Browsing by Author "Leao, Jeremias"

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    A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data
    (2023) Mota, Alex; Milani, Eder A.; Leao, Jeremias; Ramos, Pedro L.; Ferreira, Paulo H.; Junior, Oilson G.; Tomazella, Vera L. D.; Louzada, Francisco
    In this paper, we propose a new cure rate frailty regression model based on a two-parameter weighted Lindley distribution. The weighted Lindley distribution has attractive properties such as flexibility on its probability density function, Laplace transform function on closed-form, among others. An advantage of proposed model is the possibility to jointly model the heterogeneity among patients by their frailties and the presence of a cured fraction of them. To make the model parameters identifiable, we consider a reparameterized version of the weighted Lindley distribution with unit mean as frailty distribution. The proposed model is very flexible in sense that has some traditional cure rate models as special cases. The statistical inference for the model's parameters is discussed in detail using the maximum likelihood estimation under random right-censoring. Further, we present a Monte Carlo simulation study to verify the maximum likelihood estimators' behavior assuming different sample sizes and censoring proportions. Finally, the new model describes the lifetime of 22,148 patients with stomach cancer, obtained from the Fundacao Oncocentro de Sao Paulo, Brazil.
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    Statistical Inference for Generalized Power-Law Process in repairable systems
    (2024) Lopes, Tito; Tomazella, Vera L. D.; Leao, Jeremias; Ramos, Pedro L.; Louzada, Francisco
    Repairable systems are often used to model the reliability of restored components after a failure is observed. Among various reliability growth models, the power law process (PLP) or Weibull process has been widely used in industrial problems and applications. In this article, we propose a new class of model called the generalized PLP (GPLP), based on change points. These can be treated as known or unknown parameters, or interpreted as failure times. Herein, we consider the impact of all or some fixes on the failure intensity function. In this context, unlike the usual PLP, the GPLP is not restricted to the assumption of minimal repair (MR). Other situations, such as perfect, efficient, and harmful repair, can be considered. We present some special cases of the GPLP, such as the main models used to analyze repairable systems under the assumption of imperfect repair. The estimators of the proposed model parameters were obtained using the maximum likelihood method. We evaluated the performance of the parameter estimators through Monte Carlo (MC) simulations. The proposed approach is fully illustrated using two real failure time datasets.
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    Weighted Lindley frailty model: estimation and application to lung cancer data
    (2021) Mota, Alex; Milani, Eder A.; Calsavara, Vinicius F.; Tomazella, Vera L. D.; Leao, Jeremias; Ramos, Pedro L.; Ferreira, Paulo H.; Louzada, Francisco
    In this paper, we propose a novel frailty model for modeling unobserved heterogeneity present in survival data. Our model is derived by using a weighted Lindley distribution as the frailty distribution. The respective frailty distribution has a simple Laplace transform function which is useful to obtain marginal survival and hazard functions. We assume hazard functions of the Weibull and Gompertz distributions as the baseline hazard functions. A classical inference procedure based on the maximum likelihood method is presented. Extensive simulation studies are further performed to verify the behavior of maximum likelihood estimators under different proportions of right-censoring and to assess the performance of the likelihood ratio test to detect unobserved heterogeneity in different sample sizes. Finally, to demonstrate the applicability of the proposed model, we use it to analyze a medical dataset from a population-based study of incident cases of lung cancer diagnosed in the state of Sao Paulo, Brazil.