INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

Smooth Hazard Function Estimation for Interval Censored Data with Time Varying Covariates

In this paper we propose methods for smooth hazard estimation of a time variable where that variable is interval censored. These methods allow one to model the transformed hazard in terms of either smooth (smoothing splines) or linear functions of time and other relevant time varying predictor variables. We illustrate the use of this method on a dataset of hemophiliacs where the outcome, time to seroconversion for HIV, is interval censored and left-truncated.

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

Nonparametric Estimation of Survivor Function in Bivariate Competing Risk Models’

So far, in the bivariate set up, the analysis of lifetime (failure time) data with multiple causes of failure is done by treating each cause of failure separately. with failures from other causes considered as independent censoring. This approach is unrealistic in many situations. For example, in the analysis of mortality data on married couples one would be interested to compare the hazards for the same cause of death as well as to check whether death due to one cause is more important for the partners’ risk of death from other causes. In reliability analysis. one often has systems with more than one component and many systems. subsystems and components have more than one cause of failure. Design of high-reliability systems generally requires that the individual system components have extremely high reliability even after long periods of time. Knowledge of the failure behaviour of a component can lead to savings in its cost of production and maintenance and. in some cases, to the preservation of human life. For the purpose of improving reliability. it is necessary to identify the cause of failure down to the component level. By treating each cause of failure separately with failures from other causes considered as independent censoring, the analysis of lifetime data would be incomplete. Motivated by this. we introduce a new approach for the analysis of bivariate competing risk data using the bivariate vector hazard rate of Johnson and Kotz (1975).

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Parametric accelerated failure time models with random effects and an application to kidney transplant survival

Accelerated failure time models with a shared random component are described, and are used to evaluate the effect of explanatory factors and different transplant centres on survival times following kidney transplantation. Different combinations of the distribution of the random effects and baseline hazard function are considered and the fit of such models to the transplant data is critically assessed. A mixture model that combines short- and long-term components of a hazard function is then developed, which provides a more flexible model for the hazard function. The model can incorporate different explanatory variables and random effects in each component. The model is straightforward to fit using standard statistical software, and is shown to be a good fit to the transplant data. Copyright (C) 2004 John Wiley Sons, Ltd.

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped unimodal increasing and decreasing hazard rate functions The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter The maximum likelihood estimation procedure is discussed A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples Three real datasets Illustrate the methodology (C) 2010 Elsevier B V All rights reserved

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved

Default mercado de crédito parcelado para bens duráveis : veículos automotores

The present work aims to study the macroeconomic factors influence in credit risk for installment autoloans operations. The study is based on 4.887 credit operations surveyed in the Credit Risk Information System (SCR) hold by the Brazilian Central Bank. Using Survival Analysis applied to interval censured data, we achieved a model to estimate the hazard function and we propose a method for calculating the probability of default in a twelve month period. Our results indicate a strong time dependence for the hazard function by a polynomial approximation in all estimated models. The model with the best Akaike Information Criteria estimate a positive effect of 0,07% for males over de basic hazard function, and 0,011% for the increasing of ten base points on the operation annual interest rate, toward, for each R$ 1.000,00 on the installment, the hazard function suffer a negative effect of 0,28% , and an estimated elevation of 0,0069% for the same amount added to operation contracted value. For de macroeconomics factors, we find statistically significant effects for the unemployment rate (-0,12%) , for the one lag of the unemployment rate (0,12%), for the first difference of the industrial product index(-0,008%), for one lag of inflation rate (-0,13%) and for the exchange rate (-0,23%). We do not find statistic significant results for all other tested variables.

Essays on price dynamics

Esta tese tem como objetivo principal aproximar a evidencia empirica existente sobre os agregados macroeconomicos com as novas evidencias empiricas baseadas nos micro dados de precos ao consumidor, tendo como base os modelos padroes de rigidez de preco utilizados na literatura de politica monetaria. Para isso, esta tese utiliza a base de dados individuais de precos ao consumidor no Brasil fornecida pela Fundacao Getulio Vargas. Especificamente, esta tese foca em tres temas principais: a existencia de variac˜oes temporararias de precos, a heterogeneidade na rigidez de precos entre firmas de um mesmo setor e o formato das func˜oes hazard. Os resultados mostram que: existe de fato uma correlac˜ao entre as variaveis referentes as mudancas temporararias de precos e os agregados macroeconomicos; a heterogeneidade na rigidez de precos entre firmas de um mesmo setor apresenta efeitos significativos sobre a dinamica dos agregados macroeconomicos; e por fim, o formato mais geral da func˜ao hazard proposta nesta tese possibilita novas dinamicas dos agregados macroeconomicos.

Regras de preços e efeitos de política monetária e fiscal

Esta tese é composta por três ensaios, dois deles analisam regras de preços e o outro faz uma análise de política fiscal. Cada ensaio forma um capítulo da tese. No primeiro capítulo, acrescentamos heterogeneidade a um modelo de regras de preços endógenas dependentes do tempo para analisar os efeitos reais de uma política de desinflação em um ambiente de credibilidade imperfeita. Inicialmente avaliamos os custos da desinflação em uma economia onde a credibilidade é exógena. Depois, relaxamos essa hipótese permitindo que os agentes atualizem suas crenças sobre o tipo de policymaker com que se deparam. Como resultado, em ambos os casos, a heterogeneidade amplia os efeitos reais de uma política de desinflação. Em seguida, mostramos que o modelo calibrado replica bem, e melhor do que o modelo com homogeneidade entre os agentes, a dinâmica do produto e da inflação durante a política de desinflação de Volcker. O segundo capítulo introduz uma especificação geral para hazard function com que se deparam os price setters. Diferentes especificações da hazard function podem levar a resultados muito distintos da dinâmica agregada da economia, mesmo quando as durações de preços são as mesmas entre diferentes especificações de hazard functions. Este resultado vale tanto para economias homogêneas quanto heterogêneas. O terceiro capítulo analisa os efeitos dos choques de gastos do governo sobre a dinâmica do consumo privado em um modelo DSGE (Dynamic Stochastic General Equilibrium) Novo-keynesiano com uma pequena economia aberta. Incorporamos ao modelo consumidores não-ricardianos e mostramos que a presença desse tipo de consumidor além de não evitar a queda do consumo privado, a intensifica depois de um curto espaço de tempo. Analisamos também a sensibilidade da dinâmica do consumo a diferentes graus de abertura da economia, a parâmetros de preferências e de políticas.

Ensaios sobre política monetária

Esta tese é composta de três ensaios a respeito de política monetária. O primeiro ensaio aborda o canal em que as crises financeiras aumentam a ineficiência alocativa nos países emergentes. O segundo ensaio trata do grau de não-neutralidade da moeda no Brasil de acordo com o modelo de Golosov e Lucas (2007). O terceiro ensaio estima a inclinação da hazard function da precifi cação para o Brasil pela metodologia de Finite Mixture Model.

Progression of articular and extraarticular damage in oligoarticular juvenile idiopathic arthritis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The complementary exponential power lifetime model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análise clássica e bayesiana do modelo Weibull modificado generalizado

Pós-graduação em Matematica Aplicada e Computacional - FCT