Dissertations / Theses on the topic 'Parametric survival models'

A non-proportional hazards model is developed. The model can accommodate right censored, interval censored and double interval censored data sets. There is also an extension of the model to include multiplicative gamma frailties. The basic model is an extension of the dynamic Bayesian survival model developed by Gamerman (1987), but with some alterations and using a different method of model fitting. The model developed here, the Normal Dynamic Survival Model, models both the log-baseline hazard and covariate effects by a piecewise constant and correlated process, based on some division of the time axis. Neighbouring piecewise constant parameters are related by a simple evolution equation: normal with mean zero and unknown variance to be estimated. The method of estimation is to use Markov chain Monte Carlo simulations: Gibbs sampling with a Metropolis-Hastings step. For double interval censored data an iterative data augmentation procedure is considered: exploiting the comparative ease at which interval censored observations may be modelled. The model is applied within a range of well known, and illustrative data sets, with convincing results. In addition the impact of censoring is investigated by a simulation study.

Estimating causal effects in clinical trials is often complicated by treatment noncompliance and missing outcomes. In time-to-event studies, estimation is further complicated by censoring. Censoring is a type of missing outcome, the mechanism of which may be non-ignorable. While new estimates have recently been proposed to account for noncompliance and missing outcomes, few studies have specifically considered time-to-event outcomes, where even the intention-to-treat (ITT) estimator is potentially biased for estimating causal effects of assigned treatment. In this thesis, we develop a series of parametric potential-outcome (PPO) survival models, for the analysis of randomised controlled trials (RCT) with time-to-event outcomes and noncompliance. Both ignorable and non-ignorable censoring mechanisms are considered. We approach model-fitting from a likelihood-based perspective, using the EM algorithm to locate maximum likelihood estimators. We are not aware of any previous work that addresses these complications jointly. In addition, we give new formulations for the average causal effect (ACE) and the complier average causal effect (CACE) to suit survival analysis. To illustrate the likelihood-based method proposed in this thesis, the HIP breast cancer trial data \citep{Baker98, Shapiro88} were re-analysed using specific PPO-survival models, the Weibull and log-normal based PPO-survival models, which assume that the failure time and censored time distributions both follow Weibull or log-normal distributions. Furthermore, an extended PPO-survival model is also derived in this thesis, which permits investigation into the impact of causal effect after accommodating certain pre-treatment covariates. This is an important contribution to the potential outcomes, survival and RCT literature. For comparison, the Frangakis-Rubin (F-R) model \citep{Frangakis99} is also applied to the HIP breast cancer trial data. To date, the F-R model has not yet been applied to any time-to-event data in the literature.

An efficient way of analyzing survival clinical data such as cancer data is a great concern to health experts. In this study, we investigate and propose an efficient way of handling survival clinical data. Simulation studies were conducted to compare performances of various forms of survival model techniques using an R package ``survsim". Models performance was conducted with varying sample sizes as small ($n5000$). For small and mild samples, the performance of the semi-parametric outperform or approximate the performance of the parametric model. However, for large samples, the parametric model outperforms the semi-parametric model. We compared the effectiveness and reliability of our proposed techniques using a real clinical data of mild sample size. Finally, systematic steps on how to model and explain the proposed techniques on real survival clinical data was provided.

Le premier objectif de la thèse est de présenter un test d'ajustement pour les modèles paramétriques couramment utilisés en l'analyse de survie, la fiabilité, les sciences sociales, l'ingénierie, la santé publique et la démographie, en présence de censure à droite. Nous développons un logiciel en langue R pour les modèles paramétrique. Le modèle de Birnbaum-Saunders (BS) est utilisé pour la test d'ajustement pour les modèles AFT paramétriques et en analyse de système redondant. L'autre contribution porte sur l'analyse de système redondant composé avec une composante en état hot et l'autre en réserve fonctionnent en état warm pour augmenter la fiabilité de systeme. Nous calculons la fiabilité du système en termes de Fonction de répartition et nous donnons l'intervalle de confiance asymptotique
This is an increasing importance in survival analysis and reliability to select a suitable basic model for further inquiries of the data. Little deviation in basic model can cause serious problems in final results. The presence of censoring and accelerated stresses make this task more difficult. Chi-square type goodness of fit tests are most commonly used for model selection. Many modifications in chi-square tests have been proposed by various researcher. The first aim of the thesis is to present a goodness of fit test for wide rage of parametric models (shape-scale families) commonly used in survival analysis, social sciences, engineering, public health and demography, in presence of right censoring. We give the explicit forms of the quadratic form of the test statistic (NRR test) for various models and apply the test on real data. We develop a computer program in R-language for all models. A separate section is dedicated for the test in demography. We focus on the Birnbaum-Saunders (BS) distribution for goodness of fit test for parametric AFT-model and analysis of redundant system.The other purpose of the thesis is to give the analysis of redundant system. To ensure high reliability of the main components of the systems, standby units are used. The main component is replaced by the standby unit automatically, if it fails. The standby unit can be in warm, hot, or cold state. We give the procedure of one main and (n-1) standby units placed in hot state, and give the detailed analysis of one main and one standby unit using BS parametric family. We use Sedyakin's physical principal and the approach of accelerated failure time model for the analysis of redundant system. This approach is different from the traditional ones in the literature but difficulties in calculations. We calculate the reliability of the system in terms of distribution function (unreliability function) and asymptotic confidence interval

