Dissertations / Theses on the topic 'Kaplan-Meier Estimate'

Introdução: O câncer de orofaringe representa 10 a 12 % entre todos os tumores malignos do trato aero digestivo superior com incidência crescente nos Estados Unidos e Europa. O Papillomavírus humano (HPV) está associado aos tumores de orofaringe em até 63%, promovendo uma evolução e prognóstico melhor. Objetivo: Descrever a prevalência do HPV em carcinomas de células escamosas de orofaringe tratados por cirurgia. Analisar a associação entre a presença do HPV e as características demográficas, clínicas, patológicas e terapêuticas. Avaliar a importância da presença do HPV na sobrevida livre de doença e sobrevida global. Método: Pesquisamos a presença do Papillomavirus humano, por PCR, no anátomo patológico. A descrição da amostra foi realizada através de média, frequência absoluta e relativa. Foi estimada a prevalência do HPV e seu respectivo intervalo de 95% de confiança. A análise da associação entre a presença de HPV e as características demográficas, clínicas e patológicas, foi feita pelo teste de associação pelo quiquadrado. A análise da sobrevida livre de doença e sobrevida global foi feita pelo estimador produto limite de Kaplan-Meier e modelos de risco proporcionais de Cox. Resultados: Os pacientes apresentavam idade variando de 34 a 78 anos, com uma média de 56,9 anos. Apenas 10 mulheres no estudo, totalizando com 76 homens. A maioria dos pacientes eram brancos (83,7%). Até 6 meses foi o tempo que a maioria dos pacientes apresentaram como início dos sintomas (69,0%). O sintoma mais comum foi a odinofagia (38,4%). A amígadala foi a localização mais frequente (69,8%). Quanto ao estádio clínico, o III e o IV apresentavam a maior frequência (71,4%). Forma realizadas cirurgias amplas como as bucofaringectomias em 76 pacientes (88,4%). O esvaziamento cervical ipsilateral foi realizado em 81 pacientes (94,2%) e no contralateral em apenas 21 (24,4%). A prevalência do HPV foi de 57%, e o tipo mais comum foi o 16, em 83,6%. A única associação estatisticamente significativa entre as variáveis do estudo com o HPV, foi o tabagismo, onde todos os não fumantes apresentavam HPV. As taxas de sobrevida livre de doença foram 73,9%, 65,9 e 57,9% respectivamente para 12, 24 e 60 meses. Houve diferença estatisticamente significativa com piores taxas, para idade menor que 55 anos e margens comprometidas. A presença do HPV não influenciou a sobrevida livre de doença, nem a sobrevida global. As taxas de sobrevida global foram 75,6%, 54,7% e 43,0%, respectivamente aos 12, 24 e 60 meses. Houveram piores taxas para o paciente etilista e com recidiva.Conclusão:A presença do HPV não se mostrou importante, como fator prognóstico, nessa série cirúrgica se o paciente for etilista e ou tabagista<br>Introduction:Oropharynx cancer is considered to enact approximately 10 to 12% of the cases among all malignant tumors from the upper aero digestive tract showing significant growth in its frequency rate in The United States and Europe. Human papillomavirus (HPV) is associated to oropharynx cancer in up to 63% of the cases, promoting better evolution and prognostic.Objective:Describe the prevalence of the HPV in oropharynx squamous cells carcinoma submitted to surgery. Investigate the association between HPV presence and the demographic, clinical, pathologic and therapeutic features. Estimate the importance of the HPV existence on the diseasefree survival and overall survival. Material andMethods: The existence of Human papillomavirus was studied through the use of PCR. The sample account was conducted through average, absolute and relative frequency. It has been estimated the prevalence of HPV and its corresponding 95% confidence interval. The association analysis between the presence of HPV and the demographic, clinical and pathological features was completed by the Qui-square association test. The disease-free survival timeline and the overall survival were estimated using the product limit estimator Kaplan-Meier and Cox proportional hazards model. Results: The studied patients were aged between 34 and 78, showing an average of 56.9 years of age. There were only 10 women in the study, thus presenting 76 men. Most of the patients were white (83.7%). It has been ascertained that 69.0% of the patients presented the symptoms onset up to the sixth month of the disease. The most common symptom among 38.4% of the cases was odinophagy. In regards to the tumor location 69.8% were found in the amygdala.Clinical stagings III and IV were found to be the ones with greater representation among patients (71.4%). Extensive surgeries such as bucopharyngectomy were performed in 76 patients (88.4%). In order to treat ipsilateral neck 81 patients underwent neck dissection (94.2%). Contralateral neck dissection was applied in 21 patients (24.4%). The prevalence of HPV was of 57%, and the most common type was 16, present in 83.6% of the cases. It was possible to notice smoking as the only statistically significant association, which showed all nonsmoking having HPV. The disease-free survival rates were of 73.9%, 65.9% and 57.9% to 12, 24 and 60 months respectively. The study has shown significant statistical difference with worse rates, to the ones under 55 years of age and presenting compromised margins. HPV presence did not influence the disease-free survival timeline, or the overall survival. The overall survival rates were of 75.6%, 54.7% and 43.0% to 12, 24 and 60 months respectively. Worse rates were found in alcoholic patients as well as in relapse cases. Conclusion: In these surgical series, HPV existence was not identified as an important prognosis factor when considering smokers and/or alcoholic patients

