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When someone walks into an insurance company and wants to purchase life insurance, the insurance company has to consider an important question: How long will this client live? His date of death is not exactly predictable, so the insurer does not know exactly when the life insurance benefits will be payable. However, the insurer can use a model that can calculate human mortality. With this mortality model, probabilities of deaths at particular ages can be calculated. Rather than trying to figure out when a client dies, the convention in actuarial science is to phrase things in terms of survival models. There are popular survival functions that enable insurers to perform this calculation. With these functions, insurers are able to efficiently provide this service and ensure that life insurance will continue to be a thriving field of work. After we define basic notation and terms, we look at standard survival models. Then we consider a recently proposed model by Chi Heem Wong and Albert K. Tsui.

It is common practice to use Cox-Snell residuals to check for overall goodness of tin survival models. We evaluate the presumed relation of unit exponentially dis-tributed residuals for a good model t and evaluate under some violations of themodel. This is done graphically with the usual graphs of Cox-Snell residual andformally using Kolmogorov-Smirnov goodness of t test. It is observed that residu-als from a correctly tted model follow unit exponential distribution. However, theCox-Snell residuals do not seem to be sensitive to the violations of the model.

Survival models are used in analysing time-to-event data. This type of data is very common in medical research. The Cox proportional hazard model is commonly used in analysing time-to-event data. However, this model is based on the proportional hazard (PH) assumption. Violation of this assumption often leads to biased results and inferences. Once non-proportionality is established, there is a need to consider time-varying effects of the covariates. Several models have been developed that relax the proportionality assumption making it possible to analyse data with time-varying effects of both baseline and time-updated covariates. I present various approaches for handling time-varying covariates and time-varying effects in time-to-event models. They include the extended Cox model which handles exogenous time-dependent covariates using the counting process formulation introduced by cite{andersen1982cox}. Andersen and Gill accounts for time varying covariates by each individual having multiple observations with the total-at-risk follow up for each individual being further divided into smaller time intervals. The joint models for the longitudinal and time-to-event processes and its extensions (parametrization and multivariate joint models) were used as it handles endogenous time-varying covariates appropriately. Another is the Aalen model, an additive model which accounts for time-varying effects. However, there are situations where all the covariates of interest do not have time-varying effects. Hence, the semi-parametric additive model can be used. In conclusion, comparisons are made on the results of all the fitted models and it shows that choice of a particular model to fit is influenced by the aim and objectives of fitting the model. In 2002, an AntiRetroviral Treatment (ART) service was established in the Cape Town township of Gugulethu, South Africa. These models will be applied to an HIV/AIDS observational dataset obtained from all patients who initiated ART within the programme between September 2002 and June 2007.

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.

Orientador: Cícero Rafael Barros Dias / Resumo: Os critérios de elegibilidade e a escolha das premissas atuariais são essenciais para a estimação dos custos de um plano previdenciário e das contribuições de seus participantes. Em relação aos planos públicos previdenciários brasileiros − majoritariamente deficitários −, pode-se afirmar que a análise atuarial é prejudicada pela má qualidade dos registros sobre os servidores, seus cônjuges e dependentes. Esse quadro tem justificado a adoção das hipóteses mínimas estabelecidas pela legislação, nem sempre validadas pelos testes de aderência. Esse contexto evidencia a necessidade de ampliação de estudos técnicos sobre as premissas que impactam no cálculo atuarial. Em especial, destaca-se a idade e o tempo de contribuição para aposentadoria, dada sua centralidade na propositura de reformas previdenciárias. Assim, objetiva-se analisar, mediante estudo de caso, a aplicabilidade de modelos de sobrevivência pouco explorados para estimação de variáveis relevantes na definição dessas premissas, o "tempo de postergação de aposentadoria" e o "tempo de permanência no serviço público", observando ainda − de forma complementar − seus efeitos sobre os cálculos atuariais. Para tanto, foram sistematizadas as informações de 2630 servidores e ex-servidores vinculados, entre 1960 e 2016, ao Regime Próprio de Previdência Social (RPPS) do município de Cabedelo/PB (IPSEMC). Utilizaram-se modelos de sobrevivência não paramétricos, paramétricos e semiparamétricos, com abordagens tradicionais e de risc... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Eligibility criteria and actuarial premise selection are essential for estimating costs of an insurance plan and its participant’s contributions. Regarding Brazilian public social security plans − running for the most part in budget deficit −, it can be said that actuarial analysis is made difficult due to the bad quality of records on the public servants, their spouses and dependents. This situation has justified the adoption of minimal hypotheses as established by law, which are not always validated by adhesion tests. This context exposes the need for increased technical studies on the premises that influence actuarial calculation. Age and contribution time for retirement are especially relevant, given their central position in proposed changes to social security. We thus aim to analyze, based on case studies, the applicability of little-explored survival models for estimating variables that are relevant in defining these premises, "retirement postponement time" and "public service permanence time", while also observing their effect on actuarial calculation. To that end, we have indexed information on 2630 current and former public servants working under the Regime Próprio de Previdência Social (RPPS) from the municipality of Cabedelo (IPSEMC − PB/Brazil) between 1960 and 2016. Non-parametric, parametric and semi-parametric survival models were employed, with traditional and competitive risk approaches under the multiple state perspective. The models were generally well adj... (Complete abstract click electronic access below) / Doutor