The dependence between survival times and covariates is described e.g. by proportional hazard models. We consider partly parametric Cox models and discuss here the estimation of interesting parameters. We represent the ma- ximum likelihood approach and extend the results of Huang (1999) from linear to nonlinear parameters. Then we investigate the least squares esti- mation and formulate conditions for the a.s. boundedness and consistency of these estimators.

In survival studies the values of some covariates may change over time. It is natural to incorporate such time dependent covariates into the model to be used in the survival analysis. A standard approach is to use the semi parametric extended Cox proportional hazard model. An alternative is to extend a standard parametric model, such as a Weibull regression model, to include time-dependent covariates. However, the use of such simple parametric models may be too restrictive. Therefore in this thesis we further extend the Weibull regression model with time dependent covariates by using splines to give greater flexibility. The use of Cox, simple parametric and Weibull spline models is illustrated with and without time dependent covariates on two large survival data sets supplied by NHS Blood and Transplant. One data set involves times to graft failure of patients who have undergone a corneal transplant and contains many fixed covariates and one time-dependent covariate with at most one change point. The other data set concerns time to death of heart transplant patients and contains many fixed covariates and a time-dependent covariate with possibly many change points. A simulation study is used to evaluate and compare likelihood-based methods of inference for the competing models. In the first stage attention is focused on selection of the number of knots in the Weibull spline model in the simple case with no covariates. Stage two examines the results of inferences from the Weibull splines model with fixed covariates. Stage three compares the results of inferences for parameters in the extended Cox model and two simple parametric models with time-dependent covariates. Finally, stage four examines the Weibull splines model with time-dependent covariates.

In doctoral thesis redundant systems and degradation models are considered. To ensure high reliability of important elements of the system, the stand-by units can be used. These units are commuted and operate instead of the main failed unit. The stand-by units can function in the different conditions: “hot”, “cold” or “warm” reserving. In the thesis systems with “warm” stand-by units are analyzed. Hypotheses of smooth commuting are formulated and goodness-of-fit tests for these hypotheses are constructed. Nonparametric and parametric point and interval estimation procedures are given. Modeling and statistical estimation of reliability of systems from failure time and degradation data are considered.
Daktaro disertacijos tyrimo objektai yra rezervuotos sistemos ir degradaciniai modeliai. Norint užtikrinti svarbių sistemos elementų aukštą patikimumą, naudojami jų rezerviniai elementai, kurie gali būti įjungiami sugedus šiems pagrindiniams elementams. Rezerviniai elementai gali funkcionuoti skirtinguose režimuose: „karštame“, „šaltame“ arba „šiltame“. Disertacijoje yra nagrinėjamos sistemos su „šiltai“ rezervuotais elementais. Darbe suformuluojama rezervinio elemento „sklandaus įjungimo“ hipotezė ir konstruojami statistiniai kriterijai šiai hipotezei tikrinti. Nagrinėjami neparametrinio ir parametrinio taškinio bei intervalinio vertinimo uždaviniai. Disertacijoje nagrinėjami pakankamai bendri degradacijos modeliai, kurie aprašo elementų gedimų intensyvumą kaip funkciją kiek naudojamų apkrovų, tiek ir degradacijos lygio, kuri savo ruožtu modeliuojama naudojant stochastinius procesus.

This thesis introduces methods used in time-to-date analysis. It is written generally and so usable in dealing with any example. The thesis deals with problem of censoring, which means, that some observations occurred after the following, which is typical for the lifetime analysis. Methods mentioned in the thesis are nonparametric and parametric estimates of the survival function and their characteristics, and regression models, concretely Cox model and accelerated failure time model, which examine effect of the covariates on survival function. In the thesis is beside survival function presented hazard function, which express intensity of the analyzed event and cumulative hazard function, which is created as the name suggests by cumulative summation of the hazard function. Estimates of these functions are obtainable from survival function and for parametric estimate often exists formula resulting from parameters of used distribution. Empirical part of the thesis introduces influence of several different types and degrees of censoring on parametric and nonparametric estimates of the survival function, mean and median. The other empirical example is the usage of regression analysis on the data from the lungs cancer research made by Mayo Clinic.

