Academic literature on the topic 'Kaplan-Meier estimation'

Previous studies have been made of the usefulness and effectiveness of survival analysis in transportation and traffic engineering studies with incomplete data in which the Kaplan–Meier estimate is proposed for determining traffic capacity distribution. However, well-known estimators like Kaplan–Meier and Nelson–Aalen have several disadvantages that make it difficult to obtain the traffic capacity distribution. First, neither estimator is defined for all values of traffic flows possible. That is, the maximum flow followed by a breakdown defines the final point of the estimated distribution curve. Therefore, parametric fitting tools have to be applied to obtain the remaining portion of the curve. Moreover, the discontinuity and nonsmoothness of the Kaplan–Meier and Nelson–Aalen estimates make it difficult to ensure the robustness of the estimation. In this paper the Kaplan–Meier and Nelson–Aalen nonparametric estimators are used to obtain the traffic capacity function of four freeway sections. Then a Bayesian nonparametric estimator, which is shown to be a Bayesian extension of the Kaplan–Meier estimator, is introduced for estimating the capacity distribution. This estimator assumes a Dirichlet process prior for the survival function under the minimization of a squared-error loss function. The results indicate that the curves obtained by using the Bayesian estimation method are smoother than those obtained with the other estimator. This smoothness also ensures the continuity in the vicinity of censored observations. Furthermore, the Bayesian estimates can be obtained for any traffic flow value regardless of the availability of data only for certain ranges of observations (including censored data).

The paper deals with the estimation of survival function of a particular random variable of interest in proportional hazard model of random censorship under the condition that data are randomly censored by k independent variables. Estimators are constructed using results from Abdushukurov (1984), Cheng and Lin (1984), Ebrahimi (1985) and Kaplan and Meier (1958). The asymptotic behaviour of all these estimators is investigated. Numerical results are provided to calculate the efficiencies of ACL and Ebrahimi's estimators in comparsion to classical Kaplan-Meier (1958) estimator.

This study presents a novel methodology to investigate the nonparametric estimation of a survival probability under random censoring time using the ranked observations from a Partially Rank-Ordered Set (PROS) sampling design and employs it in a hematological disorder study. The PROS sampling design has numerous applications in medicine, social sciences and ecology where the exact measurement of the sampling units is costly; however, sampling units can be ordered by using judgment ranking or available concomitant information. The general estimation methods are not directly applicable to the case where samples are from rank-based sampling designs, because the sampling units do not meet the identically distributed assumption. We derive asymptotic distribution of a Kaplan-Meier (KM) estimator under PROS sampling design. Finally, we compare the performance of the suggested estimators via several simulation studies and apply the proposed methods to a real data set. The results show that the proposed estimator under rank-based sampling designs outperforms its counterpart in a simple random sample (SRS).

We discuss the kernel estimation of a density function based on censored data when the survival and the censoring times form the stationary negatively associated (NA) sequences. Under certain regularity conditions, the Berry-Esseen type bounds are derived for the kernel density estimator and the Kaplan-Meier kernel density estimator at a fixed pointx.

The distribution of the length of a typical chord of a stationary random set is an interesting feature of the set's whole distribution. We give a nonparametric estimator of the chord length distribution and prove its strong consistency. We report on a simulation experiment in which our estimator compared favourably to a reduced sample estimator. Both estimators are illustrated by applying them to an image sample from a yoghurt ferment. We briefly discuss the closely related problem of estimation of the linear contact distribution. We show by a simulation experiment that a transformation of our estimator of the chord length distribution is more efficient than a Kaplan-Meier type estimator of the linear contact distribution.

The distribution of the length of a typical chord of a stationary random set is an interesting feature of the set's whole distribution. We give a nonparametric estimator of the chord length distribution and prove its strong consistency. We report on a simulation experiment in which our estimator compared favourably to a reduced sample estimator. Both estimators are illustrated by applying them to an image sample from a yoghurt ferment. We briefly discuss the closely related problem of estimation of the linear contact distribution. We show by a simulation experiment that a transformation of our estimator of the chord length distribution is more efficient than a Kaplan-Meier type estimator of the linear contact distribution.

