Likelihood-based risk estimation for variance-gamma models

Although the variance-gamma distribution is a flexible model for log-returns of financial assets, so far it has found rather limited applications in finance and risk management. One of the reasons is that maximum likelihood estimation of its parameters is not straightforward. We develop an EM-type algorithm based on Nitithumbundit and Chan (An ECM algorithm for skewed multivariate variance gamma distribution in normal mean–variance representation, arXiv:1504.01239, 2015) that bypasses the evaluation of the full likelihood, which may be difficult because the density is not in closed form and is unbounded for small values of the shape parameter. Moreover, we study the relative efficiency of our approach with respect to the maximum likelihood estimation procedures implemented in the VarianceGamma and ghyp R packages. Extensive simulation experiments and real-data analyses suggest that the multicycle ECM algorithm gives the best results in terms of root-mean-squared-error, for both parameter and value-at-risk estimation. The performance of the routines in the ghyp R package is similar but not as good, whereas the VarianceGamma package produces worse results, especially when the shape parameter is small.     

Quasi-random numbers for copula models

The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Besides sampling methods such as the conditional distribution method (based on a one-to-one transformation), it is also shown that typically faster sampling methods (based on stochastic representations) can be used to improve upon classical Monte Carlo methods when pseudo-random number generators are replaced by quasi-random number generators. This opens the door to quasi-random numbers for models well beyond independent margins or the multivariate normal distribution. Detailed examples (in the context of finance and insurance), illustrations and simulations are given and software has been developed and provided in the R packages copula and qrng.     

Prognostic assessment of repeatedly measured time-dependent biomarkers,with application to dilated cardiomyopathy

We propose new time-dependent sensitivity, specificity, ROC curves and net reclassification indices that can take into account biomarkers or scores that are repeatedly measured at different time-points. Inference proceeds through inverse probability weighting and resampling. The newly proposed measures exploit the information contained in biomarkers measured at different visits, rather than using only the measurements at the first visits. The contribution is illustrated via simulations and an original application on patients affected by dilated cardiomiopathy. The aim is to evaluate if repeated binary measurements of right ventricular dysfunction bring additive prognostic information on mortality/urgent heart transplant. It is shown that taking into account the trajectory of the new biomarker improves risk classification, while the first measurement alone might not be sufficiently informative. The methods are implemented in an R package (longROC), freely available on CRAN.     

Stability of feature selection in classification issues for high-dimensional correlated data

Handling dependence or not in feature selection is still an open question in supervised classification issues where the number of covariates exceeds the number of observations. Some recent papers surprisingly show the superiority of naive Bayes approaches based on an obviously erroneous assumption of independence, whereas others recommend to infer on the dependence structure in order to decorrelate the selection statistics. In the classical linear discriminant analysis (LDA) framework, the present paper first highlights the impact of dependence in terms of instability of feature selection. A second objective is to revisit the above issue using a flexible factor modeling for the covariance. This framework introduces latent components of dependence, conditionally on which a new Bayes consistency is defined. A procedure is then proposed for the joint estimation of the expectation and variance parameters of the model. The present method is compared to recent regularized diagonal discriminant analysis approaches, assuming independence among features, and regularized LDA procedures, both in terms of classification performance and stability of feature selection. The proposed method is implemented in the R package FADA, freely available from the R repository CRAN.     

A Generalized Log-Normal Model for Grouped Survival Data

It is common to have experiments in which it is not possible to observe the exact lifetimes but only the interval where they occur. This sort of data presents a high number of ties and it is called grouped or interval-censored survival data. Regression methods for grouped data are available in the statistical literature. The regression structure considers modeling the probability of a subject's survival past a visit time conditional on his survival at the previous visit. Two approaches are presented: assuming that lifetimes come from (1) a continuous proportional hazards model and (2) a logistic model. However, there may be situations in which none of the models are adequate for a particular data set. This article proposes the generalized log-normal model as an alternative model for discrete survival data. This model was introduced by Chen (1995 Chen , G. ( 1995 ). Generalized Log-normal distributions with reliability application . Comput. Stat. Data Anal. 19 : 300 – 319 . [Google Scholar]) and it is extended in this article for grouped survival data. A real example related to a Chagas disease illustrates the proposed model.     

