Agatha Sacramento Rodrigues

In this paper, we propose two novel defective survival models within the Gamma–G family: the defective Gamma–Gompertz and the defective Gamma–Dagum distributions. In contrast to the corresponding Gamma–G mixture cure formulation, in which the Gamma–G distributional parameters are combined with an explicit cure fraction mixing parameter, the proposed defective formulation induces the cure fraction through the limiting behavior of the survival function. Thus, within the same Gamma–G baseline structure, the model avoids introducing an additional cure fraction parameter. The motivation for these new models lies in the limited set of defective distributions currently available, despite the increasing demand for flexible cure rate models in biomedical applications. By extending the defective property to the Gamma–G construction, our approach fills this methodological gap while providing models that are both interpretable and computationally efficient. We show that the Gamma–G construction preserves defectiveness whenever the baseline distribution is defective, thus establishing a coherent theoretical foundation. Both models allow covariate effects through regression structures on shape, scale, and, in the case of the Gamma–Dagum distribution, on the cure fraction parameter, resulting in flexible and interpretable specifications. Parameters are estimated via maximum likelihood, and an extensive Monte Carlo study confirms estimator consistency and accurate coverage in finite samples. The practical relevance of the models is illustrated with two large clinical datasets on melanoma and cervical cancer from the São Paulo Cancer Registry. Results reveal that the proposed models provide competitive goodness-of-fit and offer useful insights into long-term survival compared to traditional cure rate approaches. Overall, this work introduces a unifying and flexible framework for defective survival models, extending their applicability and delivering practical improvements over existing cure models.

In this paper, we propose two novel defective survival models within the Gamma–G family: the Defective Gamma–Gompertz and the Defective Gamma–Da- gum distributions. Unlike classical mixture cure models, our formulation incorporates the cure fraction directly into the survival function through the defective property of the baseline distribution, avoiding the need for an explicit mixing parameter. The motivation for these new models lies in the limited set of defective distributions currently available, despite the increasing demand for flexible and parsimonious cure rate models in biomedical applications. By extending the defective property to the Gamma–G construction, our approach fills this methodological gap while providing models that are both interpretable and computationally efficient. We show that the Gamma–G construction preserves defectiveness whenever the baseline distribution is defective, thus establishing a coherent theoretical foundation. Both models allow covariate effects through regression structures on shape, scale, and, in the case of the Gamma–Dagum distribution, on the cure-fraction parameter, resulting in parsimonious and interpretable specifications. Parameters are estimated via maximum likelihood, and an extensive Monte Carlo study confirms estimator consistency and accurate coverage in finite samples. The practical relevance of the models is illustrated with two large clinical datasets on melanoma and cervical cancer from the São Paulo Cancer Registry. Results reveal that the proposed models not only provide superior goodness-of-fit but also offer clearer insights into long-term survival compared to traditional cure-rate approaches. Overal, this work introduces a unifying and flexible framework for defective survival models, extending their applicability and delivering practical improvements over existing cure models.

In this article, we propose the zero-adjusted defective Gompertz model incorporating gamma frailty, aimed at jointly modeling survival data where excess zeros and cure fractions coexist, a frequent challenge in biomedical and public health studies. Traditional survival models often fail to capture these complexities simultaneously, limiting their applicability in real-world medical data. The proposed approach integrates the flexibility of the Gompertz distribution with structural adjustments for zero inflation and defective survival functions, while the inclusion of a gamma frailty term accounts for unobserved heterogeneity at the individual level. Through extensive Monte Carlo simulations and bootstrap analyses, we demonstrate the model’s consistency and reliability of parameter estimates. Applications to real medical data, including insulin use among pregnant women with gestational diabetes, illustrate the model’s practical utility in accurately identifying both cured and zero-adjusted subpopulations, offering a robust and versatile framework for analyzing complex survival patterns in health research.

This paper presents a parametric quantile regression model for survival data that incorporates a cure fraction, addressing limitations of traditional survival models related to clinical interpretability and their limited capacity to account for cured individuals. The proposed model is built upon the exponentiated Weibull distribution and employs a logarithmic link between survival quantiles and covariates, offering a flexible and interpretable framework. Parameter estimation is conducted via an expectation-maximization algorithm within the maximum likelihood framework. Monte Carlo simulation studies assess the model’s performance under varying censoring levels and sample sizes, confirming its ability to yield stable estimates and reliable inference across diverse scenarios. An application to gastric cancer data demonstrates the model’s effectiveness in capturing heterogeneity and uncovering clinically relevant patterns. This methodology advances survival analysis by integrating cure fraction modeling with quantile-based inference in a coherent and robust manner.

