, d = 0.9), while having no effect on pH. Beta-alanine also enhanced motivation and perceived state during the HIT block. There were no between-group differences in adaptations to the training block, namely increased buffering capacity (+7.9 ± 11.9 %, p = 0.04, d = 0.6, n = 14) and glycogen storage (+30 ± 47 %, p = 0.04, d = 0.5, n = 16). CONCLUSIONS Beta-alanine did not affect buffering considerably, but has beneficial effects on severe exercise metabolism as well as psychological parameters during intense training phases.

Recognition memory across the lifespan: the impact of word frequency and study-test interval on estimates of familiarity and recollection

The goal of this study was to investigate recognition memory performance across the lifespan and to determine how estimates of recollection and familiarity contribute to performance. In each of three experiments, participants from five groups from 14 up to 85 years of age (children, young adults, middle-aged adults, young-old adults, and old-old adults) were presented with high- and low-frequency words in a study phase and were tested immediately afterwards and/or after a one day retention interval. The results showed that word frequency and retention interval affected recognition memory performance as well as estimates of recollection and familiarity. Across the lifespan, the trajectory of recognition memory followed an inverse u-shape function that was neither affected by word frequency nor by retention interval. The trajectory of estimates of recollection also followed an inverse u-shape function, and was especially pronounced for low-frequency words. In contrast, estimates of familiarity did not differ across the lifespan. The results indicate that age differences in recognition memory are mainly due to differences in processes related to recollection while the contribution of familiarity-based processes seems to be age-invariant.

Multiple independent genetic factors at NOS1AP modulate the QT interval in a multi-ethnic population.

Extremes of electrocardiographic QT interval are associated with increased risk for sudden cardiac death (SCD); thus, identification and characterization of genetic variants that modulate QT interval may elucidate the underlying etiology of SCD. Previous studies have revealed an association between a common genetic variant in NOS1AP and QT interval in populations of European ancestry, but this finding has not been extended to other ethnic populations. We sought to characterize the effects of NOS1AP genetic variants on QT interval in the multi-ethnic population-based Dallas Heart Study (DHS, n = 3,072). The SNP most strongly associated with QT interval in previous samples of European ancestry, rs16847548, was the most strongly associated in White (P = 0.005) and Black (P = 3.6 x 10(-5)) participants, with the same direction of effect in Hispanics (P = 0.17), and further showed a significant SNP x sex-interaction (P = 0.03). A second SNP, rs16856785, uncorrelated with rs16847548, was also associated with QT interval in Blacks (P = 0.01), with qualitatively similar results in Whites and Hispanics. In a previously genotyped cohort of 14,107 White individuals drawn from the combined Atherosclerotic Risk in Communities (ARIC) and Cardiovascular Health Study (CHS) cohorts, we validated both the second locus at rs16856785 (P = 7.63 x 10(-8)), as well as the sex-interaction with rs16847548 (P = 8.68 x 10(-6)). These data extend the association of genetic variants in NOS1AP with QT interval to a Black population, with similar trends, though not statistically significant at P<0.05, in Hispanics. In addition, we identify a strong sex-interaction and the presence of a second independent site within NOS1AP associated with the QT interval. These results highlight the consistent and complex role of NOS1AP genetic variants in modulating QT interval.

The IFNL3/4 ΔG variant increases susceptibility to cytomegalovirus retinitis among HIV-infected patients.

BACKGROUND Cytomegalovirus (CMV) retinitis is a major cause of visual impairment and blindness among patients with uncontrolled HIV infections. Whereas polymorphisms in interferon-lambda 3 (IFNL3, previously named IL28B) strongly influence the clinical course of hepatitis C, few studies examined the role of such polymorphisms in infections due to viruses other than hepatitis C virus. OBJECTIVES To analyze the association of newly identified IFNL3/4 variant rs368234815 with susceptibility to CMV-associated retinitis in a cohort of HIV-infected patients. DESIGN AND METHODS This retrospective longitudinal study included 4884 white patients from the Swiss HIV Cohort Study, among whom 1134 were at risk to develop CMV retinitis (CD4 nadir <100 /μl and positive CMV serology). The association of CMV-associated retinitis with rs368234815 was assessed by cumulative incidence curves and multivariate Cox regression models, using the estimated date of HIV infection as a starting point, with censoring at death and/or lost follow-up. RESULTS A total of 40 individuals among 1134 patients at risk developed CMV retinitis. The minor allele of rs368234815 was associated with a higher risk of CMV retinitis (log-rank test P = 0.007, recessive mode of inheritance). The association was still significant in a multivariate Cox regression model (hazard ratio 2.31, 95% confidence interval 1.09-4.92, P = 0.03), after adjustment for CD4 nadir and slope, HAART and HIV-risk groups. CONCLUSION We reported for the first time an association between an IFNL3/4 polymorphism and susceptibility to AIDS-related CMV retinitis. IFNL3/4 may influence immunity against viruses other than HCV.