In population-based cancer studies, researchers are often only interested in cancer-specific survival to determine variations in the impact of cancer in different population groups. In such cases, the net survival measure is usually reported. However, this is of little relevance for patients as it does not consider the probability of dying from other causes before dying from cancer, otherwise known as competing risks. Therefore, alternative measures that take this into account are required for a better representation of cancer survival in the real-world. Measures estimated from within this framework provide a more meaningful interpretation for patients which can be communicated to facilitate treatment-related decisions. Differences in interpretation between various cancer survival measures, and when they are appropriate, has led to some confusion amongst non-statisticians. This motivates the development of publicly available tools to improve understanding and communication. Thus, an aim of this thesis is to develop an interactive web-tool to aid interpretation of various important cancer survival measures that are commonly reported. Although not a new concept, many often fail to account for competing risks when it is necessary for a study. Even when accounted for, many apply the theory, or report analyses incorrectly. Recently, efforts have been made to make competing risks methods more accessible for researchers from within the increasingly popular flexible parametric modelling framework. However, much work is yet to be done, especially as cancer registry datasets are becoming larger with more detailed covariate information. This means that models are increasing in complexity and more computationally efficient methods are required. With this in mind, the primary aim of this PhD is to further develop competing risks methods from within the flexible parametric modelling framework. Particular focus is on obtaining predictions with less computational effort that facilitate communication of risk when interest is in prognosis.

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The purpose of this thesis is to firstly analyze the determinants on the survival of United States Marine Corps Officers, and secondly, to develop the methodology to optimize the accessions of prior and non-prior enlisted officers. Using data from the Marine Corps Officer Accession Career file (MCCOAC), the Cox Proportional Hazards Model is used to estimate the effects of officer characteristics on their survival as a commissioned officer in the USMC. A Markov model for career transition is combined with fiscal data to determine the optimum number of prior and non-prior enlisted officers under the constraints of force structure and budget. The findings indicate that prior enlisted officers have a better survival rate than their non-prior enlisted counterparts. Additionally, officers who are married, commissioned through MECEP, graduate in the top third of their TBS class, and are assigned to a combat support MOS have a better survival rate than officers who are unmarried, commissioned through USNA, graduate in the middle third of their TBS class, and are assigned to either combat or combat service support MOS. The findings also indicate that the optimum number of prior enlisted officer accessions may be considerably lower than recent trends and may differ across MOS. Based on the findings; it is recommended that prior enlisted officer accession figures be reviewed.
Major, Australian Army

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Esta dissertaÃÃo tem por objetivo calcular as taxas de sobrevivÃncia dos participantes de Fundos de PensÃo do setor elÃtrico nacional, bem como encontrar o modelo paramÃtrico de sobrevivÃncia que melhor represente os dados em estudo. Para desenvolvimento do trabalho utilizamos dados de 14 entidades com informaÃÃes de participantes ativos e aposentados, com exceÃÃo dos invÃlidos, referentes ao perÃodo de 2001 a 2009, totalizando um nÃmero total de 100.000 vidas analisadas. Para calcular as taxas brutas de sobrevivÃncia, utilizamos o mÃtodo indireto, descrito em Ferreira (1985). ApÃs o cÃlculo das taxas originais, efetuamos o processo de suavizaÃÃo por mÃdias mÃveis, visando corrigir as flutuaÃÃes indesejadas obtidas na curva bruta de sobrevivÃncia. Mesmo apÃs o processo de suavizaÃÃo, optamos por restringir o estudo Ãs idades dentro do intervalo de 25 a 85 anos, dado o baixo nÃmero de Ãbitos e expostos nas idades supramencionadas. A partir da curva suavizada, aplicamos os modelos paramÃtricos de sobrevivÃncia de Gompertz, Gompertz-Makeham, Thiele e Helingman-Pollard, para testar o melhor ajuste da equaÃÃo. Os resultados mostraram que nenhum dos modelos paramÃtricos analisados se mostrou com robustez estatÃstica suficiente para se proceder a uma anÃlise preditiva com confiabilidade aceitÃvel.
This paper aims to calculate the survival rates of the participants of the Pension Funds electricity sector as well as finding the parametric survival model that best represents the data in the study. For development work we used data from 14 organizations with information of participants and retirees, with the exception of the disabled, for the period 2001 to 2009, amounting to a total of 100,000 lives analyzed. To calculate the crude rates of survival using the indirect method described in Ferreira (1985). After calculation of the original rates, we make the process of smoothing by moving averages in order to correct the unwanted fluctuations in the curve obtained crude survival. Even after the smoothing process, we chose to restrict the study to age within the range of 25 to 85 years, given the low number of deaths at ages above and exposed. From the smooth curve we apply the parametric models of survival Gompertz, Gompertz-Makeham, Thiele and Helingman-Pollard, to test the best fit of the equation. The results showed that none of the models proved to be analyzed with parametric statistical robust enough to conduct a predictive analysis with acceptable reliability.

