Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Association of dietary fat intakes with risk of esophageal and gastric cancer in the NIH-AARP diet and health study

The aim of our study was to investigate whether intakes of total fat and fat subtypes were associated with esophageal adenocarcinoma (EAC), esophageal squamous cell carcinoma (ESCC), gastric cardia or gastric noncardia adenocarcinoma. From 1995–1996, dietary intake data was reported by 494,978 participants of the NIH-AARP cohort. The 630 EAC, 215 ESCC, 454 gastric cardia and 501 gastric noncardia adenocarcinomas accrued to the cohort. Cox proportional hazards regression was used to examine the association between the dietary fat intakes, whilst adjusting for potential confounders. Although apparent associations were observed in energy-adjusted models, multivariate adjustment attenuated results to null [e.g., EAC energy adjusted hazard ratio (HR) and 95% confidence interval (95% CI) 1.66 (1.27–2.18) p for trend <0.01; EAC multivariate adjusted HR (95% CI) 1.17 (0.84–1.64) p for trend 5 0.58]. Similar patterns were also observed for fat subtypes [e.g., EAC saturated fat, energy adjusted HR (95% CI) 1.79 (1.37–2.33) p for trend <0.01; EAC saturated fat, multivariate adjusted HR (95% CI) 1.27 (0.91–1.78) p for trend 5 0.28]. However, in multivariate models an inverse association for polyunsaturated fat (continuous) was seen for EAC in subjects with a body mass index (BMI) in the normal range (18.5–<25 kg/m2) [HR (95% CI) 0.76 (0.63–0.92)], that was not present in overweight subjects [HR (95% CI) 1.04 (0.96–1.14)], or in unstratified analysis [HR (95% CI) 0.97 (0.90–1.05)]. p for interaction 5 0.02. Overall, we found null associations between the dietary fat intakes with esophageal or gastric cancer risk; although a protective effect of polyunsaturated fat intake was seen for EAC in subjects with a normal BMI.

The role of private care in the interval between diagnosis and treatment of breast cancer in Northern Ireland: an analysis of Registry data

Objective: To examine the differences in the interval between diagnosis and initiation of treatment among women with breast cancer in Northern Ireland.

Design: A cross-sectional observational study.
Setting: All breast cancer care patients in the Northern Ireland Cancer Registry in 2006.
Participants: All women diagnosed and treated for breast cancer in Northern Ireland in 2006.
Main outcome measure: The number of days between diagnosis and initiation of treatment for breast cancer.

Results: The mean (median) interval between diagnosis and initiation of treatment among public patients was 19 (15) compared with 14 (12) among those whose care involved private providers. The differences between individual public providers were as marked as those between the public and private sector - the mean (median) ranging between 14 (12) and 25 (22) days. Multivariate models revealed that the differences were evident when a range of patient characteristics were controlled for including cancer stage.

Conclusions: A relatively small number of women received care privately in Northern Ireland but experienced shorter intervals between diagnosis and initiation of treatment than those who received care wholly in the public system. The variation among public providers was as great as that between the public and private providers. The impact of such differences on survival and in light of waiting time targets introduced in Northern Ireland warrants investigation.

Integrating personality research and animal contest theory:Aggressiveness in the green swordtail xiphophorus helleri

Aggression occurs when individuals compete over limiting resources. While theoretical studies have long placed a strong emphasis on context-specificity of aggression, there is increasing recognition that consistent behavioural differences exist among individuals, and that aggressiveness may be an important component of individual personality. Though empirical studies tend to focus on one aspect or the other, we suggest there is merit in modelling both within- and among-individual variation in agonistic behaviour simultaneously. Here, we demonstrate how this can be achieved using multivariate linear mixed effect models. Using data from repeated mirror trials and dyadic interactions of male green swordtails, Xiphophorus helleri, we show repeatable components of (co)variation in a suite of agonistic behaviour that is broadly consistent with a major axis of variation in aggressiveness. We also show that observed focal behaviour is dependent on opponent effects, which can themselves be repeatable but were more generally found to be context specific. In particular, our models show that within-individual variation in agonistic behaviour is explained, at least in part, by the relative size of a live opponent as predicted by contest theory. Finally, we suggest several additional applications of the multivariate models demonstrated here. These include testing the recently queried functional equivalence of alternative experimental approaches, (e.g., mirror trials, dyadic interaction tests) for assaying individual aggressiveness. © 2011 Wilson et al.