Submitted by Luis Guilherme Macena (guilhermelg2004@gmail.com) on 2013-04-08T16:55:05Z No. of bitstreams: 1 Laurinda Yoko Shinzato Higa_TESE.pdf: 1486069 bytes, checksum: f70375f751ecd6d4742cf70048bbdb2e (MD5)<br>Made available in DSpace on 2013-04-08T16:55:05Z (GMT). No. of bitstreams: 1 Laurinda Yoko Shinzato Higa_TESE.pdf: 1486069 bytes, checksum: f70375f751ecd6d4742cf70048bbdb2e (MD5) Previous issue date: 2011<br>Fundação Oswaldo Cruz. Instituto Fernandes Figueira. Departamento de Ensino. Programa de Pós-Graduação em Saúde da Criança e da Mulher. Rio de Janeiro, RJ, Brasil<br>Introdução: A fibrose cística (FC) é uma doença genética, de transmissão autossômica recessiva, que compromete múltiplos órgãos, que apresenta curso crônico e progressivo sendo considerada potencialmente letal. Objetivos: Estimar a sobrevivência dos pacientes com FC e os fatores de risco associados à redução no tempo de sobrevivência. Métodos: Tratou-se de uma coorte aberta de casos diagnosticados entre 01/01/1990 e 10/10/2009 no Centro de Referência em FC do RJ, CRFC-RJ, Brasil na qual se analisou a sobrevivência global e fatores de risco associados com a sobrevida dos pacientes. O período de risco iniciou-se na idade ao diagnóstico e terminou na idade quando ocorreu o óbito por FC, a perda de seguimento ou o fim do estudo. Os fatores analisados foram: sexo, motivo da suspeita diagnóstica, genótipo, número de órgãos comprometidos, estado nutricional, colonização bacteriana, reposição enzimática e década do diagnóstico. As curvas de sobrevivência foram estimadas pelo método Kaplan- Meier, ajustadas para truncamento à esquerda e para dados censurados à direita. A seguir, as hazard ratios (HR) foram estimadas pelo modelo de Cox, utilizando o processo de contagem, tendo a idade como escala de tempo e avaliadas pelo teste de razão de verossimilhança, e os modelos comparados pela análise de resíduos. Resultados: A população (n=177) apresentou o predomínio do sexo feminino (56%) e a idade mediana ao diagnóstico foi 14 meses. A idade mediana de sobrevivência foi 20,8 anos. Após o diagnóstico 81% sobreviveram até cinco anos; 70% até 10 anos e 61% até 14,5 anos. O modelo explicou 19,9% dos efeitos e incluiu seis covariáveis: colonização por Pseudomonas aeruginosa, isolada e associada (HR = 10,30; IC95% = 2,41-43,97), por Staphylococcus aureus (HR=4,50; IC95% = 0,93-1,85), por outras bactérias (HR=3,38; IC95% = 0,92-1,32), sexo feminino (HR=1,95; IC95% = 0,96-3,96), estado nutricional ≤ p5 (HR=1,94; IC95% = 0,94-3,98) e diagnóstico na década de 1990 (HR=4,34; IC95% = 1,50-12,52). Conclusão: Este estudo de coorte de 177 pacientes com FC mostrou uma idade mediana de sobrevivência de 20,8 anos dos pacientes no CRFC-RJ. Foram confirmados os efeitos das covariáveis que, presentes ao diagnóstico, se associaram a maior mortalidade. A intervenção nestas covariáveis promoverá a recuperação nutricional, a erradicação da Pseudomonas aeruginosa ou o adiamento da colonização crônica, dessa forma aumentando a sobrevivência.<br>Introduction: Cystic Fibrosis (CF) is a rare genetic disease, of autossomal recessive transmission, with multiple organ involvement, progressive course and potentially lethal. Objective: To study the CF patients survival and to find the factors associated with. Methods: In an open cohort of cases diagnosed between 01/01/1990 and 10/10/2009 in a CF reference center in Rio de Janeiro, we analyzed global survival and risk factors associated with the survival of CF patients. The at-risk period started at the age of CF diagnosis and ended at age of death, loss of follow-up or end of the study. The factors analyzed were gender, presentation mode, genotype, number of involved organs, nutritional state, bacterial colonization, enzyme replacement and decade of diagnosis. Survival curves were estimated by Kaplan-Meier (KM) adjusted for left truncation and right censored data. Hazard ratios (HR) were estimated by Cox model using counting process approach with age as time scale and evaluated by likelihood ratio test. Model diagnostic was conducted by residuals analysis. Results: The majority of the population (n=177) was female (56%) and during the study the median age at diagnosis was 14 months. The median survival was of 20.8 years. After diagnosis, 81% survived up to 5 years, 70% up to 10 and 61% up to 14.5. The model explained 19.9% of the effects and included six covariates: Pseudomonas aeruginosa colonization, isolated or associated (HR = 10.30; 95%CI = 2.41-43.97), for Staphylococcus aureus (HR = 4.50; CI95% = 0.93-1.85), for other bacteria (HR = 3.38; CI95% = 0.92-1.32), for female gender (HR = 1.95; CI95% = 0.96-3.96), for nutritional state ≤ p5 (HR = 1.94; CI95% = 0.94-3.98), and for diagnostic decade (HR = 4.34; CI95% = 1.50-12.52). Conclusion: The strength of risk factors found at diagnosis was evident in the prognosis besides indicating that interventions may reduce morbidity by nutritional recovery and by Pseudomonas aeruginosa eradication thus increasing survival.

Made available in DSpace on 2014-07-22T13:16:48Z (GMT). No. of bitstreams: 2 Regina Elizabeth Müller.pdf: 4161979 bytes, checksum: 5df884fdb04b617145c35c1741e9b502 (MD5) license.txt: 1914 bytes, checksum: 7d48279ffeed55da8dfe2f8e81f3b81f (MD5) Previous issue date: 2011<br>Fundação Oswaldo Cruz. Instituto Nacional de Saúde da Mulher, da Criança e do Adolescente Fernandes Figueira. Rio de Janeiro, RJ, Brasil.<br>Introdução: A cardiopatia reumática persiste como a principal doença cardiovascular adquirida em crianças e adultos jovens em todo o mundo, sendo responsável por altas taxas de morbimortalidade e evoluindo com frequência para a necessidade de cirurgia cardíaca valvar em pacientes na fase aguda ou crônica da doença. Objetivo: Estimar os fatores associados e o tempo desde o diagnóstico até a cirurgia cardíaca valvar em crianças e adolescentes portadores de cardiopatia reumática, em um centro cardiológico de referência terciária no Rio de Janeiro. Material e Métodos: estudo observacional longitudinal de base hospitalar, utilizando metodologia de análise de sobrevivência, para estimativa do tempo até a cirurgia, e modelo de regressão de Cox, para avaliar as razões de risco associadas segundo as covariáveis. A coorte foi composta por pacientes com 3 a 20 anos, cadastrados no Instituto Nacional de Cardiologia no Rio de Janeiro entre julho de 1986 e junho de 2006 e acompanhados até setembro de 2011. O diagnóstico da lesão valvar foi confirmado pelo exame Doppler-ecocardiográfico. As covariáveis, avaliadas no início do acompanhamento, foram reunidas em três dimensões: sociodemográfica (sexo, grupo etário, cor da pele, região de moradia e década do diagnóstico); clínica (apresentação clínica, classe funcional, número de surtos anteriores, profilaxia secundária, endocardite infecciosa e fibrilação atrial); e ecocardiográfica (lesão valvar por tipo e gravidade; diâmetro do átrio esquerdo, diâmetro sistólico do ventrículo esquerdo, função ventricular esquerda, hipertensão arterial pulmonar, e ruptura de cordoalha mitral). O banco de dados foi elaborado com o programa ACCESS 2000 e a análise estatística foi realizada pelo programa R versão 2.13.1. Foi considerado significativo o valor de - 0,05. Resultados: a coorte foi composta por 348 pacientes, 58% do sexo feminino, com idade mediana ao cadastro de 12,5 anos, e de 21,5 anos ao final do acompanhamento. O tempo médio de seguimento foi de 9,0 anos (2-21 anos). O evento cirurgia cardíaca ocorreu em 39% da amostra, com tempo mediano até a cirurgia de 22,3 anos. Na análise univariada todas as covariáveis das três dimensões (socioedemográfica, clínica e ecocardiográfica) apresentaram significância estatística e risco para realização de cirurgia cardíaca (hazard ratio>1), com exceção apenas da covariável região de moradia (p>0,5). Na análise multivariada, o modelo final incluiu as variáveis: década do diagnóstico, classe funcional, número de surtos anteriores, endocardite infecciosa, lesão valvar por tipo e gravidade, diâmetro do átrio esquerdo, diâmetro sistólico do ventrículo esquerdo e ruptura de cordoalha mitral. Conclusões: A realização da cirurgia cardíaca em pacientes com cardiopatia reumática está associada a fatores sociodemográficos, clínicos e ecocardiográficos.<br>Introduction: Rheumatic heart disease remains as the most common acquired heart disease in children and young adults all over the world, being responsible for high mortality and morbidity rates and often demanding valve surgery in the acute or chronic phase of the disease. Objective: To estimate the time from diagnosis until valve operation and the associated factors in children and young adults with rheumatic heart disease followed up in a tertiary center for cardiovascular care in Rio de Janeiro. Methods – It is a longitudinal observational study of a hospital based population, using survival analysis methodology for time estimation and Cox regression model for hazard risk evaluation of associated variables. Cohort was composed by 3 to 20 years old patients, registered in the National Institute of Cardiology (Instituto Nacional de Cardiologia), in Rio de Janeiro, between July 1986 and June 2006, and followed up until September 2011. Valve disease diagnosis was confirmed through Doppler echocardiography examination. Variables were evaluated at the patient´s first visit and separated in three dimensions: socio demographic (gender, age group, skin color, residence region, decade of diagnosis); clinic (disease status at presentation, functional class, number of previous rheumatic episodes, secondary prophylaxis, infectious endocarditis, atrial fibrillation); echocardiographic (valve lesion and severity, left atrium diameter, systolic left ventricle diameter, left ventricle function, pulmonary hypertension, rupture of mitral chordae). The database wasbased on the program ACCESS 2000 and statistical analysis was performed using the R Program version 2.13.1. For statistical analysis was considered as significant values for  value 0.05. Results – 348 patients were included in the cohort, 58% female. Median age at the register was 12.5 years, and 21.5 years at the end of follow up. Median follow-up time was 9.0 years (2 to 21 years). 39% underwent valve operation and the median time until surgery was 22.3 years. In the univariate analysis all the variables from the three dimensions (socio demographic, clinic and echocardiographic) presented statistical significance as hazard risk in predicting valve operation (hazard ratio>1), with only one exception, that was residence region (p>0.5). In the multivariate analysis the final model included the following variables: decade of diagnosis, functional class, number of anterior rheumatic episodes, infectious endocarditis, valve lesion and severity, left atrium diameter, systolic left ventricle diameter and rupture of mitral chordate. Conclusions: Valve surgery in patients with rheumatic heart disease is associated with socio demographic, clinic and echocardiographic factors.