In many clinical studies, continuous variables such as age, blood pressure and cholesterol are measured and analyzed. Often clinicians prefer to categorize these continuous variables into different groups, such as low and high risk groups. The goal of this work is to find the cutpoint of a continuous variable where the transition occurs from low to high risk group. Different methods have been published in literature to find such a cutpoint. We extended the methods of Contal and O’Quigley (1999) which was based on the log-rank test and the methods of Klein and Wu (2004) which was based on the Score test to find the cutpoint of a continuous covariate. Since the log-rank test is a nonparametric method and the Score test is a parametric method, we are interested to see if an extension of the parametric procedure performs better when the distribution of a population is known. We have developed a method that uses the parametric score residuals to find the cutpoint. The performance of the proposed method will be compared with the existing methods developed by Contal and O’Quigley and Klein and Wu by estimating the bias and mean square error of the estimated cutpoints for different scenarios in simulated data.

Cette thèse a été conçu pour explorer les modèles dynamiques de régression, d’évaluer les inférences statistiques pour l’analyse des données de survie et de fiabilité. Ces modèles de régression dynamiques que nous avons considérés, y compris le modèle des hasards proportionnels paramétriques et celui de la vie accélérée avec les variables qui peut-être dépendent du temps. Nous avons discuté des problèmes suivants dans cette thèse.Nous avons présenté tout d’abord une statistique de test du chi-deux généraliséeY2nquiest adaptative pour les données de survie et fiabilité en présence de trois cas, complètes,censurées à droite et censurées à droite avec les covariables. Nous avons présenté en détailla forme pratique deY2nstatistique en analyse des données de survie. Ensuite, nous avons considéré deux modèles paramétriques très flexibles, d’évaluer les significations statistiques pour ces modèles proposées en utilisantY2nstatistique. Ces modèles incluent du modèle de vie accélérés (AFT) et celui de hasards proportionnels (PH) basés sur la distribution de Hypertabastic. Ces deux modèles sont proposés pour étudier la distribution de l’analyse de la duré de survie en comparaison avec d’autre modèles paramétriques. Nous avons validé ces modèles paramétriques en utilisantY2n. Les études de simulation ont été conçus.Dans le dernier chapitre, nous avons proposé les applications de ces modèles paramétriques à trois données de bio-médicale. Le premier a été fait les données étendues des temps de rémission des patients de leucémie aiguë qui ont été proposées par Freireich et al. sur la comparaison de deux groupes de traitement avec des informations supplémentaires sur les log du blanc du nombre de globules. Elle a montré que le modèle Hypertabastic AFT est un modèle précis pour ces données. Le second a été fait sur l’étude de tumeur cérébrale avec les patients de gliome malin, ont été proposées par Sauerbrei & Schumacher. Elle a montré que le meilleur modèle est Hypertabastic PH à l’ajout de cinq variables de signification. La troisième demande a été faite sur les données de Semenova & Bitukov, à concernant les patients de myélome multiple. Nous n’avons pas proposé un modèle exactement pour ces données. En raison de cela était les intersections de temps de survie.Par conséquent, nous vous conseillons d’utiliser un autre modèle dynamique que le modèle de la Simple Cross-Effect à installer ces données
This thesis was designed to explore the dynamic regression models, assessing the sta-tistical inference for the survival and reliability data analysis. These dynamic regressionmodels that we have been considered including the parametric proportional hazards andaccelerated failure time models contain the possibly time-dependent covariates. We dis-cussed the following problems in this thesis.At first, we presented a generalized chi-squared test statisticsY2nthat is a convenient tofit the survival and reliability data analysis in presence of three cases: complete, censoredand censored with covariates. We described in detail the theory and the mechanism to usedofY2ntest statistic in the survival and reliability data analysis. Next, we considered theflexible parametric models, evaluating the statistical significance of them by usingY2nandlog-likelihood test statistics. These parametric models include the accelerated failure time(AFT) and a proportional hazards (PH) models based on the Hypertabastic distribution.These two models are proposed to investigate the distribution of the survival and reliabilitydata in comparison with some other parametric models. The simulation studies were de-signed, to demonstrate the asymptotically normally distributed of the maximum likelihood estimators of Hypertabastic’s parameter, to validate of the asymptotically property of Y2n test statistic for Hypertabastic distribution when the right censoring probability equal 0% and 20%.n the last chapter, we applied those two parametric models above to three scenes ofthe real-life data. The first one was done the data set given by Freireich et al. on thecomparison of two treatment groups with additional information about log white blood cellcount, to test the ability of a therapy to prolong the remission times of the acute leukemiapatients. It showed that Hypertabastic AFT model is an accurate model for this dataset.The second one was done on the brain tumour study with malignant glioma patients, givenby Sauerbrei & Schumacher. It showed that the best model is Hypertabastic PH onadding five significance covariates. The third application was done on the data set given by Semenova & Bitukov on the survival times of the multiple myeloma patients. We did not propose an exactly model for this dataset. Because of that was an existing oneintersection of survival times. We, therefore, suggest fitting other dynamic model as SimpleCross-Effect model for this dataset

