Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing

STATA und R: eine Gegenüberstellung

Die Kapitel der Regressionsschätzung, Paneldatenanalyse, der multivariaten Datenanlyse, Survey- und Survivalanalyse, so wie Zeitreihenanlyse werden anhand einer tabellarischen Auflistung von entsprechenden STATA und R-Befehlen vorgestellt. Dabei kann die gewählte Vorgehensweise in STATA zu einem Großteil in R übersetzt und nachvollzogen werden

Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing.Dependence structure, Extremal values, Copula modeling, Copula review

Bayesian Autoregressive Frailty Models for Inference in Recurrent Events

We propose autoregressive Bayesian semi-parametric models for gap times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the frailty parameters influencing the response at different times. The order of the autoregression may be assumed unknown and is an object of inference. We consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lie within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections

Healthy, Wealthy, and Wise? Socioeconomic Status and Morbidity/Mortality

No abstract.

Bayesian Analysis of Binary Diagnostic Tests and Panel Count Data

This dissertation mainly explores several challenging topics that arise in diagnostic tests and panel count data in the Bayesian framework. Binary diagnostic tests, particularly multiple diagnostic tests with repeated measures and diagnostic procedures with a large number of raters, are studied. For panel count data, most traditional methods only handle panel count data for a single type of recurrent event. In this dissertation, we primarily focus on the case with multiple types of recurrent events. In Chapter 1, an introduction to the binary diagnostic tests data and panel count data is presented and related literature works are briefly reviewed. To make the dissertation more coherent for the later chapters, some preliminary theories and algorithms, for instance the Metropolis Hastings algorithm, are presented. Finally, an outline of the dissertation organization is put forward. In Chapter 2, a model for multiple diagnostic tests, applied repeatedly over time on each subject, is proposed; gold standard data are not required. The model is identifiable with as few as three tests; and correlation among tests at each time point in the diseased and non-diseased populations, as well as across time points is explicitly included. An efficient Markov chain Monte Carlo (MCMC) scheme allows for straightforward posterior inference. The proposed model is broadly illustrated via simulations and scaphoid fracture data from a prospective study (Duckworth et al., 2012) is analyzed. In addition, omnibus tests constructed from individual tests in parallel and serial are considered. In Chapter 3, a Bayesian hierarchical conditional independence latent class model for estimating sensitivities and specificities for a large group of tests or raters is v proposed, which is applicable to both with-gold-standard and without-gold-standard situations. Through the hierarchical structure, not only are the sensitivities and specificities of individual tests estimated, but also the diagnostic performance of the whole group of tests. For a small group of tests or raters, the proposed model is further extended by introducing pairwise covariances between tests to improve the fitting and to allow for more modeling flexibility. Correlation residual analysis is applied to detect any significant covariance between multiple tests. Just Another Gibbs Sampler (JAGS) implementation is efficiently adopted for both models. Three real data sets from literature are analyzed to explicitly illustrate the proposed methods.. In Chapter 4, a Bayesian semiparameteric approach is proposed to analyze panel count data for multiple types of recurrent events. For each type of event, the proportional mean model is adopted to model the mean count of the event, where its baseline mean function is approximated by monotone I-splines (Ramsay et al., 1988). Correlation between multiple events is modeled by common frailty terms and scale parameters. Unlike many frequentist estimating equation methods, our approach is based on the observed likelihood and makes no assumption on the relationship between the recurrent processes and the observation process. Under the Poisson process assumption, an efficient Gibbs sampler based on a novel data augmentation is developed for the MCMC sampling. Simulation studies show good estimation performance of the baseline mean functions and the regression coefficients; meanwhile the importance of including the scale parameter to flexibly accommodate the correlation between events is also demonstrated. Finally, a skin cancer data example is fully analyzed to illustrate the proposed methods. In Chapter 5, a brief summary of the studies we have completed in the previous chapters is delivered and at the same time we put forward some ideas for future work in each topic covered

Regression Modeling for Recurrent Events Possibly with an Informative Terminal Event Using R Package reReg

Recurrent event analyses have found a wide range of applications in biomedicine, public health, and engineering, among others, where study subjects may experience a sequence of event of interest during follow-up. The R package reReg offers a comprehensive collection of practical and easy-to-use tools for regression analysis of recurrent events, possibly with the presence of an informative terminal event. The regression framework is a general scalechange model which encompasses the popular Cox-type model, the accelerated rate model, and the accelerated mean model as special cases. Informative censoring is accommodated through a subject-specific frailty without any need for parametric specification. Different regression models are allowed for the recurrent event process and the terminal event. Also included are visualization and simulation tools

Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer

Readmission following discharge from an initial hospitalization is a key marker of quality of health care in the United States. For the most part, readmission has been used to study quality of care for patients with acute health conditions, such as pneumonia and heart failure, with analyses typically based on a logistic-Normal generalized linear mixed model. Applying this model to the study readmission among patients with increasingly prevalent advanced health conditions such as pancreatic cancer is problematic, however, because it ignores death as a competing risk. A more appropriate analysis is to imbed such studies within the semi-competing risks framework. To our knowledge, however, no comprehensive statistical methods have been developed for cluster-correlated semi-competing risks data. In this paper we propose a novel hierarchical modeling framework for the analysis of cluster-correlated semi-competing risks data. The framework permits parametric or non-parametric specifications for a range of model components, including baseline hazard functions and distributions for key random effects, giving analysts substantial flexibility as they consider their own analyses. Estimation and inference is performed within the Bayesian paradigm since it facilitates the straightforward characterization of (posterior) uncertainty for all model parameters including hospital-specific random effects. The proposed framework is used to study the risk of readmission among 5,298 Medicare beneficiaries diagnosed with pancreatic cancer at 112 hospitals in the six New England states between 2000-2009, specifically to investigate the role of patient-level risk factors and to characterize variation in risk across hospitals that is not explained by differences in patient case-mix

Exploring red cell distribution width as a potential risk factor in emergency bowel surgery – a retrospective cohort study

ncreased preoperative red cell distribution width (RDW) is associated with higher mortality following non-cardiac surgery in patients older than 65 years. Little is known if this association holds for all adult emergency laparotomy patients and whether it affects 30-day or long-term mortality. Thus, we examined the relationship between increased RDW and postoperative mortality. Furthermore, we investigated the prognostic worth of anisocytosis and explored a possible association between increased RDW and frailty in this cohort. We conducted a retrospective, single centre National Emergency Laparotomy Audit (NELA) database study at St Mary’s Hospital Imperial NHS Trust between January 2014 and April 2018. A total of 356 patients were included. Survival models were developed using Cox regression analysis, whereas RDW and frailty were analysed using multivariable logistic regression. Underlying model assumptions were checked, including discrimination and calibration. We internally validated our models using bootstrap resampling. There were 33 (9.3%) deaths within 30-days and 72 (20.2%) overall. Median RDW values for 30-day mortality were 13.8% (IQR 13.1%-15%) in survivors and 14.9% (IQR 13.7%-16.1%) in non-survivors, p=0.007. Similarly, median RDW values were lower in overall survivors (13.7% (IQR42 13%-14.7%) versus 14.9% (IQR 13.9%-15.9%) (p<0.001)). Mortality increased across quartiles of RDW, as did the proportion of frail patients. Anisocytosis was not associated with 30-day mortality but demonstrated a link with overall death rates. Increasing RDW was associated with a higher probability of frailty for 30-day (Odds ratio (OR) 4.3, 95% CI 1.22-14.43, (p=0.01)) and overall mortality (OR 4.9, 95% CI 1.68-14.09, (p=0.001)). We were able to show that preoperative anisocytosis is associated with greater long-term mortality after emergency laparotomy. Increasing RDW demonstrates a relationship with frailty. Given that RDW is readily available at no additional cost, future studies should prospectively validate the role of RDW in the NELA cohort nationally

Overweight and Obesity and the Demand for Primary Physician Care

The standard economic model for the demand for health care predicts that unhealthy behaviour such as being overweight or obese should increase the demand for medical care, particularly as clinical studies link obesity to a number of serious diseases. In this paper, we investigate whether overweight or obese individuals demand more medical care than normal weight individuals by estimating a finite mixture model which splits the population into frequent and non-frequent users of primary physician (GP) services according to the individual's latent health status. Based on a sample of wage-earners aged 25-60 years drawn from the National Health Interview (NHI) survey 2000 and merged to Danish register data, we compare differences in the impact of being overweight and obese relative to being normal weight on the demand for primary physician care. Estimated bodyweight effects vary across latent classes and show that being obese or overweight does not increase the demand for primary physician care among infrequent users but does so among frequent users.overweight, obesity, demand for primary physician care