Nous nous sommes intéressés dans cette étude à l'estimation de la loi de la durée de séjour en prenant en compte les individus sur lesquels l'évènement d'intérêt et la censure peuvent se produire dans un même intervalle et être observés. Pour cela, nous avons proposé deux approches d'estimation non paramétrique basées sur une approximation asymptotique quand la longueur de l'intervalle entre deux dates consécutives d'observation tend vers 0. La première est basée sur une relation intégrale et la deuxième est basée sur une restauration des durées de séjour. Nous nous sommes servis de ces approches pour monter un modèle de croissance des fruits du cacaoyer en fonction du climat. Nous avons également estimé la sensibilité (probabilité de pénétration et de réussite d'infection) des fruits en fonction de leur stade et le potentiel infectieux (nombre moyen de spores sur un fruit) par date. Ce potentiel infectieux nous permettrait de monter un modèle du potentiel infectieux en fonction des fruits attaqués. La connaissance du potentiel infectieux en fonction des fruits attaqués, de l'estimation de la sensibilité suivant les stades, de l'estimation du modèle de croissance permettra alors de monter un modèle dynamique du potentiel infectieux pour prédire le risque d'évolution de la pourriture brune des fruits du cacaoyer
We are interested in this study in estimating the lifetime distribution by taking into consideration individuals on which the interest event and the censorship can occur in the same intervaland both events were then observed. We proposed two nonparametric approaches based on an asymptotic approximation when the lengthbetween two consecutive observation days tends to 0. The first one was based on an integral relationship and the second one on a lifetime restoration. We used theses approaches to build a fruitgrowth model depending on climatic variables. We also estimated the susceptibility (success probability of attack by a spore on a fruit) of the fruit depending of its developmental stage and theinfectious potential of the disease over time.This infectious potential could help to build a model of infectious potential depending on infected fruits. The knowledge of the infectious potential depending on infected fruits, the estimation of the susceptibility of the fruit and the model of growth will allow to built a dynamic model of infectious potential to predict the evolution risk of disease progression

This thesis centers on nonparametric inferences of the cumulative hazard function of a right truncated variable. We present three variance estimators for the Nelson-Aalen estimator of the cumulative hazard function and conduct a simulation study to investigate their performances. A close match between the sampling standard deviation and the estimated standard error is observed when an estimated survival probability is not close to 1. However, the problem of poor tail performance exists due to the limitation of the proposed variance estimators. We further analyze an AIDS blood transfusion sample for which the disease latent time is right truncated. We compute three variance estimators, yielding three sets of confidence intervals. This work provides insights of two-sample tests for right truncated data in the future research.

This work introduces nonparametric models which are used in time to event data analysis. It is focused on applying these methods in medicine where it is called survival analysis. The basic techniques and problems, which can appear in survival analysis, are presented and explained here. The Kaplan -- Meier estimator of survival function is discussed in the main part. This is the most frequented method used for estimating the survival function in patients who have undergone a specific treatment. The Kaplan -- Meier estimator is also a common device in the statistical packets. In addition to estimation of survival function, the estimation of hazard function and cumulative hazard function is presented. The hazard function shows the intensity of an individual experiencing the particular event in a short time period. Special problems occur when analyzing time to event data. A distinctive feature, often present in such data, is known as censoring. That is the situation when the individual does not experience the event of interest at the time of study. The thesis covers also an empiric part, where the results of an analysis of patients with the larynx carcinoma diagnosis are shown. These patients were treated in a hospital located in České Budějovice. This analysis is based on a theory presented in the previous chapters.

Cette thèse porte sur l'étude des propriétés asymptotiques d'un estimateur non paramétrique de la densité de type Parzen-Rosenblatt, sous un modèle de données censurées à droite, vérifiant une structure de dépendance de type associé. Dans ce cadre, nous rappelons d'abord les résultats existants, avec détails, dans les cas i.i.d. et fortement mélangeant (α-mélange). Sous des conditions de régularité classiques, il est établi que la vitesse de coonvergence uniforme presque sûre de l'estimateur étudié, est optimale. Dans la partie dédiée aux résultats de cette thèse, deux résultats principaux et originaux sont présentés : le premier résultat concerne la convergence uniforme presque sûre de l'estimateur étudié sous l'hypothèse d'association. L'outil principal ayant permis l'obtention de la vitesse optimale est l'adaptation du Théorème de Doukhan et Neumann (2007), dans l'étude du terme des fluctuations (partie aléatoire) de l'écart entre l'estimateur considéré et le paramètre étudié (densité). Comme application, la convergence presque sûre de l'estimateur non paramétrique du mode est établie. Les résultats obtenus ont fait l'objet d'un article accepté pour publication dans Communications in Statistics-Theory and Methods ; Le deuxième résultat établit la normalité asymptotique de l'estimateur étudié sous le même modèle et constitute ainsi une extension au cas censuré, du résultat obtenu par Roussas (2000). Ce résultat est soumis pour publication
This thesis deals with the study of asymptotic properties of e kernel (Parzen-Rosenblatt) density estimate under associated and censored model. In this setting, we first recall with details the existing results, studied in both i.i.d. and strong mixing condition (α-mixing) cases. Under mild standard conditions, it is established that the strong uniform almost sure convergence rate, is optimal. In the part dedicated to the results of this thesis, two main and original stated results are presented : the first result concerns the strong uniform consistency rate of the studied estimator under association hypothesis. The main tool having permitted to achieve the optimal speed, is the adaptation of the Theorem due to Doukhan and Neumann (2007), in studying the term of fluctuations (random part) of the gap between the considered estimator and the studied parameter (density). As an application, the almost sure convergence of the kernel mode estimator is established. The stated results have been accepted for publication in Communications in Statistics-Theory & Methods ; The second result establishes the asymptotic normality of the estimator studied under the same model and then, constitute an extension to the censored case, the result stated by Roussas (2000). This result is submitted for publication