nÃo hÃ<br>The main objective of this research is to explore economics issues that may induce impact on lifetime of small businesses during 2002 to 2006. The group of enterprises studied was selected from database of taxpayers recorded at fiscal authority of State of CearÃ. To do that, the methodology was focused on a branch of statistics which deals with survival analysis, called duration analysis or duration modeling in economics. It was applied non-linear model whose non-parametric estimator chosen was KAPLAN-MEIER. Through that methodology, it was developed sceneries based on the following attributes: county where the enterprises were established; economics activities based on national classification, fiscal version 1.0/1.1; and, finally, the relationship between State of Cearà â as fiscal authority â and enterprises. The counties were grouped applying two parameters of stratifications: gross domestic product(GDP) per capita and investment in education per capita. Before any stratification, only counties with thirty or more enterprises starting their activities in year 2002 were considered in sceneries to analysis.<br>A dissertaÃÃo tem o objetivo de investigar fatores econÃmicos que possam influenciar na sobrevida de micros e pequenas empresas (MEPs) contribuintes do Imposto sobre OperaÃÃes relativas à CirculaÃÃo de Mercadorias e sobre PrestaÃÃes de ServiÃos de Transporte Interestadual e Intermunicipal e de ComunicaÃÃo (ICMS) do Estado do Cearà no perÃodo de 2002 à 2006. Para isso, aplicou-se uma tÃcnica estatÃstica denominada anÃlise de sobrevivÃncia a partir de modelos nÃo lineares cujo estimador nÃo-paramÃtrico escolhido foi o de KAPLAN-MEIER. Com os dados de sobrevivÃncia devidamente modelados, buscou-se estratificÃ-los focando os municÃpios dos logradouros das MEPs; dentro do que tange as operaÃÃes do ICMS, focando as atividades econÃmicas segundo a classificaÃÃo nacional de atividades econÃmicas (CNAE) versÃo fiscal 1.0/1.1; e, finalmente, observar a relaÃÃo do Estado â enquanto autoridade fiscal â com esses pequenos estabelecimentos, restringindo temporariamente seu faturamento ou mesmo baixando sua inscriÃÃo estadual, impossibilitando a continuidade de suas atividades. Dos municÃpios, utilizou-se como Ãndice de estratificaÃÃo entre as curvas de sobrevivÃncia o produto interno bruto (PIB) per capita e os investimentos mÃdio per capita em educaÃÃo daquelas empresas localizadas em municÃpios com 30 ou mais estabelecimentos ativados no ano de 2002. Dentre outras, duas importantes observaÃÃes foram identificar o municÃpio de Fortaleza como um âoutlinerâ frente aos outros municÃpios e a forte dominÃncia da curva de sobrevivÃncia das empresas que nÃo sofreram intervenÃÃo do fisco em suas atividades sobre aquelas que tiveram.

Made available in DSpace on 2014-06-11T19:32:15Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-07-05Bitstream added on 2014-06-13T18:43:23Z : No. of bitstreams: 1 caetano_sl_dr_jabo.pdf: 775583 bytes, checksum: a57f6e271b7d34656d680987f933ba7d (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>No Brasil, existem poucos estudos sobre longevidade de vacas de corte, principalmente utilizando ferramentas de análise de sobrevivência na estimação de parâmetros genéticos. Todavia, os critérios para avaliar esta característica são vários, tal que em alguns destes nem todos os registros das vacas nos rebanhos podem ser levados em consideração, devido à metodologia de análise utilizada. Uma variável que é de fácil mensuração e já faz parte da maioria dos controles zootécnicos das fazendas é a idade da vaca ao último parto (IVUP). Neste trabalho, objetivo foi avaliar a longevidade das vacas nos rebanhos utilizando a variável IVUP, por meio da metodologia de análise de sobrevivência. Esta variável foi utilizada mediante um critério para analisar a longevidade produtiva de vacas nos rebanhos. O critério adotado foi a diferença entre a data em relação ao último parto de cada vaca e a data do último parto de cada fazenda. Se esta diferença foi superior a 36 meses, a vaca falhou e foi considerada descartada. Caso contrário, esta vaca foi censurada, indicando que esta ainda poderia ter futuras parições. O critério de 36 meses foi proposto por ser período suficiente para a ocorrência de um novo parto. A metodologia de análise de sobrevivência foi utilizada por considerar dados censurados e não censurados. As variáveis: estação e ano de nascimento de cada vaca, a fazenda e a idade ao primeiro parto foram utilizadas para as análises da variável IVUP. Um estudo prévio por meio de curvas de Kaplan-Meier e o modelo de Cox, utilizando a distribuição gama para os touros, desconsiderando o parentesco entre eles, foram realizados. O software Survival Kit foi empregado para estimação dos parâmetros genéticos, levando em consideração o parentesco entre os animais. Verificou-se que a IVUP apresentou herdabilidade de 0,25, e que seu uso permite avaliar a...<br>In Brazil, there are few studies about stayability, especially using tools of survival analysis in the estimation of breeding values and heritability. The criteria for evaluating this characteristic are different, such that in some of these not all information in the herds of cows can be taken into consideration, because the method of analysis used. In addition, the definitions that consider the date of disposal of the animal affect the use of information obtained in practice, because until the cows come out of the flock may take years, thus the evaluation of their parents is impaired, since the goal is selection. A variable that is easy to measure and is already part of most controls husbandry farms are cow age at last birth (IVUP). This variable was used by one criterion to analyze the productive longevity of cows in herds. The criterion was the difference between the date from the last delivery date of each cow and the last part of each farm. If this difference was more than 36 months, the cow was considered failed and discarded. Otherwise, this cow was censored, indicating that this could still have further parities. The criterion of 36 months was proposed to be sufficient time for the occurrence of a new birth. The methodology of survival analysis was used. The variables season and year of birth of each cow, farm and age at first birth were used for analysis of variable IVUP. The objective of this study was to evaluate the performance of the variable IVUP through estimates of genetic and fixed effect, to study the longevity of cows in the herd. A previous study by Kaplan-Meier and Cox model using the gamma distribution for the bulls, disregarding the relationship between them, were performed. The Survival Kit software was used to estimate the genetic parameters, taking into account the relationship between the animals. It was found that the heritability of 0.25 for IVUP ... (Complete abstract click electronic access below)

