A Modified Cure Rate Model Based on a Piecewise Distribution with Application to Lobular Carcinoma Data

Yolanda M. Gómez (), John L. Santibañez, Vinicius F. Calsavara, Héctor W. Gómez and Diego I. Gallardo
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Yolanda M. Gómez: Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
John L. Santibañez: Departamento de Matemática, Universidad de Atacama, Copiapó 7500015, Chile
Vinicius F. Calsavara: Cedars-Sinai Medical Center, 8700 Beverly Boulevard, Los Angeles, CA 90048, USA
Héctor W. Gómez: Departamento de Estadística y Ciencia de Datos, Universidad de Antofagasta, Antofagasta 1240000, Chile
Diego I. Gallardo: Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile

Mathematics, 2024, vol. 12, issue 6, 1-14

Abstract: A novel cure rate model is introduced by considering, for the number of concurrent causes, the modified power series distribution and, for the time to event, the recently proposed power piecewise exponential distribution. This model includes a wide variety of cure rate models, such as binomial, Poisson, negative binomial, Haight, Borel, logarithmic, and restricted generalized Poisson. Some characteristics of the model are examined, and the estimation of parameters is performed using the Expectation–Maximization algorithm. A simulation study is presented to evaluate the performance of the estimators in finite samples. Finally, an application in a real medical dataset from a population-based study of incident cases of lobular carcinoma diagnosed in the state of São Paulo, Brazil, illustrates the advantages of the proposed model compared to other common cure rate models in the literature, particularly regarding the underestimation of the cure rate in other proposals and the improved precision in estimating the cure rate of our proposal.

Keywords: power piecewise exponential distribution; cure rate model; Expectation–Maximization algorithm; survival analysis; cancer dataset (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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