The Defective Beta-Gompertz Distribution for Cure Rate Regression Models

This paper introduces a novel approach to cure fraction modeling, also known as long-term survival modeling, by focusing on scenarios where a portion of observations is not susceptible to the event of interest. We propose a new defective distribution model based on the Beta distribution, specificall...

Full description

Saved in:
Bibliographic Details
Published inJournal of statistical theory and practice Vol. 19; no. 2
Main Authors Vieira Tojeiro, Cynthia Arantes, Tomazella, Vera, Jerez-Lillo, Nixon, Ramos, Pedro Luiz
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2025
Subjects
Mathematics and Statistics
Original Article
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Statistics
Beta-Gompertz Distribution
Gompertz Distribution
Beta Distribution
Regression Model
Survival Analysis
Defective Distribution
Cure Fraction
Online AccessGet full text
ISSN1559-8608
1559-8616
DOI10.1007/s42519-025-00434-6

Cover

More Information
Summary:This paper introduces a novel approach to cure fraction modeling, also known as long-term survival modeling, by focusing on scenarios where a portion of observations is not susceptible to the event of interest. We propose a new defective distribution model based on the Beta distribution, specifically utilizing the defective Gompertz distribution as a foundation, while accounting for censored data and covariates. We demonstrate that the resulting Beta-Gompertz distribution also exhibits defective characteristics, making it particularly suitable for modeling data with cure fractions. To perform inference on the parameters, maximum likelihood estimation is employed, and its asymptotic properties are examined through simulation studies. The proposed methodology is illustrated using a real-world dataset related to the survival time of patients with triple-negative breast cancer from the A.C. Camargo Cancer Center Hospital, located in São Paulo, Brazil.
ISSN:1559-8608
1559-8616
DOI:10.1007/s42519-025-00434-6