Orientador: Liciana Vaz de Arruda Silveira / Resumo: Nas pesquisas clínicas, o método usado para analisar os fatores que contribuem para a mortalidade relacionada aos mais diversos tipos de desfecho é a análise de sobrevivência. Na pesquisa clínica há mais de um resultado possível durante o acompanhamento dos dados de sobrevivência, estes são conhecidos como eventos competitivos. Na ocorrência dos eventos em que a morte é considerada um evento censurado, o modelo de risco proporcional de Cox pode ser empregado para estimar os efeitos das covariáveis sobre o risco. Entretanto, o efeito sobre o risco não pode ser diretamente afetado pela função de incidência acumulada (FIA). Assim, de maneira geral, o presente estudo teve por objetivo fazer uma abordagem dos métodos de análise de sobrevida nos aspectos paramétricos de modelos flexíveis para riscos competitivos, e aplicá-los a uma coorte do Sul da Itália, para avaliar os riscos de óbito para câncer gastrointestinal e outras causas. Trata-se de um estudo observacional retrospectivo, com um período de seguimento de dez anos, realizado em duas coortes, totalizando 2.623 indivíduos selecionados segundo a lista de eleitores dos municípios Castellana Grotte e Putgnano, na Itália. Os modelos flexíveis para riscos competitivos foram usados para avaliar as distribuições acumuladas de incidência específica por causa. Observou-se que os indivíduos com câncer gastrointestinal adeptos da dieta mediterrânea apresentam um risco constante e menor de morrer, especialmente nas etapas inicial e fina... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In clinical research, the method used to analyze the factors that contribute to mortality related to the most diverse types of outcome is the survival analysis. In clinical research there is more than one possible outcome during monitoring of survival data, these are known as competitive events. In the occurrence of events in which death is considered a censored event, the Cox proportional hazard model can be used to estimate the effects of covariates on risk. However, the effect on risk can not be directly affected by the cumulative incidence function (FIA). Thus, in general, the present study aimed to analyze the methods of survival analysis in the parametric aspects of flexible models for competitive risks, and to apply them to a cohort in the South of Italy to evaluate the risk of death for gastrointestinal cancer and other causes. This is a retrospective observational study with a follow-up period of ten years, carried out in two cohorts, totaling 2,623 individuals selected according to the list of voters of the municipalities Castellana Grotte and Putgnano, Italy. Flexible models for competitive risks were used to evaluate cumulative distributions xiii of specific incidence by cause. It was observed that individuals with gastrointestinal cancer adherents of the Mediterranean diet present a constant and lower risk of dying, especially in the initial and final stages of the follow-up, whereas this effect is less pronounced in individuals who did not adhere to the aforemen... (Complete abstract click electronic access below) / Doutor

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.

Notícias de escassez no mundo inteiro, dada a crescente demanda e o rigor na triagem clínica, levaram a necessidade de investigar métodos que mensurem o comportamento de retorno do doador de sangue, sobretudo o indivíduo que manifesta a intenção voluntária em doar. Curvas de Sobrevivência entre outros métodos estatísticos são amplamente estudados na literatura com o intuito de obter uma estimativa da chance de um doador vir a realizar uma subseqüente doação, associado ao seu perfil. O objetivo do presente estudo é identificar modelos estatísticos capazes de descrever esse comportamento utilizan do os registros do Centro Regional de Hemoterapia de Ribeirão Preto. A cons trução de modelos de longa-duração, por exemplo, pode ser um meio de evidenciar possíveis subgrupos mais propensos a retornar, além de estimar a proporção de doadores que jamais retornarão. Entre os resultados, obser vamos que apenas 40% dos doadores voluntários retornaram após um ano decorrido da primeira doação, e 20% destes jamais retornarão. O ajuste do modelo longaduração possibilitou ainda indicar alguns subgrupos de doadores prováveis e improváveis de retornar, porém tais resultados reforçam as evidências de que a motivação intrínseca é o que leva o individuo a retornar. / Reports of worldwide shortages due the increased demand and rigor of clinical screening have led to the necessity to investigate methods that measure blood donor return behavior, mainly regarding individuals who manifest the voluntary intention to donate. Survival curves, among others statistical methods, have been extensively studied in the literature in order to estimate the likelihood of a donor to make another donation, associated with his profile. The aim of the present study was to identify statistical models describing this behavior using information from the Regional Hemotherapy Center of Ribeirão Preto. The construction of long-term survival model can be a useful instrument for determining the groups more likely to donate, as well as the proportion of donors who will never return. The results obtained revealed that only 40% of the volunteer primary donors return for a new donation one year after the first, with the estimate that 20% will never return. The construction of long-term survival model still facilitated to indicate some groups likely and unlike ly donors to donate, even so such re sults reinforce the evidences that the intrinsic motivation is what prompts a donor to return.

Linguistic barriers in education?: the influence of the language in school desertionThe present work has as its objective to evaluate the effect of having a native language different than Spanish over the probability of abandoning basic schooling. For that purpose a proportional risk duration model (Cox) and an accelerated fail time model are used, using information from 2008 and 2009 ENAHO, as well as 2007 Censo Escolar. In both models we find a positive effect over the probability of leaving primary studies when having Quechua as a native language.  The results, for the case of the Quechua speakers, can show part of the effectiveness of the intercultural and bilingual education program (programa de Educación Intercultural Bilingüe or EIB in Spanish) for the reduction of inequality in the process of human capital accumulation / El presente trabajo tiene como objetivo evaluar el efecto de contar con una lengua materna distinta del castellano sobre la probabilidad de abandonar los estudios básicos en el Perú (en el nivel de primaria o secundaria). Para ello se emplea un modelo de duración de riesgo proporcional (Cox) y un modelo de tiempo de falla acelerado, utilizando información de la ENAHO 2008 y 2009, así como del Censo Escolar 2008. En ambos modelos se encuentra un efecto positivo sobre la probabilidad de abandonar los estudios durante la primaria cuando se tiene al quechua como lengua materna. Los resultados encontrados, para el caso de la población quechua, echan luces sobre la efectividad del programa de educación intercultural bilingüe (EIB) para la reducción de brechas en la acumulación de capital humano.