Les registres de population doivent donner des indications fiables et non biaisées sur les besoins de prise en charge et sur les performances du système de soins. L'étude de la survie occupe une position centrale dans la construction des indicateurs de santé. Les analyses de survie en population diffèrent de celles issues des essais thérapeutiques par les méthodes d'analyse et par des biais spécifiques qui sont étudiés dans ce travail et illustrés d'exemples. La survie relative est la méthode la plus utilisée. Dans les comparaisons, une attention particulière doit donc être portée à la mortalité utilisée dans la correction de la mortalité observée. Certains biais sont liés à la qualité de la collecte des données. Le manque d'exhaustivité sélectionne les malades de bon pronostic. L'insuffisance d'infromations conduit à créer dans les variables des catégories regroupant les informations imprécises. Ces catégories hétérogènes correspondent à des cas de mauvais pronostic peu explorés ou à des cas ordinaires mal documentés par l'enquête. Comparer des sous-groupes où la qualité de l'enquête peut varier (zones ou périodes) expose à des biais. Des problèmes, propres aux situations d'observation tels les biais d'indication, existent. La prise en compte du stade, facteur pronostic jouant un rôle majeur dans la compréhension des phénomènes observés, pose des problèmes. Un calcul décentralisé du stade peut-être à l'origine d’erreurs de classification. De plus, il existe des glissements de classification liés à une insuffisance d'exploration (faible nombre de ganglions examinés, bilan d'extension incomplet). Ces biais potentiels sont retrouvés dans l'analyse de la survie des cancers colorectaux étudiés par 6 registres français. La prise en compte de variables complémentaires, en particulier pour valider le stade, permettent d'en corriger une partie, mais les procédures de standardisation de collecte et codage sont encore insuffisantes. Faute de pouvoir utiliser les informations des certificats de décès, l'exhaustivité est difficilement évaluable dans les registres français. Malgré ces imperfections, les données fournies par les registres sont fondamentales dans la mesure des besoins. Elles permettent, par un suivi détaillé et à long terme, de calculer la prévalence (cas ayant une maladie active nécessitant des soins)

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
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

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
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
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