The objective of the present study is to investigate key aspects of ovarian and breast cancers, which are two main causes of mortality among women. Identification of the true behavior of survivorship and influential risk factors is essential in designing treatment protocols, increasing disease awareness and preventing possible causes of disease. There is a commonly held belief that African Americans have a higher risk of cancer mortality. We studied racial disparities of women diagnosed with ovarian cancer on overall and disease-free survival and found out that there is no significant difference in the survival experience among the three races: Whites, African Americans and Other races. Tumor sizes at diagnosis among the races were significantly different, as African American women tend to have larger ovarian tumor sizes at the diagnosis. Prognostic models play a major role in health data research. They can be used to estimate adjusted survival probabilities and absolute and relative risks, and to determine significantly contributing risk factors. A prognostic model will be a valuable tool only if it is developed carefully, evaluating the underlying model assumptions and inadequacies and determining if the most relevant model to address the study objectives is selected. In the present study we developed such statistical models for survival data of ovarian and breast cancers. We found that the histology of ovarian cancer had risk ratios that vary over time. We built two types of parametric models to estimate absolute risks and survival probabilities and to adjust the time dependency of the relative risk of Histology. One parametric model is based on classical probability distributions and the other is a more flexible parametric model that estimates the baseline cumulative hazard function using spline functions. In contrast to women diagnosed with ovarian cancer, women with breast cancer showed significantly different survivorship among races where Whites had a poorer overall survival rate compared to African Americans and Other races. In the breast cancer study, we identified that age and progesterone receptor status have time dependent hazard ratios and age and tumor size display non-linear effects on the hazard. We adjusted those non-proportional hazards and non-linear effects by using an extended Cox regression model in order to generate more meaningful interpretations of the data.

Les maladies du motoneurone (MNDs) et notamment la Sclérose Latérale Amyotrophique (SLA) et l’Amyotrophie Spinale liée aux mutations du gène SMN1 (SMA), sont caractérisées par une perte progressive des neurones moteurs au niveau de la moelle épinière. L’imagerie par résonance magnétique (IRM) est actuellement l’approche la plus performante pour quantifier la dégénérescence spinale. De plus, les explorations de neurophysiologie pourraient être des biomarqueurs sensibles de progression de la maladie. L’objectif de cette thèse a été d’associer l’IRM de la moelle épinière aux techniques d’évaluation neurophysiologique servant à analyser la dégénérescence dans les MNDs. Dans la SLA, nous avons montré que l’IRM cervicale est un outil efficace pour le diagnostic et la prédiction de la survie et qu’elle permet d’apprécier les patterns précoces de dégénérescence chez les sujets pre-symptomatiques porteurs de la mutation c9orf72. Dans une cohorte de patients adultes atteints de SMA, ce protocole d’IRM a été couplée à une technique de neurophysiologie servant à calculer un index de la perte d’unités motrices (MUNIX). Avec cette méthode nous avons mis en évidence une atrophie isolée de la substance grise cervicale associée à des modifications longitudinales significatives des valeurs du MUNIX. Cet index semble être le biomarqueur le plus pertinent de progression de la maladie
Motor neuron diseases (MNDs) are characterized by dysfunction and loss of ventral horn MNs in the spinal grey matter (GM). Nevertheless, different MNDs such as amyotrophic lateral sclerosis (ALS) and spinal muscular atrophy (SMA) present with specific clinical presentations. Magnetic resonance imaging (MRI) is the most powerful approach at the brain and spinal cord (SC) level to extract quantitative data on degeneration. At the same time, neurophysiological techniques including motor unit number index (MUNIX) could represent a useful tool to map MN loss. The objective of this project was to combine SC and brain MRI with MUNIX to better characterize degeneration in MNDs, with the aim of identifying possible markers of disease progression. In ALS patients, we showed that SC MRI parameters improve diagnostic and prognostic prediction. Secondly, we longitudinally analyzed a wide population of pre-symptomatic carriers of the c9orf72 mutation, detecting early and progressive cervical WM degeneration. Finally, we considered a cohort of SMN1-related adult SMA patients who underwent a SC and brain MRI protocol combined with MUNIX. We detected isolated cervical GM atrophy not associated with WM pathology. After 24 months observation time, significant MUNIX modifications were demonstrated, suggesting that neurophysiological techniques could be an effective biomarker of disease progression

The objective of the present study is to address some important questions related to prostate cancer treatments and survivorship among White and African American men. It is commonly understood that the risk of developing prostate cancer is higher in African American men than the other races. However, using parametric analysis, this study demonstrates that this perception is a "myth" not a "reality". The study further identifies the existence of racial/ethnic disparities by comparing the average mean tumor size, the median of survival time, and the survival function between White and African American men. These results underline the necessity of understanding the role of racial background in working towards improved clinical targeting, and thereby, improving clinical outcomes. Furthermore, parametric survival analysis was performed to estimate the survivorship of white men undergoing different treatments at each stage of prostate cancer. Additionally, to better understand the risk factors (age, tumor size, the interaction between age and tumor size) associated with survival time, an accelerated failure time model was developed that could accurately predict the rates of survivorship of white men at each stage of prostate cancer in accordance with whatever treatment they had received. Finally, the results of parametric survival analysis and the accelerated failure time model are compared among white men undergoing similar treatment at each stage of the disease.

