The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.

The optimal dividend barrier in the Gamma-Omega model

In the traditional actuarial risk model, if the surplus is negative, the company is ruined and has to go out of business. In this paper we distinguish between ruin (negative surplus) and bankruptcy (going out of business), where the probability of bankruptcy is a function of the level of negative surplus. The idea for this notion of bankruptcy comes from the observation that in some industries, companies can continue doing business even though they are technically ruined. Assuming that dividends can only be paid with a certain probability at each point of time, we derive closed-form formulas for the expected discounted dividends until bankruptcy under a barrier strategy. Subsequently, the optimal barrier is determined, and several explicit identities for the optimal value are found. The surplus process of the company is modeled by a Wiener process (Brownian motion).

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

The Conway-Maxwell-Poisson-generalized gamma regression model with long-term survivors

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

A multivariate frailty model for disease recurrences and survival

A multivariate frailty hazard model is developed for joint-modeling of three correlated time-to-event outcomes: (1) local recurrence, (2) distant recurrence, and (3) overall survival. The term frailty is introduced to model population heterogeneity. The dependence is modeled by conditioning on a shared frailty that is included in the three hazard functions. Independent variables can be included in the model as covariates. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The algorithm used in present application is the hybrid Metropolis-Hastings algorithm, which simultaneously updates all parameters with evaluations of gradient of log posterior density. The performance of this approach is examined based on simulation studies using Exponential and Weibull distributions. We apply the proposed methods to a study of patients with soft tissue sarcoma, which motivated this research. Our results indicate that patients with chemotherapy had better overall survival with hazard ratio of 0.242 (95% CI: 0.094 - 0.564) and lower risk of distant recurrence with hazard ratio of 0.636 (95% CI: 0.487 - 0.860), but not significantly better in local recurrence with hazard ratio of 0.799 (95% CI: 0.575 - 1.054). The advantages and limitations of the proposed models, and future research directions are discussed. ^

Study on Robustness of Correlated Frailty Model

2000 Mathematics Subject Classifi cation: 62J12.

Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients

In this paper, we present different ofrailtyo models to analyze longitudinal data in the presence of covariates. These models incorporate the extra-Poisson variability and the possible correlation among the repeated counting data for each individual. Assuming a CD4 counting data set in HIV-infected patients, we develop a hierarchical Bayesian analysis considering the different proposed models and using Markov Chain Monte Carlo methods. We also discuss some Bayesian discrimination aspects for the choice of the best model.

Gamma Knife Surgery versus Linac for Brain Metastasis: Which Technique for Which Patient? Analysis of an Historical Cohort of 63 Consecutive Patients Harboring 130 Lesions

Objectives: We present the retrospective analysis of a single-institution experience for radiosurgery (RS) in brain metastasis (BM) with Gamma Knife (GK) and Linac. Methods: From July 2010 to July 2012, 28 patients (with 83 lesions) had RS with GK and 35 patients (with 47 lesions) with Linac. The primary outcome was the local progression-free survival (LPFS). The secondary outcome was the overall survival (OS). Apart a standard statistical analysis, we included a Cox regression model with shared frailty, to modulate the within-patient correlation (preliminary evaluation showed a significant frailty effect, meaning that the correlation within patient could be ignored). Results: The mean follow-up period was 11.7 months (median 7.9, 1.7-22.7) for GK and 18.1 (median 17, 7.5-28.7) for Linac. The median number of lesions per patient was 2.5 (1-9) in GK compared with 1 (1-3) in Linac. There were more radioresistant lesions (melanoma) and more lesions located in functional areas for the GK group. The median dose was 24 Gy (GK) compared with 20 Gy (Linac). The LPFS actuarial rate was as follows: for GK at 3, 6, 9, 12, and 17 months: 96.96, 96.96, 96.96, 88.1, and 81.5%, and remained stable till 32 months; for Linac at 3, 6, 12, 17, 24, and 33 months, it was 91.5, 91.5, 91.5, 79.9, 55.5, and 17.1%, respectively (p = 0.03, chi-square test). After the Cox regression analysis with shared frailty, the p-value was not statistically significant between groups. The median overall survival was 9.7 months for GK and 23.6 months for Linac group. Uni- and multivariate analysis showed a lower GPA score and noncontrolled systemic status were associated with lower OS. Cox regression analysis adjusting for these two parameters showed comparable OS rate. Conclusions: In this comparative report between GK and Linac, preliminary analysis showed that more difficult cases are treated by GK, with patients harboring more lesions, radioresistant tumors, and highly functional located. The groups look, in this sense, very heterogeneous at baseline. After a Cox frailty model, the LPFS rates seemed very similar (p < 0.05). The OS was similar, after adjusting for systemic status and GPA score (p < 0.05). The technical reasons for choosing GK instead of Linac were the anatomical location related to highly functional areas, histology, technical limitations of Linac movements, especially lower posterior fossa locations, or closeness of multiple lesions to highly functional areas optimal dosimetry with Linac