A regressão quantílica para dados censurados é uma extensão dos modelos de regressão quantílica que, por levar em consideração a informação das observações censuradas na modelagem, e por apresentar propriedades bastante satisfatórias, pode ser vista como uma abordagem complementar às metodologias tradicionais em Análise de Sobrevivência, com a vantagem de permitir que as conclusões inferenciais sejam tomadas facilmente em relação aos tempos de sobrevivência propriamente ditos, e não em relação à taxa de riscos ou a uma função desse tempo. Além disso, em alguns casos, pode ser vista também como metodologia alternativa aos modelos clássicos quando as suposições destes são violadas ou quando os dados são heterogêneos. Apresentam-se nesta dissertação três técnicas para modelagem com regressão quantílica para dados censurados, que se diferenciam em relação às suas suposições e forma de estimação dos parâmetros. Um estudo de simulação para comparação das três técnicas para dados com distribuição normal, Weibull e log-logística é apresentado, em que são avaliados viés, erro padrão e erro quadrático médio. São discutidas as vantagens e desvantagens de cada uma das técnicas e uma delas é aplicada a um conjunto de dados reais do Instituto do Coração do Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo.<br>Censored quantile regression is an extension of quantile regression, and because it incorporates information from censored data in the modelling, and presents quite satisfactory properties, this class of models can be seen as a complementary approach to the traditional methods in Survival Analysis, with the advantage of allowing inferential conclusions to be made easily in terms of survival times rather than in terms of risk rates or as functions of survival time. Moreover, in some cases, it can also be seen as an alternative methodology to the classical models when their assumptions are violated or when modelling heterogeneity of the data. This dissertation presents three techniques for modelling censored quantile regression, which differ by assumptions and parameter estimation method. A simulation study designed with normal, Weibull and loglogistic distribution is presented to evaluate bias, standard error and mean square error. The advantages and disadvantages of each of the three techniques are then discussed and one of them is applied to a real data set from the Heart Institute of Hospital das Clínicas, University of São Paulo.

Made available in DSpace on 2014-12-17T15:34:49Z (GMT). No. of bitstreams: 1 DeborahGPG_DISSERT.pdf: 1421770 bytes, checksum: da1c0ade32fb8610306243b0cf52f13d (MD5) Previous issue date: 2014-02-20<br>Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior<br>Among the traits of economic importance to dairy cattle livestock those related to sexual precocity and longevity of the herd are essential to the success of the activity, because the stayability time of a cow in a herd is determined by their productive and reproductive lives. In Brazil, there are few studies about the reproductive efficiency of Swiss-Brown cows and no study was found using the methodology of survival analysis applied to this breed. Thus, in the first chapter of this study, the age at first calving from Swiss-Brown heifers was analyzed as the time until the event by the nonparametric method of Kaplan-Meier and the gamma shared frailty model, under the survival analysis methodology. Survival and hazard rate curves associated with this event were estimated and identified the influence of covariates on such time. The mean and median times at the first calving were 987.77 and 1,003 days, respectively, and significant covariates by the Log-Rank test, through Kaplan-Meier analysis, were birth season, calving year, sire (cow s father) and calving season. In the analysis by frailty model, the breeding values and the frailties of the sires (fathers) for the calving were predicted modeling the risk function of each cow as a function of the birth season as fixed covariate and sire as random covariate. The frailty followed the gamma distribution. Sires with high and positive breeding values possess high frailties, what means shorter survival time of their daughters to the event, i.e., reduction in the age at first calving of them. The second chapter aimed to evaluate the longevity of dairy cows using the nonparametric Kaplan-Meier and the Cox and Weibull proportional hazards models. It were simulated 10,000 records of the longevity trait from Brown-Swiss cows involving their respective times until the occurrence of five consecutive calvings (event), considered here as typical of a long-lived cow. The covariates considered in the database were age at first calving, herd and sire (cow s father). All covariates had influence on the longevity of cows by Log-Rank and Wilcoxon tests. The mean and median times to the occurrence of the event were 2,436.285 and 2,437 days, respectively. Sires that have higher breeding values also have a greater risk of that their daughters reach the five consecutive calvings until 84 months<br>Dentre as caracter?sticas de import?ncia econ?mica para a pecu?ria leiteira aquelas relacionadas com a precocidade sexual e a longevidade do rebanho s?o determinantes para o sucesso da atividade, uma vez que o tempo de perman?ncia de uma vaca num rebanho ? determinado por suas vidas produtiva e reprodutiva. No Brasil, existem poucos estudos sobre a efici?ncia reprodutiva de vacas Pardo-Su??as e n?o foi encontrado nenhum estudo abordando o uso da metodologia de an?lise de sobreviv?ncia aplicada a esta ra?a. Assim, no primeiro cap?tulo deste trabalho, a idade ao primeiro parto de novilhas Pardo-Su??as foi analisada como o tempo at? o evento por meio do m?todo n?o-param?trico de Kaplan-Meier e do modelo de fragilidade compartilhado gama, sob a metodologia de an?lise de sobreviv?ncia. Foram estimadas curvas de sobreviv?ncia e de taxa de risco associadas com este evento e verificada a influ?ncia das covari?veis consideradas sobre o tempo. Os tempos m?dio e mediano ao primeiro parto foram 987,77 e 1.003 dias, respectivamente; e as covari?veis significativas pelo teste de Log-Rank, na an?lise por Kaplan-Meier, foram esta??o de nascimento, ano de parto, touro (pai da vaca) e esta??o de parto. Na an?lise pelo modelo de fragilidade, foram preditos os valores gen?ticos e as fragilidades dos touros (pais) para o parto, modelando-se a fun??o de risco de cada vaca em fun??o da covari?vel fixa esta??o de nascimento e da covari?vel aleat?ria touro. A fragilidade seguiu a distribui??o gama. Touros com valores gen?ticos positivos e altos possuem fragilidades altas, o que significa menor tempo de sobreviv?ncia de suas filhas ao evento, ou seja, redu??o na idade ao primeiro parto delas. O segundo cap?tulo teve como objetivo avaliar a longevidade de vacas leiteiras utilizando o estimador n?o-param?trico de Kaplan-Meier e os modelos de riscos proporcionais de Weibull e de Cox. Foram simulados 10.000 registros da caracter?stica longevidade de f?meas Pardo-Su??as denotando seus respectivos tempos at? a ocorr?ncia de cinco partos consecutivos (evento), considerados aqui como t?picos de uma vaca longeva. As covari?veis consideradas no banco de dados foram a idade da vaca ao primeiro parto, o rebanho e o pai da vaca. Todas as covari?veis exerceram influ?ncia sobre a longevidade das vacas de acordo com os testes de Log-Rank e Wilcoxon. Os tempos m?dio e mediano para a ocorr?ncia do evento foram de 2.436,285 e 2.437 dias. Touros com maior valor gen?tico tamb?m possuem um maior risco de que as suas filhas alcancem os cinco partos aos 84 meses