Shared inverse Gaussian frailty models based on additive hazards

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), the shared frailty models were suggested. These models are based on the assumption that frailty acts multiplicatively to hazard rate. In this article, we assume that frailty acts additively to hazard rate. We introduce the shared inverse Gaussian frailty models with three different baseline distributions, namely the generalized log-logistic, the generalized Weibull, and exponential power distribution. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo technique to estimate the parameters involved in these models. We apply these models to a real-life bivariate survival dataset of McGilchrist and Aisbett (1991 McGilchrist, C.A., Aisbett, C.W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to the kidney infection data, and a better model is suggested for the data.     

Asynergistic Regression Based on Maximized Rank Correlation

The property of synergy and its detection are discussed. A response surface is said to possess synergy if it is monotone in each argument and its level curves are convex. Detecting this is useful in the study of combination drug therapies, where the goal is enhanced response with diminished side effect. One way to detect synergy is to fit a surface with linear level curves under the assumption of asynergy and observe the residuals. We explore an algorithm to accomplish this asynergistic regression via a reduction in dimensionality and connections to semiparametric monotonic linear index models (Cavanagh and Sherman, 1998 Cavanagh , C. , Sherman , P. ( 1998 ). Rank estimators for monotonic index models . J. Econometrics 84 : 351 – 381 .[Crossref], [Web of Science ®] , [Google Scholar]). We see that the asynergistic model is a generalized version of the monotonic linear index model where the linear level curves are not restricted to be parallel.     

Modeling bivariate survival data using shared inverse Gaussian frailty model

ABSTRACT

The shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of a random factor (frailty) and the baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and the distribution of frailty. In this paper, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions, namely the generalized Rayleigh, the weighted exponential, and the extended Weibull distributions. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. We also compare these models with the models where the above-mentioned distributions are considered without frailty. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared inverse Gaussian frailty so far. We also apply these three models by using a real-life bivariate survival data set of McGilchrist and Aisbett (1991 McGilchrist, C.A., Aisbett, C.W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to the kidney infection data and a better model is suggested for the data using the Bayesian model selection criteria.     

Objective Bayesian analysis for the multivariate skew-t model

We propose a novel Bayesian analysis of the p-variate skew-t model, providing a new parameterization, a set of non-informative priors and a sampler specifically designed to explore the posterior density of the model parameters. Extensions, such as the multivariate regression model with skewed errors and the stochastic frontiers model, are easily accommodated. A novelty introduced in the paper is given by the extension of the bivariate skew-normal model given in Liseo and Parisi (2013) to a more realistic p-variate skew-t model. We also introduce the R package mvst, which produces a posterior sample for the parameters of a multivariate skew-t model.     

Modeling of Inverse Gaussian Frailty Model for Bivariate Survival Data

Shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this article, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions namely, Weibull, generalized exponential, and exponential power distribution. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. To estimate the parameters involved in these models we adopt Markov Chain Monte Carlo (MCMC) approach. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply these three models to a real life bivariate survival data set of McGilchrist and Aisbett (1991 McGilchrist , C. A. , Aisbett , C. W. ( 1991 ). Regression with frailty in survival analysis . Biometrics 47 : 461 – 466 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to kidney infection and a better model is suggested for the data.     

Optimal network design for Bayesian spatial prediction of multivariate non-Gaussian environmental data

This paper deals with the problem of increasing air pollution monitoring stations in Tehran city for efficient spatial prediction. As the data are multivariate and skewed, we introduce two multivariate skew models through developing the univariate skew Gaussian random field proposed by Zareifard and Jafari Khaledi [21 H. Zareifard and M. Jafari Khaledi, Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process, J. Multivariate Anal. 114 (2013), pp. 16–28. doi: 10.1016/j.jmva.2012.07.003[Crossref], [Web of Science ®] , [Google Scholar]]. These models provide extensions of the linear model of coregionalization for non-Gaussian data. In the Bayesian framework, the optimal network design is found based on the maximum entropy criterion. A Markov chain Monte Carlo algorithm is developed to implement posterior inference. Finally, the applicability of two proposed models is demonstrated by analyzing an air pollution data set.     

