A truncated sample consists of realizations of a pair of random variables (L, T) subject to the constraint that L ≤T. The major study interest with a truncated sample is to find the marginal distributions of L and T. Many studies have been done with the assumption that L and T are independent. We introduce a new way to specify a Cox model for a truncated sample, assuming that the truncation time is a predictor of T, and this causes the dependence between L and T. We develop an algorithm to obtain the adjusted risk sets and use the Kaplan-Meier estimator to estimate the Marginal distribution of L. We further extend our method to more practical situation, in which the Cox model includes other covariates associated with T. Simulation studies have been conducted to investigate the performances of the Cox model and the new estimators.

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.

Health problems of the human beings in a society are one of the main components of the social security systems due to the dimension of the financial burden it might bring on individuals, employers, insurance companies and governments. Morbidity measures, such as incidence and prevalence of a specific disease in a certain population enable researchers to estimate for individuals the probability of being diagnosed or being prone to the diseases. This information is usually not tractable because of the non-availability of the convenient data or recordings for many countries as well as Turkey. Even if it is available, it is commonly limited with largely varying characteristics about the type and coverage of the diseases. In this regard, the pattern that a population follows for an acute disease may not be the same for chronic diseases. Having those indicators determined for a group of insureds will enable underwriters to have more profitable and economical premium calculation and precision on required reserve estimation. v Based on their characteristics such as acute or chronic behaviour, the gender, and the location of residency of people, the diseases show different behaviour on their occurrences. From the insurer

Os estimadores para parÃmetros populacionais em amostras coletadas pelo mÃtodo de amostragem Respondent Driven Sampling (RDS) sÃo sensÃveis à presenÃa de observaÃÃes ignoradas e tendem a subestimar os parÃmetros populacionais. A ausÃncia de um quadro de amostragem bem definido para a coleta de amostras em populaÃÃes consideradas escondidas e/ou de acesso difÃcil fez com que o RDS se tornasse uma importante ferramenta de vigilÃncia comportamental e biolÃgica nessas populaÃÃes com maior risco para o HIV, em especial no Brasil. Considerado um mÃtodo de amostragem em cadeia de referÃncia, o RDS utiliza informaÃÃes sobre as conexÃes das redes sociais para obter estimadores contingentes assintoticamente imparciais das caracterÃsticas populacionais e a precisÃo desses estimadores. Estudo multicÃntrico de corte transversal para vigilÃncia epidemiolÃgica e comportamental em populaÃÃes de HSH com 18 anos ou mais foi realizado em dez cidades brasileiras (Manaus, Recife, Salvador, Campo Grande, BrasÃlia, Curitiba, ItajaÃ, Santos, Belo Horizonte e Rio de Janeiro) no ano de 2009 e, coleta, em cada municÃpio, uma amostra pelo RDS. Neste estudo, foi oferecido o teste rÃpido para diagnÃstico da infecÃÃo por HIV Ãqueles que aceitam participar de um prÃ-aconselhamento. Todos os participantes foram inquiridos sobre a realizaÃÃo de testes anti-HIV anteriores ao da pesquisa e sobre qual o diagnÃstico obtido. Com a simulaÃÃo de uma variÃvel dicotÃmica (exemplo: sorologia para HIV positiva ou negativa) sem observaÃÃes ignoradas na rede de recrutamento do Rio de Janeiro e posteriores exclusÃes de 18 recrutados, encontra-se que, a amostra com ignorados à avaliada com base em um nÃmero de observaÃÃes significativamente menor que o da amostra original e o parÃmetro em questÃo (prevalÃncia do HIV) à subestimado. Ainda, com a imputaÃÃo Ãnica das sorologias ignoradas, no contexto descritivo, observam-se, nas amostras com imputaÃÃo, marcadores biolÃgicos que indicam valores mais acurados. No estudo multicÃntrico, para o grupo de participantes que autorrelatou sorologia positiva ou negativa para o HIV e realizou teste rÃpido na pesquisa, observa-se para os autorrelatos elevada concordÃncia (0,88) e sensibilidade de 100% com o padrÃo-ouro teste rÃpido para diagnÃstico do HIV. Finalmente, estimando a prevalÃncia para o HIV nas amostras observadas por municÃpio e geral, e, com a proposta da imputaÃÃo pelo autorrelato do HIV positivo e posterior atribuiÃÃo de sorologia HIV +/- mediante trÃs propostas de imputaÃÃes: todos sÃo negativos, proximidade dos participantes na rede de recrutamento e pela regressÃo logÃstica. Encontra-se nas amostras coletadas a estimativa geral da prevalÃncia do HIV igual a 11,1% sendo, por municÃpio, a menor prevalÃncia em Santos (2,6%) e a maior no Rio de Janeiro (17,6%). Com as imputaÃÃes as prevalÃncias tendem a aumentar e as maiores estimativas sÃo encontradas com a imputaÃÃo por meio da regressÃo logÃstica em sete de nove municÃpios avaliados por essa metodologia. A estimativa geral do HIV pela regressÃo logÃstica à 14,2% sendo, por municÃpio, a menor prevalÃncia no Recife (5,2%) e a maior em BrasÃlia (23,7%). A imputaÃÃo da sorologia de infecÃÃo por HIV pela regressÃo logÃstica ocorre por municÃpio e por intermÃdio de um modelo com acurÃcia mÃnima igual a 70%. / 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, ItajaÃ, 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%.