Dans cette thèse, nous étudions les propriétés asymptotiques de paramètres fonctionnels conditionnels en statistique non paramétrique, quand la variable explicative prend ses valeurs dans un espace de dimension infinie. Dans ce cadre non paramétrique, on considère les estimateurs des paramètres fonctionnels usuels, tels la loi conditionnelle, la densité de probabilité conditionnelle, ainsi que le quantile conditionnel. Le premier travail consiste à proposer un estimateur du quantile conditionnel et de prouver sa convergence uniforme sur un sous-ensemble compact. Afin de suivre la convention dans les études biomédicales, nous considérons une suite de v.a {Ti, i ≥ 1} identiquement distribuées, de densité f, censurée à droite par une suite aléatoire {Ci, i ≥ 1} supposée aussi indépendante, identiquement distribuée et indépendante de {Ti, i ≥ 1}. Notre étude porte sur des données fortement mélangeantes et X la covariable prend des valeurs dans un espace à dimension infinie.Le second travail consiste à établir la normalité asymptotique de l’estimateur à noyau du quantile conditionnel convenablement normalisé, pour des données fortement mélangeantes, et repose sur la probabilité de petites boules. Plusieurs applications à des cas particuliers ont été traitées. Enfin, nos résultats sont appliqués à des données simulées et montrent la qualité de notre estimateur<br>In this thesis, we study some asymptotic properties of conditional functional parameters in nonparametric statistics setting, when the explanatory variable takes its values in infinite dimension space. In this nonparametric setting, we consider the estimators of the usual functional parameters, as the conditional law, the conditional probability density, the conditional quantile. We are essentially interested in the problem of forecasting in the nonparametric conditional models, when the data are functional random variables. Firstly, we propose an estimator of the conditional quantile and we establish its uniform strong convergence with rates over a compact subset. To follow the convention in biomedical studies, we consider an identically distributed sequence {Ti, i ≥ 1}, here density f, right censored by a random {Ci, i ≥ 1} also assumed independent identically distributed and independent of {Ti, i ≥ 1}. Our study focuses on dependent data and the covariate X takes values in an infinite space dimension. In a second step we establish the asymptotic normality of the kernel estimator of the conditional quantile, under α-mixing assumption and on the concentration properties on small balls of the probability measure of the functional regressors. Many applications in some particular cases have been also given

Dans cette thèse, nous étudions des modèles définis par des équations de moments conditionnels. Une grande partie de modèles statistiques (régressions, régressions quantiles, modèles de transformations, modèles à variables instrumentales, etc.) peuvent se définir sous cette forme. Nous nous intéressons au cas des modèles avec un paramètre à estimer de dimension finie, ainsi qu’au cas des modèles semi paramétriques nécessitant l’estimation d’un paramètre de dimension finie et d’un paramètre de dimension infinie. Dans la classe des modèles semi paramétriques étudiés, nous nous concentrons sur les modèles à direction révélatrice unique qui réalisent un compromis entre une modélisation paramétrique simple et précise, mais trop rigide et donc exposée à une erreur de modèle, et l’estimation non paramétrique, très flexible mais souffrant du fléau de la dimension. En particulier, nous étudions ces modèles semi paramétriques en présence de censure aléatoire. Le fil conducteur de notre étude est un contraste sous la forme d’une U-statistique, qui permet d’estimer les paramètres inconnus dans des modèles généraux<br>In this dissertation we study statistical models defined by condition estimating equations. Many statistical models could be stated under this form (mean regression, quantile regression, transformation models, instrumental variable models, etc.). We consider models with finite dimensional unknown parameter, as well as semiparametric models involving an additional infinite dimensional parameter. In the latter case, we focus on single-index models that realize an appealing compromise between parametric specifications, simple and leading to accurate estimates, but too restrictive and likely misspecified, and the nonparametric approaches, flexible but suffering from the curse of dimensionality. In particular, we study the single-index models in the presence of random censoring. The guiding line of our study is a U-statistics which allows to estimate the unknown parameters in a wide spectrum of models

Master of Science<br>Department of Statistics<br>Paul I. Nelson<br>Quantiles are useful in describing distributions of component lifetimes. Data, consisting of the lifetimes of sample units, used to estimate quantiles are often censored. Right censoring, the setting investigated here, occurs, for example, when some test units may still be functioning when the experiment is terminated. This study investigated and compared the performance of parametric and nonparametric estimators of quantiles from right censored data generated from Weibull and Lognormal distributions, models which are commonly used in analyzing lifetime data. Parametric quantile estimators based on these assumed models were compared via simulation to each other and to quantile estimators obtained from the nonparametric Kaplan- Meier Estimator of the survival function. Various combinations of quantiles, censoring proportion, sample size, and distributions were considered. Our simulation show that the larger the sample size and the lower the censoring rate the better the performance of the estimates of the 5th percentile of Weibull data. The lognormal data are very sensitive to the censoring rate and we observed that for higher censoring rates the incorrect parametric estimates perform the best. If you do not know the underlying distribution of the data, it is risky to use parametric estimates of quantiles close to one. A limitation in using the nonparametric estimator of large quantiles is their instability when the censoring rate is high and the largest observations are censored. Key Words: Quantiles, Right Censoring, Kaplan-Meier estimator