Flexible parametric modelling of the hazard function in breast cancer studies

In cancer research, study of the hazard function provides useful insights into disease dynamics, as it describes the way in which the (conditional) probability of death changes with time. The widely utilized Cox proportional hazard model uses a stepwise nonparametric estimator for the baseline hazard function, and therefore has a limited utility. The use of parametric models and/or other approaches that enables direct estimation of the hazard function is often invoked. A recent work by Cox et al. [6 Cox, C., Chu, H., Schneider, M. F. and Munoz, A. 2007. Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat. Med., 26: 4352–4374. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] has stimulated the use of the flexible parametric model based on the Generalized Gamma (GG) distribution, supported by the development of optimization software. The GG distribution allows estimation of different hazard shapes in a single framework. We use the GG model to investigate the shape of the hazard function in early breast cancer patients. The flexible approach based on a piecewise exponential model and the nonparametric additive hazards model are also considered.     

Variable selection for survival data with a class of adaptive elastic net techniques

The accelerated failure time (AFT) models have proved useful in many contexts, though heavy censoring (as for example in cancer survival) and high dimensionality (as for example in microarray data) cause difficulties for model fitting and model selection. We propose new approaches to variable selection for censored data, based on AFT models optimized using regularized weighted least squares. The regularized technique uses a mixture of \(\ell _1\) and \(\ell _2\) norm penalties under two proposed elastic net type approaches. One is the adaptive elastic net and the other is weighted elastic net. The approaches extend the original approaches proposed by Ghosh (Adaptive elastic net: an improvement of elastic net to achieve oracle properties, Technical Reports 2007) and Hong and Zhang (Math Model Nat Phenom 5(3):115–133 2010), respectively. We also extend the two proposed approaches by adding censoring observations as constraints into their model optimization frameworks. The approaches are evaluated on microarray and by simulation. We compare the performance of these approaches with six other variable selection techniques-three are generally used for censored data and the other three are correlation-based greedy methods used for high-dimensional data.     

The generalized exponential cure rate model with covariates

In this article, we consider a parametric survival model that is appropriate when the population of interest contains long-term survivors or immunes. The model referred to as the cure rate model was introduced by Boag 1 Boag, J. W. 1949. Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J. R. Stat. Soc. Ser. B, 11: 15–53.  [Google Scholar] in terms of a mixture model that included a component representing the proportion of immunes and a distribution representing the life times of the susceptible population. We propose a cure rate model based on the generalized exponential distribution that incorporates the effects of risk factors or covariates on the probability of an individual being a long-time survivor. Maximum likelihood estimators of the model parameters are obtained using the the expectation-maximisation (EM) algorithm. A graphical method is also provided for assessing the goodness-of-fit of the model. We present an example to illustrate the fit of this model to data that examines the effects of different risk factors on relapse time for drug addicts.     

Modeling Australian twin data using shared positive stable frailty models based on reversed hazard rate

Unobserved heterogeneity, also called frailty, is a major concern in the application of survival analysis. The shared frailty models allow for the statistical dependence between the observed survival data. In this paper, we consider shared positive stable frailty model with the reversed hazard rate (RHR) with three different baseline distributions, namely the exponentiated Gumbel, the generalized Rayleigh, and the generalized inverse Rayleigh distributions. With these three baseline distributions we propose three different shared frailty models. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared positive stable frailty with the RHR so far. We also apply these three models by using a real-life bivariate survival data set of Australian twin data given by Duffy et a1. (1990 Duffy, D.L., Martin, N.G., Mathews, J.D. (1990). Appendectomy in Australian twins. Aust. J. Hum. Genet. 47(3):590–592.[PubMed], [Web of Science ®] , [Google Scholar]) and a better model is suggested for the data.     

Autocovariance Function of the Fractionally Integrated Separable Spatial ARMA (FISSARMA) Models

Spatial modeling is important in many fields and there are various kinds of spatial models. One of such models is known as the fractionally integrated separable spatial ARMA (FISSARMA) model. In the area of time series analysis, Sowell (1992 Sowell, F. (1992). Maximum likelihood estimation of stationary univariate fractionally integrated time series models. J. Econ. 53:165–188.[Crossref], [Web of Science ®] , [Google Scholar]) has established the autocovariance function of the long-memory models using hypergeometric function. In this paper we will extend Sowell’s work for FISSARMA models.     