Survival models with cure fractions, known as long-term survival models, are widely used in epidemiology to account for both immune and susceptible patients regarding a failure event. In such studies, it is also necessary to estimate unobservable heterogeneity caused by unmeasured prognostic factors. Moreover, the hazard function may exhibit a non-monotonic shape, specifically, an unimodal hazard function. In this article, we propose a long-term survival model based on a defective version of the Dagum distribution, incorporating a power variance function frailty term to account for unobservable heterogeneity. This model accommodates survival data with cure fractions and non-monotonic hazard functions. The distribution is reparameterized in terms of the cure fraction, with covariates linked via a logit link, allowing for direct interpretation of covariate effects on the cure fraction—an uncommon feature in defective approaches. We present maximum likelihood estimation for model parameters, assess performance through Monte Carlo simulations, and illustrate the model’s applicability using two health-related datasets: severe COVID-19 in pregnant and postpartum women and patients with malignant skin neoplasms.

This study aimed to present a new proposal for the calculation of estimates of induced abortion in Brazil using the indirect method, based on hospital admissions due to abortion complications applying the Guttmacher Institute methodology. Data from the Brazilian Hospital Information System of the Brazilian Unified National Health System (SIH/SUS, acronym in Portuguese) were used to identify hospital admissions due to abortion with public funding and from the Brazilian National Agency for Private Health Insurance and Plans (ANS, acronym in Portuguese) for admissions with supplementary health funding. Correction factors were used to exclude hospital admissions due to miscarriage by the woman’s age group, and data from the 2016 National Abortion Survey (PNA, acronym in Portuguese) were used to review the correction factor for complications that did not require hospitalization, based on the simulation of scenarios with different parameters of population coverage of healthcare plans and frequency of induced abortions in SUS and supplementary health patients. Using this new proposal, a total unsafe abortion rate of 8.7 per 1,000 women aged 10-49 was estimated for 2015, with 9.9 in SUS patients and 5,4 in supplementary health patients, and a total unsafe abortion ratio of 18.5 per 100 live births, with 21.1 in SUS patients and 11.2 in supplementary health patients. This new calculation proposal is an advance because it includes data about hospital admissions of supplementary health and a correction factor for complications that did not result in hospitalization using empirical data from the 2016 PNA. This factor is based on available data and is expected to be improved as new evidence is generated, especially evidence that reflects the specificities of the various regions of the country.

Este estudo teve como objetivo apresentar a nova proposta de cálculo das estimativas de aborto induzido no Brasil por método indireto, baseada nas internações hospitalares por complicações de aborto, utilizando a metodologia do Instituto Guttmacher. Foram utilizados dados do Sistema de Informação Hospitalar do Sistema Único de Saúde (SIH/SUS) para identificações de internações por aborto com financiamento público e da Agência Nacional de Saúde Suplementar (ANS) para aquelas com financiamento pela saúde suplementar. Foram utilizados fatores de correção para descontar internações por abortos espontâneos por faixa etária da mulher e utilizados dados da Pesquisa Nacional de Aborto (PNA) de 2016 para revisão do fator de correção de complicações que não necessitaram de internações, a partir da simulação de cenários com parâmetros distintos de cobertura populacional de planos de saúde e frequência de abortos induzidos em usuárias do SUS e da saúde suplementar. Utilizando essa nova proposta, foi estimada, para 2015, uma taxa de aborto induzido total de 8,7 por 1.000 mulheres de 10-49 anos, sendo de 9,9 em usuárias do SUS e de 5,4 em usuárias da saúde suplementar, e uma razão de aborto induzido total de 18,5 por 100 nascidos vivos, com valores de 21,1 em usuárias do SUS e 11,2 em usuárias da saúde suplementar. Essa nova proposta de cálculo avança ao incorporar dados de internações da saúde suplementar e fator de correção para complicações que não resultaram em internação baseado em dados empíricos da PNA 2016. Esse fator se baseia nos dados atualmente disponíveis e espera-se que possa ser aprimorado à medida que novas evidências sejam produzidas, principalmente as que retratam as particularidades e especificidades das diversas regiões do país.