The association between refractive cutoffs for spectacle provision and visual improvement among school-aged children in South Africa.

OBJECTIVES: To evaluate different refractive cutoffs for spectacle provision with regards to their impact on visual improvement and spectacle compliance. DESIGN: Prospective study of visual improvement and spectacle compliance. PARTICIPANTS: South African school children aged 6-19 years receiving free spectacles in a programme supported by Helen Keller International. METHODS: Refractive error, age, gender, urban versus rural residence, presenting and best-corrected vision were recorded for participants. Spectacle wear was observed directly at an unannounced follow-up examination 4-11 months after initial provision of spectacles. The association between five proposed refractive cutoff protocols and visual improvement and spectacle compliance were examined in separate multivariate models. MAIN OUTCOMES: Refractive cutoffs for spectacle distribution which would effectively identify children with improved vision, and those more likely to comply with spectacle wear. RESULTS: Among 8520 children screened, 810 (9.5%) received spectacles, of whom 636 (79%) were aged 10-14 years, 530 (65%) were girls, 324 (40%) had vision improvement > or = 3 lines, and 483 (60%) were examined 6.4+/-1.5 (range 4.6 to 10.9) months after spectacle dispensing. Among examined children, 149 (31%) were wearing or carrying their glasses. Children meeting cutoffs < or = -0.75 D of myopia, > or = +1.00 D of hyperopia and > or = +0.75 D of astigmatism had significantly greater improvement in vision than children failing to meet these criteria, when adjusting for age, gender and urban versus rural residence. None of the proposed refractive protocols discriminated between children wearing and not wearing spectacles. Presenting vision and improvement in vision were unassociated with subsequent spectacle wear, but girls (p < or = 0.0006 for all models) were more likely to be wearing glasses than were boys. CONCLUSIONS: To the best of our knowledge, this is the first suggested refractive cutoff for glasses dispensing validated with respect to key programme outcomes. The lack of association between spectacle retention and either refractive error or vision may have been due to the relatively modest degree of refractive error in this African population.

Spectacle acceptance among secondary school students in rural China: the Xichang Pediatric Refractive Error Study (X-PRES)--report 5.

PURPOSE: To assess determinants of spectacle acceptance and use among rural Chinese children. METHODS: Children with uncorrected acuity < or = 6/12 in either eye and whose presenting vision could be improved > or = 2 lines with refraction were identified from a school-based sample of 1892 students. Information on obtaining glasses and the benefits of spectacles was provided to children, families, and teachers. Purchase of new spectacles and reasons for nonpurchase were assessed by direct inspection and interview 3 months later. RESULTS: Among 674 (35.6%) children requiring spectacles (mean age, 14.7 +/- 0.8 years), 597 (88.6%) were followed up. Among 339 children with no glasses at baseline, 30.7% purchased spectacles, whereas 43.2% of 258 children with inaccurate glasses replaced them. Most (70%) subjects paid US$13 to $26. Among children with bilateral vision < or = 6/18, 45.6% bought glasses. In multivariate models, presenting vision < 6/12 (P < 0.009), refractive error < -2.0 D (P < 0.001), and amount willing to pay for glasses (P = 0.01) were predictors of purchase. Reasons for nonpurchase included satisfaction with current vision (78% of those with glasses at baseline, 49% of those without), concerns over price or parental refusal (18%), and fear glasses would weaken the eyes (13%). Only 26% of children stated that they usually wore their new glasses. CONCLUSIONS: Many families in rural China will pay for glasses, though spectacle acceptance was < 50%, even among children with poor vision. Acceptance could be improved by price reduction, education showing that glasses will not harm the eyes, and parent-focused interventions.

Visual morbidity due to inaccurate spectacles among school children in rural China: the See Well to Learn Well Project, report 1.