Local influence diagnostics for generalized linear mixed models with overdispersion

Since the seminal paper by Cook and Weisberg [9 R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman &; Hall, London, 1982. [Google Scholar]], local influence, next to case deletion, has gained popularity as a tool to detect influential subjects and measurements for a variety of statistical models. For the linear mixed model the approach leads to easily interpretable and computationally convenient expressions, not only highlighting influential subjects, but also which aspect of their profile leads to undue influence on the model's fit [17 E. Lesaffre and G. Verbeke, Local influence in linear mixed models, Biometrics 54 (1998), pp. 570–582. doi: 10.2307/3109764[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. Ouwens et al. [24 M.J.N.M. Ouwens, F.E.S. Tan, and M.P.F. Berger, Local influence to detect influential data structures for generalized linear mixed models, Biometrics 57 (2001), pp. 1166–1172. doi: 10.1111/j.0006-341X.2001.01166.x[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] applied the method to the Poisson-normal generalized linear mixed model (GLMM). Given the model's nonlinear structure, these authors did not derive interpretable components but rather focused on a graphical depiction of influence. In this paper, we consider GLMMs for binary, count, and time-to-event data, with the additional feature of accommodating overdispersion whenever necessary. For each situation, three approaches are considered, based on: (1) purely numerical derivations; (2) using a closed-form expression of the marginal likelihood function; and (3) using an integral representation of this likelihood. Unlike when case deletion is used, this leads to interpretable components, allowing not only to identify influential subjects, but also to study the cause thereof. The methodology is illustrated in case studies that range over the three data types mentioned.     

A zero-inflated non default rate regression model for credit scoring data

The aim of this paper is to propose a survival credit risk model that jointly accommodates three types of time-to-default found in bank loan portfolios. It leads to a new framework that extends the standard cure rate model introduced by Berkson and Gage (1952 Berkson, J., and R. P. Gage. 1952. Survival curve for cancer patients following treatment. Journal of the American Statistical Association 47 (259):501–15.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) regarding the accommodation of zero-inflations. In other words, we propose a new survival model that takes into account three different types of individuals which have so far not been jointly accounted for: (i) an individual with an event at the starting time (zero time); (ii) non susceptible for the event, or (iii) susceptible for the event. Considering this, the zero-inflated Weibull non default rate regression models, which include a multinomial logistic link for the three classes, are presented using an application for credit scoring data. The parameter estimation is reached by the maximum-likelihood estimation procedure and Monte Carlo simulations are carried out to assess its finite sample performance.     

Calibration of Proportional Hazards and Accelerated Failure Time Models

Given a prognostic model based on one population, one may ask: Can this model be used to accurately predict disease in a different population? When the underlying rate of disease differs in the new population, the model must be calibrated. van Houwelingen (2000 van Houwelingen , H. ( 2000 ). Validation, calibration, revision and combination of prognostic survival models . Statistics in Medicine 19 : 3401 – 3415 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) considered this calibration problem focusing on proportional hazards models. We extend the validation by calibration to the log-logistic accelerated failure time model. We use calibration of proportional hazards models and log-logistic accelerated failure time models to examine whether a survival model based on the Framingham Heart Study can be applied to diverse studies around the world.     

Unified multivariate survival model with a surviving fraction: an application to a Brazilian customer churn data

In this paper we propose a new lifetime model for multivariate survival data in presence of surviving fractions and examine some of its properties. Its genesis is based on situations in which there are m types of unobservable competing causes, where each cause is related to a time of occurrence of an event of interest. Our model is a multivariate extension of the univariate survival cure rate model proposed by Rodrigues et al. [37 J. Rodrigues, V.G. Cancho, M. de Castro, and F. Louzada-Neto, On the unification of long-term survival models, Statist. Probab. Lett. 79 (2009), pp. 753–759. doi: 10.1016/j.spl.2008.10.029[Crossref], [Web of Science ®] , [Google Scholar]]. The inferential approach exploits the maximum likelihood tools. We perform a simulation study in order to verify the asymptotic properties of the maximum likelihood estimators. The simulation study also focus on size and power of the likelihood ratio test. The methodology is illustrated on a real data set on customer churn data.