Solvency considerations in the gamma-omega surplus model

Ce mémoire de maîtrise traite de la théorie de la ruine, et plus spécialement des modèles actuariels avec surplus dans lesquels sont versés des dividendes. Nous étudions en détail un modèle appelé modèle gamma-omega, qui permet de jouer sur les moments de paiement de dividendes ainsi que sur une ruine non-standard de la compagnie. Plusieurs extensions de la littérature sont faites, motivées par des considérations liées à la solvabilité. La première consiste à adapter des résultats d’un article de 2011 à un nouveau modèle modifié grâce à l’ajout d’une contrainte de solvabilité. La seconde, plus conséquente, consiste à démontrer l’optimalité d’une stratégie de barrière pour le paiement des dividendes dans le modèle gamma-omega. La troisième concerne l’adaptation d’un théorème de 2003 sur l’optimalité des barrières en cas de contrainte de solvabilité, qui n’était pas démontré dans le cas des dividendes périodiques. Nous donnons aussi les résultats analogues à l’article de 2011 en cas de barrière sous la contrainte de solvabilité. Enfin, la dernière concerne deux différentes approches à adopter en cas de passage sous le seuil de ruine. Une liquidation forcée du surplus est mise en place dans un premier cas, en parallèle d’une liquidation à la première opportunité en cas de mauvaises prévisions de dividendes. Un processus d’injection de capital est expérimenté dans le deuxième cas. Nous étudions l’impact de ces solutions sur le montant des dividendes espérés. Des illustrations numériques sont proposées pour chaque section, lorsque cela s’avère pertinent.

Solvency considerations in the gamma-omega surplus model

Ce mémoire de maîtrise traite de la théorie de la ruine, et plus spécialement des modèles actuariels avec surplus dans lesquels sont versés des dividendes. Nous étudions en détail un modèle appelé modèle gamma-omega, qui permet de jouer sur les moments de paiement de dividendes ainsi que sur une ruine non-standard de la compagnie. Plusieurs extensions de la littérature sont faites, motivées par des considérations liées à la solvabilité. La première consiste à adapter des résultats d’un article de 2011 à un nouveau modèle modifié grâce à l’ajout d’une contrainte de solvabilité. La seconde, plus conséquente, consiste à démontrer l’optimalité d’une stratégie de barrière pour le paiement des dividendes dans le modèle gamma-omega. La troisième concerne l’adaptation d’un théorème de 2003 sur l’optimalité des barrières en cas de contrainte de solvabilité, qui n’était pas démontré dans le cas des dividendes périodiques. Nous donnons aussi les résultats analogues à l’article de 2011 en cas de barrière sous la contrainte de solvabilité. Enfin, la dernière concerne deux différentes approches à adopter en cas de passage sous le seuil de ruine. Une liquidation forcée du surplus est mise en place dans un premier cas, en parallèle d’une liquidation à la première opportunité en cas de mauvaises prévisions de dividendes. Un processus d’injection de capital est expérimenté dans le deuxième cas. Nous étudions l’impact de ces solutions sur le montant des dividendes espérés. Des illustrations numériques sont proposées pour chaque section, lorsque cela s’avère pertinent.

Model risk in the pricing of exotic options

The growth experimented in recent years in both the variety and volume of structured products implies that banks and other financial institutions have become increasingly exposed to model risk. In this article we focus on the model risk associated with the local volatility (LV) model and with the Variance Gamma (VG) model. The results show that the LV model performs better than the VG model in terms of its ability to match the market prices of European options. Nevertheless, both models are subject to significant pricing errors when compared with the stochastic volatility framework.

Gamma Knife radiosurgery after previous microvascular decompression decreases the chances of pain free in classical trigeminal neuralgia

Purpose: To evaluate the safety-efficacy of Gamma Knife surgery (GKS) as a second treatment for classical trigeminal neuralgia (CTN), and the influence of prior microvascular decompression (MVD). Methods: Between July 1992 and November 2010, 737 patients have been operated with GKRS for ITN and prospectively evaluated in Timone University Hospital in Marseille, France. Among these, 54 patients had a previous history of MVD. Radiosurgery using a Gamma Knife (model B or C or Perfexion) was performed on the basis of on both MR and CT targeting. A single 4 mm isocenter was positioned in the cisternal portion of the trigeminal nerve at a median distance of 7.6 mm (range 3.9-11.9) anteriorly to the emergence of the nerve (retrogasserian target). A median maximum dose of 85 Gy (range 70-90) was delivered. Here, the 45 patients with previous MVD and a follow-up longer than one year are evaluated (the patients with megadolichobasilar artery compression and multiple sclerosis were excluded). Results: The median age in this series was 56.75 years (range 28.09-82.39). The median follow-up period was 39.48 months (range 14.10-144.65). All the patients had a past history of surgery, with at least one previous failed MVD, but also radiofrequency lesion (RFL) in 16 patients (35.6%), balloon microcompression in 7 (15.6%) and glycerol rhizotomy in 1 (2.2%). Thirty-five patients (77.8%) were initially pain free after GKS within a median time of 14 days (range 0, 180). Patients from this group had less probability of being pain free compared to our global population of essential trigeminal neuralgia without previous MVD history (p=0.010, hazard ratio of 0.64). Their probability of remaining pain free at 3, 5, 7 and 10 years was 66.5%, 59.1%, 59.1% and 44.3%, respectively. Twelve patients (34.3%) initially pain free experienced a recurrence with a median delay of 31.21 months (range 3.40-89.93). The hypoesthesia actuarial rate at 1 year was 9.1% and remained stable till 12 years with a median delay of onset of 8 months (range 8-8). Conclusions: Retrogasserian GKS proofed to be safe and effective on the long-term basis even after failed previous MVD. Even if the initial result of pain free was only 77.8%, the toxicity was low with only 9.1% hypoesthesia. No patient reported a bothersome hypoesthesia. The probability of maintaining pain relief in the long-term was of 44.3% at 10 years.