MOTA, Rosa Maria Salani. Respondent Driven Sampling (RDS) aplicado à população de homens que fazem sexo com homens no Brasil. 2012. 189 f. Tese (Doutorado em Saúde Pública) - Universidade Federal do Ceará. Faculdade de Medicina, Fortaleza, 2012.
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The estimators for population parameters in samples collected by sampling Respondent Driven Sampling (RDS) are sensitive to the presence of observations ignored and tends to underestimate the population parameters. The absence of a clearly defined sampling frame for the collection of samples from populations considered hidden and/or difficult access made the RDS became an important tool for biological and behavioral surveillance in these populations at higher risk for HIV, especially Brazil. Considered a method of sampling in the reference chain, RDS uses information about the connections of social networks for specific asymptotically unbiased estimators of population characteristics and accuracy of these estimators. Multicenter cross-sectional epidemiological and behavioral surveillance for MSM populations in 18 years or more was conducted in 10 cities (Manaus, Recife, Salvador, Campo Grande, Brasilia, Curitiba, Itajaí, Santos, Belo Horizonte and Rio de Janeiro) in 2009 and collected in each municipality, a sample through RDS. This study offered the rapid test for diagnosis of HIV infection to those who agreed to participate in a pre-counseling. All participants were asked about testing for HIV prior to the research and about which the diagnosis obtained. By simulating a dichotomous variable (eg, HIV serology positive or negative) without comment ignored in recruiting network in Rio de Janeiro and later recruited 18 deletions, that is, the unknown sample is evaluated from a number of observations significantly smaller than the original sample and the parameter in question (HIV prevalence) is underestimated. Still, with the allocation of single serology ignored in the descriptive context, it is observed in samples with attribution, biological markers indicating that more accurate values. Multicentre study for the group of participants who self-reported positive or negative serology for HIV rapid test and performed the research notes to self-reports, high correlation (0.88) and 100% sensitivity with gold standard rapid test for HIV diagnosis. Finally, estimating the prevalence of HIV in the samples observed by county and general, and the proposed allocation of the self-reported HIV positive and HIV serology subsequent assignment of + / - through three proposed charges: are all negative, proximity of the participants in the network recruitment and by logistic regression. It is found in samples collected from the estimated overall HIV prevalence was equal to 11.1%, by municipality, the lower prevalence in Santos (2.6%) and highest in Rio de Janeiro (17.6%).With the charges tend to increase the prevalence and the highest estimates are found with the imputation logistic regression in 7 of 9 municipalities assessed by this methodology. The estimated overall HIV logistic regression is 14.2% and, by municipality, the lower prevalence in Recife (5.2%) and highest in Brasilia (23.7%). The allocation of serology for HIV by the Logistic Regression occurs by municipality and by a model with a minimum accuracy of 70%.
Os estimadores para parâmetros populacionais em amostras coletadas pelo método de amostragem Respondent Driven Sampling (RDS) são sensíveis à presença de observações ignoradas e tendem a subestimar os parâmetros populacionais. A ausência de um quadro de amostragem bem definido para a coleta de amostras em populações consideradas escondidas e/ou de acesso difícil fez com que o RDS se tornasse uma importante ferramenta de vigilância comportamental e biológica nessas populações com maior risco para o HIV, em especial no Brasil. Considerado um método de amostragem em cadeia de referência, o RDS utiliza informações sobre as conexões das redes sociais para obter estimadores contingentes assintoticamente imparciais das características populacionais e a precisão desses estimadores. Estudo multicêntrico de corte transversal para vigilância epidemiológica e comportamental em populações de HSH com 18 anos ou mais foi realizado em dez cidades brasileiras (Manaus, Recife, Salvador, Campo Grande, Brasília, Curitiba, Itajaí, Santos, Belo Horizonte e Rio de Janeiro) no ano de 2009 e, coleta, em cada município, uma amostra pelo RDS. Neste estudo, foi oferecido o teste rápido para diagnóstico da infecção por HIV àqueles que aceitam participar de um pré-aconselhamento. Todos os participantes foram inquiridos sobre a realização de testes anti-HIV anteriores ao da pesquisa e sobre qual o diagnóstico obtido. Com a simulação de uma variável dicotômica (exemplo: sorologia para HIV positiva ou negativa) sem observações ignoradas na rede de recrutamento do Rio de Janeiro e posteriores exclusões de 18 recrutados, encontra-se que, a amostra com ignorados é avaliada com base em um número de observações significativamente menor que o da amostra original e o parâmetro em questão (prevalência do HIV) é subestimado. Ainda, com a imputação única das sorologias ignoradas, no contexto descritivo, observam-se, nas amostras com imputação, marcadores biológicos que indicam valores mais acurados. No estudo multicêntrico, para o grupo de participantes que autorrelatou sorologia positiva ou negativa para o HIV e realizou teste rápido na pesquisa, observa-se para os autorrelatos elevada concordância (0,88) e sensibilidade de 100% com o padrão-ouro teste rápido para diagnóstico do HIV. Finalmente, estimando a prevalência para o HIV nas amostras observadas por município e geral, e, com a proposta da imputação pelo autorrelato do HIV positivo e posterior atribuição de sorologia HIV +/- mediante três propostas de imputações: todos são negativos, proximidade dos participantes na rede de recrutamento e pela regressão logística. Encontra-se nas amostras coletadas a estimativa geral da prevalência do HIV igual a 11,1% sendo, por município, a menor prevalência em Santos (2,6%) e a maior no Rio de Janeiro (17,6%). Com as imputações as prevalências tendem a aumentar e as maiores estimativas são encontradas com a imputação por meio da regressão logística em sete de nove municípios avaliados por essa metodologia. A estimativa geral do HIV pela regressão logística é 14,2% sendo, por município, a menor prevalência no Recife (5,2%) e a maior em Brasília (23,7%). A imputação da sorologia de infecção por HIV pela regressão logística ocorre por município e por intermédio de um modelo com acurácia mínima igual a 70%.

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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.
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.

This chapter investigates change-point (hazard rate) probability models for the random survival time in some population of interest. A parametric probability distribution is assumed with parameters to be estimated from a sample of observed survival times. If a change-point parameter, denoted by τ‎, is included to represent the time at which there is a discrete change in hazard rate, then the model is non-standard. The profile log-likelihood, with τ‎ as profiling parameter, has a discontinuous jump at every τ‎ equal to a sampled value, becoming unbounded as τ‎ tends to the largest observation. It is known that maximum likelihood estimation can still be used provided the range of τ‎ is restricted. It is shown that the alternative maximum product of spacings method is consistent without restriction on τ‎. Censored observations which commonly occur in survival-time data can be accounted for using Kaplan-Meier estimation. A real data numerical example is given.