Genetic association study of QT interval highlights role for calcium signaling pathways in myocardial repolarization

The QT interval, an electrocardiographic measure reflecting myocardial repolarization, is a heritable trait. QT prolongation is a risk factor for ventricular arrhythmias and sudden cardiac death (SCD) and could indicate the presence of the potentially lethal mendelian long-QT syndrome (LQTS). Using a genome-wide association and replication study in up to 100,000 individuals, we identified 35 common variant loci associated with QT interval that collectively explain ∼8-10% of QT-interval variation and highlight the importance of calcium regulation in myocardial repolarization. Rare variant analysis of 6 new QT interval-associated loci in 298 unrelated probands with LQTS identified coding variants not found in controls but of uncertain causality and therefore requiring validation. Several newly identified loci encode proteins that physically interact with other recognized repolarization proteins. Our integration of common variant association, expression and orthogonal protein-protein interaction screens provides new insights into cardiac electrophysiology and identifies new candidate genes for ventricular arrhythmias, LQTS and SCD.

In search of the internal structure of the processes underlying interval timing in the sub-second and the second range: A confirmatory factor analysis approach

One of the earliest accounts of duration perception by Karl von Vierordt implied a common process underlying the timing of intervals in the sub-second and the second range. To date, there are two major explanatory approaches for the timing of brief intervals: the Common Timing Hypothesis and the Distinct Timing Hypothesis. While the common timing hypothesis also proceeds from a unitary timing process, the distinct timing hypothesis suggests two dissociable, independent mechanisms for the timing of intervals in the sub-second and the second range, respectively. In the present paper, we introduce confirmatory factor analysis (CFA) to elucidate the internal structure of interval timing in the sub-second and the second range. Our results indicate that the assumption of two mechanisms underlying the processing of intervals in the second and the sub-second range might be more appropriate than the assumption of a unitary timing mechanism. In contrast to the basic assumption of the distinct timing hypothesis, however, these two timing mechanisms are closely associated with each other and share 77% of common variance. This finding suggests either a strong functional relationship between the two timing mechanisms or a hierarchically organized internal structure. Findings are discussed in the light of existing psychophysical and neurophysiological data.

The effects of type of interval, sensory modality, base duration, and psychophysical task on the discrimination of brief time intervals

The present study was designed to investigate the influences of type of psychophysical task (two-alternative forced-choice [2AFC] and reminder tasks), type of interval (filled vs. empty), sensory modality (auditory vs. visual), and base duration (ranging from 100 through 1,000 ms) on performance on duration discrimination. All of these factors were systematically varied in an experiment comprising 192 participants. This approach allowed for obtaining information not only on the general (main) effect of each factor alone, but also on the functional interplay and mutual interactions of some or all of these factors combined. Temporal sensitivity was markedly higher for auditory than for visual intervals, as well as for the reminder relative to the 2AFC task. With regard to base duration, discrimination performance deteriorated with decreasing base durations for intervals below 400 ms, whereas longer intervals were not affected. No indication emerged that overall performance on duration discrimination was influenced by the type of interval, and only two significant interactions were apparent: Base Duration × Type of Interval and Base Duration × Sensory Modality. With filled intervals, the deteriorating effect of base duration was limited to very brief base durations, not exceeding 100 ms, whereas with empty intervals, temporal discriminability was also affected for the 200-ms base duration. Similarly, the performance decrement observed with visual relative to auditory intervals increased with decreasing base durations. These findings suggest that type of task, sensory modality, and base duration represent largely independent sources of variance for performance on duration discrimination that can be accounted for by distinct nontemporal mechanisms.

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^