Dans ce travail, nous étudions quelques aspects de l’estimation fonctionnelle pour des données incomplètes (censurées). Plus précisément, nous nous intéressons à la fonction mode et à la fonction mode conditionnel pour lesquelles nous construisons des estimateurs et étudions le comportement asymptotique. Les estimateurs proposés se positionnent comme alternatives à la prévision par la fonction de régression. Dans un premier travail, nous considérons une suite de v. A. {T_i , i [supérieur ou =]1} indépendante et identiquement distribuée (iid), de densité f , censurée à droite par une suite aléatoire {Ci , i [supérieur ou = à]1} supposée iid et indépendante de {T_i , i [supérieur ou = à]1}. Nous nous intéressons à un problème de régression de T par une covariable multi-dimensionnelle X. Nous établissons la convergence et la normalité asymptotique des estimateurs à noyau de la fonction mode conditionnel et de la densité conditionnelle. Nous obtenons des intervalles de confiance en utilisant la méthode du "plug-in" pour les paramètres inconnus. Une étude sur des données simulées de taille finie illustre la qualité de nos estimateurs. Dans un second travail, nous traitons le cas du mode simple défini par θ = arg max_{t. IR} f (t). Dans ce cas, la suite {T_i , i [supérieur ou = à]1} est supposée stationnaire et fortement mélangeante, alors que les {C_i , i [supérieur ou = à]1} sont iid. Nous construisons un estimateur du mode (basé sur un estimateur à noyau de la densité) dont nous établissons la convergence presque sûre. Le dernier travail de cette thèse généralise les résultats de convergence du mode conditionnel au cas où les {T_i , i [supérieur ou = à]1} sont fortement mélangeant<br>In this work, we address the problem of estimating the mode and conditional mode functions, for independent and dependent data, under random censorship. Firstly, we consider an independent and identically distributed (iid) sequence random variables (rvs) {T_i , i [equal to or higher than]1}, with density f. This sequence is right-censored by another iid sequence of rvs {Ci , i[equal to or higher than]1} which is supposed to be independent of {T_i , i [equal to or higher than]1}. We are interested in the regression problem of T given a covariable X. We state convergence and asymptomatic normality of Kernel-based estimators of conditional density and mode. Using the “plug-in” method for the unknown parameters, confidence intervals are gicen. Also simulations are drawn. In a second step we deal with the simple mode, given by par θ = arg max_{t. IR} f (t). Here, the sequence {T_i , i [equal to or higher than]1} is supposed to be stationary and strongly mixing whereas the {Ci , i[equal to or higher than]1} are iid. We build a mode estimator (based on a density kernel estimator) for which we state the almost sure consistency. Finally, we extend the conditional mode consistency results to the case where the {T_i , i [equal to or higher than]1} are strongly mixing

Resumo: No Brasil, existem poucos estudos sobre longevidade de vacas de corte, principalmente utilizando ferramentas de análise de sobrevivência na estimação de parâmetros genéticos. Todavia, os critérios para avaliar esta característica são vários, tal que em alguns destes nem todos os registros das vacas nos rebanhos podem ser levados em consideração, devido à metodologia de análise utilizada. Uma variável que é de fácil mensuração e já faz parte da maioria dos controles zootécnicos das fazendas é a idade da vaca ao último parto (IVUP). Neste trabalho, objetivo foi avaliar a longevidade das vacas nos rebanhos utilizando a variável IVUP, por meio da metodologia de análise de sobrevivência. Esta variável foi utilizada mediante um critério para analisar a longevidade produtiva de vacas nos rebanhos. O critério adotado foi a diferença entre a data em relação ao último parto de cada vaca e a data do último parto de cada fazenda. Se esta diferença foi superior a 36 meses, a vaca falhou e foi considerada descartada. Caso contrário, esta vaca foi censurada, indicando que esta ainda poderia ter futuras parições. O critério de 36 meses foi proposto por ser período suficiente para a ocorrência de um novo parto. A metodologia de análise de sobrevivência foi utilizada por considerar dados censurados e não censurados. As variáveis: estação e ano de nascimento de cada vaca, a fazenda e a idade ao primeiro parto foram utilizadas para as análises da variável IVUP. Um estudo prévio por meio de curvas de Kaplan-Meier e o modelo de Cox, utilizando a distribuição gama para os touros, desconsiderando o parentesco entre eles, foram realizados. O software Survival Kit foi empregado para estimação dos parâmetros genéticos, levando em consideração o parentesco entre os animais. Verificou-se que a IVUP apresentou herdabilidade de 0,25, e que seu uso permite avaliar a ... (Resumo completo, clicar acesso eletrônico abaixo)<br>Abstract: In Brazil, there are few studies about stayability, especially using tools of survival analysis in the estimation of breeding values and heritability. The criteria for evaluating this characteristic are different, such that in some of these not all information in the herds of cows can be taken into consideration, because the method of analysis used. In addition, the definitions that consider the date of disposal of the animal affect the use of information obtained in practice, because until the cows come out of the flock may take years, thus the evaluation of their parents is impaired, since the goal is selection. A variable that is easy to measure and is already part of most controls husbandry farms are cow age at last birth (IVUP). This variable was used by one criterion to analyze the productive longevity of cows in herds. The criterion was the difference between the date from the last delivery date of each cow and the last part of each farm. If this difference was more than 36 months, the cow was considered failed and discarded. Otherwise, this cow was censored, indicating that this could still have further parities. The criterion of 36 months was proposed to be sufficient time for the occurrence of a new birth. The methodology of survival analysis was used. The variables season and year of birth of each cow, farm and age at first birth were used for analysis of variable IVUP. The objective of this study was to evaluate the performance of the variable IVUP through estimates of genetic and fixed effect, to study the longevity of cows in the herd. A previous study by Kaplan-Meier and Cox model using the gamma distribution for the bulls, disregarding the relationship between them, were performed. The Survival Kit software was used to estimate the genetic parameters, taking into account the relationship between the animals. It was found that the heritability of 0.25 for IVUP ... (Complete abstract click electronic access below)<br>Orientador: Danísio Prado Munari<br>Coorientador: Claudia Cristina Paro da Paz<br>Coorientador: Raysildo Barbosa Lobo<br>Banca: João Ademir de Oliveira<br>Banca: Henrique Nunes De Oliveira<br>Banca: Roberto Carvalheiro<br>Banca: Lenira El Faro Zadra<br>Doutor

Nous considérons des modèles de régression où la variable expliquée est censurée à droite aléatoirement. Nous proposons de nouveaux estimateurs de la fonction de régression dans des modèles paramétriques, et nous proposons une procédure de test non paramétrique d'adéquation à ces modèles. Nous prolongeons ces méthodes à l'étude du modèle semi-paramétrique "single-index", généralisant ainsi des techniques de réduction de dimension utilisées en l'absence de censure. Nous nous penchons tout d'abord sur le cas d'un modèle où la variable de censure est indépendante de la variable expliquée ainsi que des variables explicatives. Nous travaillons dans un second temps dans un cadre moins restrictif où la variable expliquée et la censure sont indépendantes conditionnellement aux variables explicatives. Une difficulté spécifique à ce dernier type de modèle tient en l'impossibilité des techniques actuelles à estimer une espérance conditionnelle (de façon paramétrique ou non) en présence de plus d'une<br />variable explicative. Nous développons une nouvelle approche de réduction de la dimension afin de résoudre ce problème.