Mestrado em Decisão Económica e Empresarial
No presente estudo, foram aplicados vários modelos para estimar a função de sobrevivência relativa aos tempos decorridos entre a prestação de um serviço e a sua cobrança. O estudo envolveu dados experimentais, obtidos através da base de dados dos Órgãos de Comunicação Social notificados para pagar a Taxa de Regulação e Supervisão à Entidade Reguladora para a Comunicação Social. Antes de proceder à estimação dos modelos propostos, foi introduzida uma análise detalhada dos dados, baseada em estatísticas descritivas e cruzamentos de variáveis. Ao nível da estimação, considerou-se os seguintes modelos: 1) Kaplan-Meier; 2) Modelo de Cox com hazard proporcional; 3) Exponencial; 4) Weibull; 5) Log-Logístico. Numa última fase, foi feita uma análise de resíduos utilizando a metodologia de Cox-Snell. Os resultados permitem concluir que as variáveis Valor a pagar e Ano têm um contributo importante na explicação do tempo entre a prestação de um serviço de regulação e a sua cobrança.

Le fonctionnement d'un système, de façon générale, peut être affecté par un incident imprévu. Lorsque cet incident a de lourdes conséquences tant sur l'intégrité du système que sur la qualité de ses produits, on dit alors qu'il se situe dans le cadre des événements dits extrêmes. Ainsi, de plus en plus les chercheurs portent un intérêt particulier à la modélisation des événements extrêmes pour diverses études telles que la fiabilité des systèmes et la prédiction des différents risques pouvant entraver le bon fonctionnement d'un système en général. C'est dans cette optique que s'inscrit la présente thèse. Nous utilisons la Théorie des Valeurs Extrêmes (TVE) et les statistiques d'ordre extrême comme outil d'aide à la décision dans la modélisation et la gestion des risques dans l'usinage et l'aviation. Plus précisément, nous modélisons la surface de rugosité de pièces usinées et la fiabilité de l'outil de coupe associé par les statistiques d'ordre extrême. Nous avons aussi fait une modélisation à l'aide de l'approche dite du "Peaks-Over Threshold, POT" permettant de faire des prédictions sur les éventuelles victimes dans l'Aviation Générale Américaine (AGA) à la suite d'accidents extrêmes. Par ailleurs, la modélisation des systèmes soumis à des facteurs d'environnement ou covariables passent le plus souvent par les modèles à risque proportionnel basés sur la fonction de risque. Dans les modèles à risque proportionnel, la fonction de risque de base est généralement de type Weibull, qui est une fonction monotone; l'analyse du fonctionnement de certains systèmes comme l'outil de coupe dans l'industrie a montré qu'un système peut avoir un mauvais fonctionnement sur une phase et s'améliorer sur la phase suivante. De ce fait, des modifications ont été apportées à la distribution de Weibull afin d'avoir des fonctions de risque de base non monotones, plus particulièrement les fonctions de risque croissantes puis décroissantes. En dépit de ces modifications, la prise en compte des conditions d'opérations extrêmes et la surestimation des risques s'avèrent problématiques. Nous avons donc, à partir de la loi standard de Gumbel, proposé une fonction de risque de base croissante puis décroissante permettant de prendre en compte les conditions extrêmes d'opérations, puis établi les preuves mathématiques y afférant. En outre, un exemple d'application dans le domaine de l'industrie a été proposé. Cette thèse est divisée en quatre chapitres auxquels s'ajoutent une introduction et une conclusion générales. Dans le premier chapitre, nous rappelons quelques notions de base sur la théorie des valeurs extrêmes. Le deuxième chapitre s'intéresse aux concepts de base de l'analyse de survie, particulièrement à ceux relatifs à l'analyse de fiabilité, en proposant une fonction de risque croissante-décroissante dans le modèle à risques proportionnels. En ce qui concerne le troisième chapitre, il porte sur l'utilisation des statistiques d'ordre extrême dans l'usinage, notamment dans la détection de pièces défectueuses par lots, la fiabilité de l'outil de coupe et la modélisation des meilleures surfaces de rugosité. Le dernier chapitre porte sur la prédiction d'éventuelles victimes dans l'Aviation Générale Américaine à partir des données historiques en utilisant l'approche "Peaks-Over Threshold"
The operation of a system in general may at any time be affected by an unforeseen incident. When this incident has major consequences on the system integrity and the quality of system products, then it is said to be in the context of extreme events. Thus, increasingly researchers have a particular interest in modeling such events with studies on the reliability of systems and the prediction of the different risks that can hinder the proper functioning of a system. This thesis takes place in this very perspective. We use Extreme Value Theory (EVT) and extreme order statistics as a decision support tool in modeling and risk management in industry and aviation. Specifically, we model the surface roughness of machined parts and the reliability of the associated cutting tool with the extreme order statistics. We also did a modeling using the "Peaks-Over Threshold, POT" approach to make predictions about the potential victims in the American General Aviation (AGA) following extreme accidents. In addition, the modeling of systems subjected to environmental factors or covariates is most often carried out by proportional hazard models based on the hazard function. In proportional hazard models, the baseline risk function is typically Weibull distribution, which is a monotonic function. The analysis of the operation of some systems like the cutting tool in the industry has shown that a system can deteriorated on one phase and improving on the next phase. Hence, some modifications have been made in the Weibull distribution in order to have non-monotonic basic risk functions, more specifically, the increasing-decreasing risk function. Despite these changes, taking into account extreme operating conditions and overestimating risks are problematics. We have therefore proposed from Gumbel's standard distribution, an increasingdecreasing risk function to take into account extreme conditions, and established mathematical proofs. Furthermore, an example of the application in the field of industry was proposed. This thesis is organized in four chapters and to this must be added a general introduction and a general conclusion. In the first chapter, we recall some basic notions about the Extreme Values Theory. The second chapter focuses on the basic concepts of survival analysis, particularly those relating to reliability analysis by proposing a function of increasing-decreasing hazard function in the proportional hazard model. Regarding the third chapter, it deals with the use of extreme order statistics in industry, particularly in the detection of defective parts, the reliability of the cutting tool and the modeling of the best roughness surfaces. The last chapter focuses on the prediction of potential victims in AGA from historical data using the Peaks-Over Threshold approach

