The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation

Diego I. Gallardo (), Yolanda M. Gómez, Héctor J. Gómez, María José Gallardo-Nelson and Marcelo Bourguignon
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Diego I. Gallardo: Mathematics Department, Faculty of Engineering, University of Atacama, Copiapó 1530000, Chile
Yolanda M. Gómez: Mathematics Department, Faculty of Engineering, University of Atacama, Copiapó 1530000, Chile
Héctor J. Gómez: Department of Mathematical and Physical Sciences, Faculty of Engineering, Catholic University of Temuco, Temuco 4780000, Chile
María José Gallardo-Nelson: Medicine Department, Faculty of Medicine, University of Atacama, Copiapó 1530000, Chile
Marcelo Bourguignon: Statistics Department, Federal University of Rio Grande do Norte, Natal 59078-970, Brazil

Mathematics, 2023, vol. 11, issue 3, 1-16

Abstract: This paper proposes, for the first time, the use of an asymmetric positive and heavy-tailed distribution in a cure rate model context. In particular, it introduces a cure-rate survival model by assuming that the time-to-event of interest follows a slash half-normal distribution and that the number of competing causes of the event of interest follows a power series distribution, which defines six new cure rate models. Several properties of the model are derived and an alternative expression for the cumulative distribution function of the model is presented, which is very useful for the computational implementation of the model. A procedure based on the expectation–maximization algorithm is proposed for the parameter estimation. Two simulation studies are performed to assess some properties of the estimators, showing the good performance of the proposed estimators in finite samples. Finally, an application to a bone marrow transplant data set is presented.

Keywords: half-normal distribution; kurtosis; power series; blood and marrow transplantation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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