Les aliments peuvent être contaminés par certaines substances chimiques, qui, lorsqu'elles sont ingérées à des doses trop importantes, peuvent engendrer des problèmes de santé. Notre but est d'évaluer la probabilité que l'exposition au contaminant dépasse durablement une dose tolérable par l'organisme que nous appelons risque. La modélisation de la queue de distribution par des lois extrêmes permet de quantifier un risque très faible. Dans les autres cas, l'estimateur empirique du risque s'écrit comme une U-statistique généralisée, ce qui permet d'en dériver les propriétés asymptotiques. Des développements statistiques permettent d'intégrer à ce modèle la censure des données de contamination. Enfin, un modèle économétrique de décomposition de données ménage en données individuelles nous permet de proposer une nouvelle méthode de quantification du risque de long terme prenant en compte l'accumulation du contaminant et sa lente dégradation par l'organisme.

Le risque attribuable (RA) mesure la proportion de cas de maladie qui peuvent être attribués à une exposition au niveau de la population. Plusieurs définitions et méthodes d'estimation du RA ont été proposées pour des données de survie. En utilisant des simulations, nous comparons quatre méthodes d'estimation du RA dans le contexte de l'analyse de survie : deux méthodes non paramétriques basées sur l'estimateur de Kaplan-Meier, une méthode semi-paramétrique basée sur le modèle de Cox à risques proportionnels et une méthode paramétrique basée sur un modèle à risques proportionnels avec un risque de base constant par morceaux. Nos travaux suggèrent d'utiliser les approches semi-paramétrique et paramétrique pour l'estimation du RA lorsque l'hypothèse des risques proportionnels est vérifiée. Nous appliquons nos méthodes aux données de la cohorte E3N pour estimer la proportion de cas de cancer du sein invasif attribuables à l'utilisation de traitements hormonaux de la ménopause (THM). Nous estimons qu'environ 9 % des cas de cancer du sein sont attribuables à l'utilisation des THM à l'inclusion. Dans le cas d'une exposition protectrice, une alternative au RA est la fraction préventive (FP) qui mesure la proportion de cas de maladie évités. Cette mesure n'a pas été considérée dans le contexte de l'analyse de survie. Nous proposons une définition de la FP dans ce contexte et des méthodes d'estimation en utilisant des approches semi-paramétrique et paramétrique avec une extension permettant de prendre en compte les risques concurrents. L'application aux données de la cohorte des Trois Cités (3C) estime qu'environ 9 % de cas d'accident vasculaire cérébral peuvent être évités chez les personnes âgées par l'utilisation des hypolipémiants. Notre étude montre que la FP peut être utilisée pour évaluer l'impact des médicaments bénéfiques dans les études de cohorte tout en tenant compte des facteurs de confusion potentiels et des risques concurrents<br>The attributable risk (AR) measures the proportion of disease cases that can be attributed to an exposure in the population. Several definitions and estimation methods have been proposed for survival data. Using simulations, we compared four methods for estimating AR defined in terms of survival functions: two nonparametric methods based on Kaplan-Meier's estimator, one semiparametric based on Cox's model, and one parametric based on the piecewise constant hazards model. Our results suggest to use the semiparametric or parametric approaches to estimate AR if the proportional hazards assumption appears appropriate. These methods were applied to the E3N women cohort data to estimate the AR of breast cancer due to menopausal hormone therapy (MHT). We showed that about 9% of cases of breast cancer were attributable to MHT use at baseline. In case of a protective exposure, an alternative to the AR is the prevented fraction (PF) which measures the proportion of disease cases that could be avoided in the presence of a protective exposure in the population. The definition and estimation of PF have never been considered for cohort studies in the survival analysis context. We defined the PF in cohort studies with survival data and proposed two estimation methods: a semiparametric method based on Cox’s proportional hazards model and a parametric method based on a piecewise constant hazards model with an extension to competing risks. Using data of the Three-City (3C) cohort study, we found that approximately 9% of cases of stroke could be avoided using lipid-lowering drugs (statins or fibrates) in the elderly population. Our study shows that the PF can be estimated to evaluate the impact of beneficial drugs in observational cohort studies while taking potential confounding factors and competing risks into account

L'analyse de durées de vie censurées est utilisée dans des domaines d'application variés et différentes possibilités ont été proposées pour la modélisation de telles données. Nous nous intéressons dans cette thèse à deux types de modélisation différents, le modèle de Cox stratifié avec indicateurs de strates aléatoirement manquants et le modèle de régression linéaire censuré à droite. Nous proposons des méthodes d'estimation des paramètres et établissons les propriétés asymptotiques des estimateurs obtenus dans chacun de ces modèles. Dans un premier temps, nous considérons une généralisation du modèle de Cox qui permet à différents groupes de la population, appelés strates, de posséder des fonctions d'intensité de base différentes tandis que la valeur du paramètre de régression est commune. Dans ce modèle à intensité proportionnelle stratifié, nous nous intéressons à l'estimation des paramètres lorsque l'indicateur de strate est manquant pour certains individus de la population. Des estimateurs du maximum de vraisemblance non paramétrique pour les paramètres du modèle sont proposés et nous montrons leurs consistance et normalité asymptotique. L'efficacité du paramètre de régression est établie et des estimateurs consistants de sa variance asymptotique sont également obtenus. Pour l'évaluation des estimateurs du modèle, nous proposons l'utilisation de l'algorithme Espérance-Maximisation et le développons dans ce cas particulier. Dans un second temps, nous nous intéressons au modèle de régression linéaire lorsque la donnée réponse est censurée aléatoirement à droite. Nous introduisons un nouvel estimateur du paramètre de régression minimisant un critère des moindres carrés pénalisé et pondéré par des poids de Kaplan-Meier. Des résultats de consistance et normalité asymptotique sont obtenus et une étude de simulations est effectuée pour illustrer les propriétés de cet estimateur de type LASSO. La méthode bootstrap est utilisée pour l'estimation de la variance asymptotique<br>Life data analysis is used in various application fields. Different methods have been proposed for modelling such data. In this thesis, we are interested in two distinct modelisation types, the stratified Cox model with randomly missing strata indicators and the right-censored linear regression model. We propose methods for estimating the parameters and establish the asymptotic properties of the obtained estimators in each of these models. First, we consider a generalization of the Cox model, allowing different groups, named strata, of the population to have distinct baseline intensity functions, whereas the regression parameter is shared by all the strata. In this stratified proportional intensity model, we are interested in the parameters estimation when the strata indicator is missing for some of the population individuals. Nonparametric maximum likelihood estimators are proposed for the model parameters and their consistency and asymptotic normality are established. We show the efficiency of the regression parameter and obtain consistent estimators of its variance. The Expectation-Maximization algorithm is proposed and developed for the evaluation of the estimators of the model parameters. Second, we are interested in the regression linear model when the response data is randomly right-censored. We introduce a new estimator of the regression parameter, which minimizes a Kaplan-Meier-weighted penalized least squares criterion. Results of consistency and asymptotic normality are obtained and a simulation study is conducted in order to investigate the small sample properties of this LASSO-type estimator. The bootstrap method is used for the estimation of the asymptotic variance

碩士<br>東海大學<br>統計學系<br>90<br>The Greenwood estimate (GE) is commonly employed for estimating the variance of the Kaplan-Meier estimate (KME) even though it underestimates the variance. To correct the bias of GE , Zhao (1996) proposed an alternative, called the homogenetic estimate (HE). In this note, we point out that HE actually estimates the variance of the reduced sample estimate (RE) and can seriously overestimate that of KME. We also derive the explict relation between HE and GE and give some notes on the use of HE. KEYWORDS: Greenwood estimate;homogenetic estimate;reduced sample estimate.