PURPOSE: Inadequately corrected refractive error is the leading cause of visual disability among children in China; inaccurate spectacles are a potential cause. The prevalence and visual impact of spectacle inaccuracy were studied among rural, secondary-school children, to determine the optimal timing for updating of refraction. METHODS: A random sample of children from years 1 and 2 in all junior and senior high schools in Fuyang Township, Guangdong Province, underwent ocular examination. All children who reported wearing glasses received cycloplegic refraction, vision assessment, and measurement of current spectacles. RESULTS: Among 3226 examined children, 733 (22.7%) reported owning spectacles. Refractive error and spectacle power were assessed for 588 (80.2%) children. They had a mean age of 15.0 +/- 1.6 years; 70.2% were girls, 83.3% had more than -1.5 D of myopia, and 17.9% had presenting vision < or = 6/12 in the better eye. The glasses of 48.8% of children were inaccurate by > or = 1 D; inaccuracy was > or = 2 D in 17.7%. Children with inaccurate glasses (> or = 1 D) had presenting vision in the better eye significantly (P < 0.001) worse than that of children with accurate glasses, and 30.3% had presenting acuity < or = 6/12. In multivariate models, younger age (P = 0.004), more myopic refractive error (P < 0.001), and having glasses > or = 1 year old (P = 0.04) were associated with inaccurate spectacles. DISCUSSION: Inaccurate spectacles are common and are associated with significant visual impairment among children in rural China. Reducing outdated glasses could lessen the visual burden, although refractive services may have to be offered on an annual basis for optimal benefit.

Population density and refractive error among Chinese children.

PURPOSE: China is urbanizing rapidly, and the prevalence of myopia is high. This study was conducted to identify the reasons for observed differences in the prevalence of myopia among urban versus rural Chinese children. METHODS: All children with uncorrected acuity of 6/12 or worse and a 50% random sample of children with vision better than 6/12 at all secondary schools in mixed rural-urban Liangying Township, Guangdong, underwent cycloplegic refraction, and provided data on age, gender, parental education, weekly near work and time outdoors, and urban development level of respondents' neighborhoods (12-item questionnaire). Population density of 32 villages and urban zones in Liangying was calculated from census figures (mean population density, 217 persons/km(2); range, 94-957; mean for Guangdong, 486). RESULTS: Among 5844 eligible children, 4612 (78.9%) had parental consent and completed examinations; 2957 were refracted per protocol, and 2480 (83.9%) of these had questionnaire data. Those with completed examinations were more likely to be girls (P < 0.001), and questionnaire respondents were more myopic (P = 0.02), but otherwise did not differ significantly from nonrespondents. In multivariate models, older age (P < 0.001), more near work (P = 0.02), and higher population density (P = 0.003), but not development index, parental education, or time outdoors were significantly associated with more myopic refractive error. CONCLUSIONS: Higher population density appears to be associated with myopia risk, independent of academic activity, time spent outdoors, familial educational level, or economic development, factors that have been thought to explain higher myopia prevalence among urban children. Mechanisms for this apparent association should be sought.

Willingness to pay for potential enhancements to a low-cost cataract surgical package in rural southern China.

PURPOSE: To assess determinants of patients' willingness to pay (WTP) for potential components of a multi-tiered cataract surgical package offered by a non-governmental organization (NGO) in rural China. DESIGN: Cross-sectional study. METHODS: Demographic and clinical data were collected from 505 patients presenting for cataract screening or surgery in Yangjiang, China. Willingness to pay for potential enhancements to the current surgery package was assessed using a bidding format with random payment cards. RESULTS: Among 426 subjects (84.4%) completing interviews, the mean age was 73.9 ± 7.3 years, 67.6% were women and 73% (n = 310) would pay for at least one offering, with 33-38% WTP for each item. Among those who would pay, the mean WTP for food was US$1.68 ± 0.13, transportation US$3.24 ± 0.25, senior surgeon US$50.0 ± 3.36 and US$89.4 ± 4.19 for an imported intra-ocular lens (IOL). The estimated total recovery from these enhancements under various assumptions would be US$20-50 (compared to the current programme price of US$65). In multivariate models, WTP for the senior surgeon increased with knowledge of a person previously operated for cataract (OR = 2.13, 95% CI 1.42-3.18, p < 0.001). Willingness to pay for the imported IOL increased with knowledge of a previously operated person (OR = 1.85, 95% CI 1.24-2.75, p < 0.01) and decreased with age >75 years (OR = 0.61, 0.40-0.93, p < 0.05). CONCLUSIONS: Opportunities exist to increase cataract programme revenues through multi-tiered offerings in this setting, allowing greater subsidization of low-income patients. Personal familiarity with cataract surgery is important in determining WTP. © 2011 The Authors. Acta Ophthalmologica © 2011 Acta Ophthalmologica Scandinavica Foundation.