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in ful lment of the requirements for the degree of Master of Science in Statistics November, 2017
This study presents survival modelling and evaluation of risk factors of graft survival in the context of kidney transplant data generated in South Africa. Beyond the Kaplan-Meier estimator, the Cox proportional hazard (PH) model is the standard method used in identifying risk factors of graft survival after kidney transplant. The Cox PH model depends on the proportional hazard assumption, which is rarely met. Assessing and accounting for this assumption is necessary before using this model. When the PH assumption is not valid, modi cation of the Cox PH model could o er more insight into parameter estimates and the e ect of time-varying predictors at di erent time points. This study aims to identify the survival model that will e ectively describe the study data by employing the Cox PH and parametric accelerated failure time (AFT) models. To identify the risk factors that mediate graft survival after kidney transplant, secondary data involving 751 adults that received a single kidney transplant in Charlotte Maxeke Johannesburg Academic Hospital between 1984 and 2004 was analysed. The graft survival of these patients was analysed in three phases (overall, short-term and long-term) based on the follow-up times. The Cox PH and AFT models were employed to determine the signi cant risk factors. The purposeful method of variable selection based on the Cox PH model was used for model building. The performance of each model was assessed using the Cox-Snell residuals and the Akaike Information Criterion. The t of the appropriate model was evaluated using deviance residuals and the delta-beta statistics. In order to further assess how appropriately the best model t the study data for each time period, we simulated a right-censored survival data based on the model parameter-estimates. Overall, the PH assumption was violated in this study. By extending the standard Cox PH model, the resulting models out-performed the standard Cox PH model. The evaluation methods suggest that the Weibull model is the most appropriate in describing the overall graft survival, while the log-normal model is more reasonable in describing short-and long-term graft survival. Generally, the AFT models out-performed the standard Cox regression model in all the analyses. The simulation study resulted in parameter estimates comparable with the estimates from the real data. Factors that signi cantly in uenced graft survival are recipient age, donor type, diabetes, delayed graft function, ethnicity, no surgical complications, and interaction between recipient age and diabetes. Statistical inferences made from the appropriate survival model could impact on clinical practices with regards to kidney transplant in South Africa. Finally, limitations of the study are discussed in the context of further studies.
MT 2018

Informative random censoring survival data are often seen in clinical trials. However, the methodology to deal with this kind of data has not been well developed due to difficulty of identifying the information. Several methods were proposed, for example, by citet{Sia1}. We use simulation studies to investigate sensitivity of these methods and show that the maximum likelihood estimation (MLE) method provides narrower confidence intervals than citet{Sia1}. This is true and expected under the same assumption as in citet{Sia1}. However, we were able to give practical guidelines on how to guess at the missing information of random censoring. We give conditions to obtain more precise estimators for survival data analyses, providing a user-friendly R program. Two real-life data sets are used to illustrate the application of this methodology.
Biostatistics