碩士<br>東海大學<br>統計學研究所<br>86<br>Stute and Wang (1994) considered the problem of estimating the integralS(r)=∫rdF, based on a possibly censored sample from a distribution F, where r is an F-integrable function. They proposed a Kaplan-Meier integralSn^(r) to approximate S(r) and derived an explict formula for thedelete-1 jackknife estimate of Sn^(r).In a small simulation study for themean lifetimes of exponential variables,they claimed that jackknifing ledto a reduction of bias.In this note, it is pointed out that Sn^(r) is basedon a defective distribution, and therefore Sn^(r) and the delete-1jackknife estimate of Sn^(r) are both badly biased. According to Efron (1981),we propose a modified estimator Sn~(r) and derive explicit formulas for thedelete-1 and delete-2 jackknife estimates of Sn~(r).Simulation resultsdemonstrate that the modified estimates are much less biased than thosefrom Stute and Wang (1994).KEY WORDS: jackknife; Kaplan-Meier estimators;censored data.-1 -aThe jackknife estimates of a Kaplan-Meier integral-zeng- 0-a - 1-ajackknife-aKaplan-Meier estimators-acensored data

碩士<br>靜宜大學<br>應用數學研究所<br>92<br>We consider the problem of estimating the integral , based on a possibly censored sample from a distribution , where is an function. According to Efron (1981), we propose an estimator and derive explicit formulas for the delete-1 , delete-2 and delete-3 jackknife estimates of . Simulation results demonstrate that jackknifing may lead to a considerable reduction of the bias.

碩士<br>國立中正大學<br>數理統計研究所<br>87<br>Many biological or medical experiments have the goal to estimate the survival function of a specified population of perishable subjects。 The procedure for estimating survival curve from data using Kaplan-Meier(in 1958) and Life-Table (or Actuarial) methods are well known。 Kaplan-Meier give a maximum likelihood estimate called the product-limit estimate to estimate survival function。 But this method is liberal and lack of accuracy， when it cannot be properly applies to the problem with censored data。 Then， Actuarial method gives an adjusted way to calculate the number of individuals exposed to risk, but it is still imprecise。 Thispaper has two proposals : (1) suggest an improvement of the product-limit estimator which make the survival function more reasonable。 (2) to prove that the survival estimator using simulation as a tool in Kaplan-Meier Method are not consistent the claimed with C.L.T. result 。

The mechanisms that control growth processes in biology tissues have attracted continuous research interest despite their complexity. With the emergence of big data experimental approaches there is an urgent need to develop statistical and computational models to fit the experimental data and that can be used to make predictions to guide future research. In this work we apply statistical methods on growth process of different biological tissues, focusing on development of neuron dendrites and tumor cells. We first examine the neuron cell growth process, which has implications in neural tissue regenerations, by using a computational model with uniform branching probability and a maximum overall length constraint. One crucial outcome is that we can relate the parameter fits from our model to real data from our experimental collaborators, in order to examine the usefulness of our model under different biological conditions. Our methods can now directly compare branching probabilities of different experimental conditions and provide confidence intervals for these population-level measures. In addition, we have obtained analytical results that show that the underlying probability distribution for this process follows a geometrical progression increase at nearby distances and an approximately geometrical series decrease for far away regions, which can be used to estimate the spatial location of the maximum of the probability distribution. This result is important, since we would expect maximum number of dendrites in this region; this estimate is related to the probability of success for finding a neural target at that distance during a blind search. We then examined tumor growth processes which have similar evolutional evolution in the sense that they have an initial rapid growth that eventually becomes limited by the resource constraint. For the tumor cells evolution, we found an exponential growth model best describes the experimental data, based on the accuracy and robustness of models. Furthermore, we incorporated this growth rate model into logistic regression models that predict the growth rate of each patient with biomarkers; this formulation can be very useful for clinical trials. Overall, this study aimed to assess the molecular and clinic pathological determinants of breast cancer (BC) growth rate in vivo.

In reliability studies, the goal is to gain knowledge about a product's failure times or life expectancy. Precedence tests do not require large sample sizes and are used in reliability studies to compare the life-time distributions from two samples. Precedence tests are useful since they provide reliable results early in a life-test and the surviving units can be used in other tests. Ng and Balakrishnan (2010) proposed a precedence-type test based on the Kaplan-Meier estimator of the cumulative distribution function. A precedence-type test based on the Nelson-Aalen estimator of the cumulative hazard function has been proposed. This test was developed for both Type-II right censoring and progressive Type-II right censoring. Numerical results, including illustrative examples, critical values and a power study have been provided. The results from this test were compared with those from the test based on the Kaplan-Meier estimator.

Health technology assessment: case study on breast carcinoma treatment in the Czech Republic Bc. Lenka Šlegerová January 4, 2019 Abstract This thesis proposes an original method for assessing total costs of med- ical treatment. It defines the semi-Markov model with four states that are associated with specific costs of the treatment, and not with patients' health statuses. This method is applied to individuals' treatment data drawn from the Czech clinical practice in the treatment of the metastatic HER2+ breast cancer. The aim is to assess the cost-effectiveness of adding medication per- tuzumab to the combination of trastuzumab+docetaxel within first-line therapy and to examine whether using individual data on Czech patients and the economic conditions leads to different results from foreign stud- ies. Furthermore, employing censored data from the clinical practice in the thesis complicates the estimation of patients' overall survival in compari- son to clinical-trials data that form random samples. Therefore, survival functions were not only estimated by the Kaplan-Meier estimator but also using the Cox proportional hazard model and the Accelerated failure time model that both control for the effects of included covariates. The addition of pertuzumab does not result in significantly longer pa- tients'...

The objective of the study was to identify the factors that affect the survival lifetime of HIV+ terminal patients in rural district hospitals of Albert Luthuli municipality in the Mpumalanga province of South Africa. A cohort of HIV+ terminal patients was retrospectively followed from 2010 to 2017 until a patient died, was lost to follow-up or was still alive at the end of the observation period. Nonparametric survival analysis and semiparametric survival analysis methods were used to analyse the data. Through Cox proportional hazards regression modelling, it was found that ART adherence (poor, fair, good), Age, Follow-up mass, Baseline sodium, Baseline viral load, Follow CD4 count by Treatment (Regimen 1) interaction and Follow-up lymphocyte by TB history (yes, no) interaction had significant effects on survival lifetime of HIV+ terminal patients (p-values<0.1). Furthermore, through quantile regression modelling, it was found that short, medium and long survival times of HIV+ patients, respectively represented by the 0.1, 0.5 and 0.9 quantiles, were not necessarily significantly affected by the same factors.<br>Statistics<br>M. Sc. (Statistics)