Multivariate Statistical Analysis Applied to an IL6 Signal Transduction Model in Hepatocytes

This paper introduces the application of linear multivariate statistical techniques, including partial least squares (PLS), canonical correlation analysis (CCA) and reduced rank regression (RRR), into the area of Systems Biology. This new approach aims to extract the important proteins embedded in complex signal transduction pathway models.The analysis is performed on a model of intracellular signalling along the janus-associated kinases/signal transducers and transcription factors (JAK/STAT) and mitogen activated protein kinases (MAPK) signal transduction pathways in interleukin-6 (IL6) stimulated hepatocytes, which produce signal transducer and activator of transcription factor 3 (STAT3).A region of redundancy within the MAPK pathway that does not affect the STAT3 transcription was identified using CCA. This is the core finding of this analysis and cannot be obtained by inspecting the model by eye. In addition, RRR was found to isolate terms that do not significantly contribute to changes in protein concentrations, while the application of PLS does not provide such a detailed picture by virtue of its construction.This analysis has a similar objective to conventional model reduction techniques with the advantage of maintaining the meaning of the states prior to and after the reduction process. A significant model reduction is performed, with a marginal loss in accuracy, offering a more concise model while maintaining the main influencing factors on the STAT3 transcription.The findings offer a deeper understanding of the reaction terms involved, confirm the relevance of several proteins to the production of Acute Phase Proteins and complement existing findings regarding cross-talk between the two signalling pathways.

Dynamic Density Forecasts for Multivariate Asset Returns

We propose a simple and flexible framework for forecasting the joint density of asset returns. The multinormal distribution is augmented with a polynomial in (time-varying) non-central co-moments of assets. We estimate the coefficients of the polynomial via the Method of Moments for a carefully selected set of co-moments. In an extensive empirical study, we compare the proposed model with a range of other models widely used in the literature. Employing a recently proposed as well as standard techniques to evaluate multivariate forecasts, we conclude that the augmented joint density provides highly accurate forecasts of the “negative tail” of the joint distribution.

An Examination of Transformation Techniques to Investigate and Interpret Multivariate Geochemical Data Analysis: Tellus Case Study

This research aims to use the multivariate geochemical dataset, generated by the Tellus project, to investigate the appropriate use of transformation methods to maintain the integrity of geochemical data and inherent constrained behaviour in multivariate relationships. The widely used normal score transform is compared with the use of a stepwise conditional transform technique. The Tellus Project, managed by GSNI and funded by the Department of Enterprise Trade and Development and the EU’s Building Sustainable Prosperity Fund, involves the most comprehensive geological mapping project ever undertaken in Northern Ireland. Previous study has demonstrated spatial variability in the Tellus data but geostatistical analysis and interpretation of the datasets requires use of an appropriate methodology that reproduces the inherently complex multivariate relations. Previous investigation of the Tellus geochemical data has included use of Gaussian-based techniques. However, earth science variables are rarely Gaussian, hence transformation of data is integral to the approach. The multivariate geochemical dataset generated by the Tellus project provides an opportunity to investigate the appropriate use of transformation methods, as required for Gaussian-based geostatistical analysis. In particular, the stepwise conditional transform is investigated and developed for the geochemical datasets obtained as part of the Tellus project. The transform is applied to four variables in a bivariate nested fashion due to the limited availability of data. Simulation of these transformed variables is then carried out, along with a corresponding back transformation to original units. Results show that the stepwise transform is successful in reproducing both univariate statistics and the complex bivariate relations exhibited by the data. Greater fidelity to multivariate relationships will improve uncertainty models, which are required for consequent geological, environmental and economic inferences.

Slow Release Drug Dissolution Profile Prediction in Pharmaceutical Manufacturing: a Multivariate and Machine Learning Approach

Slow release drugs must be manufactured to meet target specifications with respect to dissolution curve profiles. In this paper we consider the problem of identifying the drivers of dissolution curve variability of a drug from historical manufacturing data. Several data sources are considered: raw material parameters, coating data, loss on drying and pellet size statistics. The methodology employed is to develop predictive models using LASSO, a powerful machine learning algorithm for regression with high-dimensional datasets. LASSO provides sparse solutions facilitating the identification of the most important causes of variability in the drug fabrication process. The proposed methodology is illustrated using manufacturing data for a slow release drug.