Indiana University-Purdue University Indianapolis (IUPUI)
Background: Many authors have indicated that HIV-infected patients mortality risk is higher immediately following the start of Antiretroviral Therapy. However, mortality rate of HIV-infected patients is expected to decrease after starting Antiretroviral Therapy (ART) potentially complicating accurate statistical estimation of patient survival and, more generally, effective monitoring of the evolution of the worldwide epidemic. Method: In this thesis, we determine if mortality of HIV-patients increases or decreases after the initiation of ART therapy using flexible survival modelling techniques. To achieve this objective, this study uses semi-parametric statistical models for fitting and estimating survival time using different covariates. A combination of the Weibull distribution with splines is compared to the usual Weibull, exponential, and gamma distribution parametric models, and the Cox semi-parametric model. The objective of this study is to compare these models to find the best fitting model so that it can then be used to improve modeling of the survival time and explore the pattern of change in mortality rates for a cohort of HIV-infected patients recruited in a care and treatment program in Uganda. Results: The analysis shows that flexible survival Weibull models are better than usualoff-parametric and semi-parametric model fitting according to the AIC criterion. Conclusion: The mortality of HIV-patients is high right after the initiation of ART therapy and decreases rapidly subsequently.

碩士
國立中央大學
統計研究所
105
Rodrigues et al. (2009) proposed the Conway-Maxwell-Poisson (COM-Poisson) distribution as a model for a cure rate in censored survival data. We consider computational algorithms for maximum likelihood estimation under the Bernoulli cure rate model, a special case of the COM-Poisson cure rate model. The Weibull distribution (Balakrishnan and Pal 2016) and the generalized gamma distribution (Balakrishnan and Pal 2015) are considered as lifetime distributions. We obtain all the expressions of the score function and Hessian matrix to perform the Newton-Raphson and EM algorithms. Simulations are conducted to compare the performance between the EM algorithm and Newton-Raphson algorithms. Finally, a real data is analyzed to illustrate the methods.

碩士
國立臺灣大學
流行病學與預防醫學研究所
99
Background How long can a human immunodeficiency virus (HIV)-infected patient live is a crucial question, especially for the evaluation of the cost-effectiveness of medical interventions. A semi-parametric survival extrapolation method has been developed based on a logit survival ratio W between a patient cohort and a reference population. If the excess hazard of a specific disease/exposure remains constant, then the logit survival ratio curve will converge to a straight line over time, which allows linear extrapolation to estimate survival beyond the follow-up time. The accuracy of short-term projection has been validated, while the validity and accuracy of life-long projection remains unclear. Method and Principal Findings We used a subset of the Life Span Study (LSS) cohort, which comprised atomic bomb survivors from Hiroshima and Nagasaki and is one of the longest follow-up data cohorts in the world. With this dataset, we tested the validity and accuracy of life-long semi-parametric extrapolation as well as developed mathematical criteria for applying this method to data of limited sample size. We first proved the biological premise that disease/exposure is associated with premature mortality when compared with age- and gender-matched general populations, which is mathematically equivalent to a negative slope in the logit W plot at all times. In addition, we developed a slope-time diagnostic plot. Using those cohort members with >1000 mGy radiation exposure as the index group, we found that (1) the logit W curve continued to converge toward zero at the end of a 48-year follow-up, which indicated that extrapolation based on the right end of the curve should provide a more accurate estimate than that based on the central part of the curve; (2) the slope of the logit W curve can have large random variation if the length of time used for regression is short, such as 6 months, and the diagnostic plot allows users to select the shortest time length that provides a stable slope estimation; (3) a 38-year extrapolation from the end of the 10 year (1950–1960) follow-up data, using the above-stated criteria to select the length of time and the time period for regression, yielded an accurate projection in comparison with the actual 38-year follow-up (1960–1998) data if the cohort members without radiation exposure were used as the source of reference. If the 1960 life table is used as the source of reference, then the projection will underestimate the true long-term survival due to the discrepancy between the time period and the cohort life expectancy. Conclusion Long-term semi-parametric survival extrapolation can be valid and accurate. The recommended steps in applying this methodology are as follows: 1.Create a logit W(t) plot from the follow-up data. 2.Create Slope-Time diagnostic plots using different lengths of time (for example: 6, 12, 24, 36, and 48 months) for regression. Select the shortest length of time that provides stable slope estimation without significant random variations. 3.For the selected diagnostic plot, exclude the time periods with positive slopes and find the time period as close to the end of the follow-up time as possible to obtain the best slope estimate for extrapolation.

碩士
國立中央大學
統計研究所
103
In this study, we establish a more general semi-parametric joint model, which can deal with not only the single event but also the multiple events. We use the unspecified baseline hazard with Cox proportional hazards model or accelerated failure time model to fit the multiple event times with correlation between the events described by shared frailty model. We assume that frailty factor is from the generalized gamma distribution. When estimating the parameters, we treat the random effects from linear mixed effect model and shared frailty model as missing values, thus expectation-maximization algorithm can be implemented to find the maximum likelihood estimates. In E-step, Monte Carlo integration method is used to approximate complex integrals. In M-step, we adopt Nelder-Mead simplex method to find the maximum likelihood estimates. AIDS data is used to demonstrate the usefulness of the proposed method.