The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation
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 o...
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| Format: | Article |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/3/518 |
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| author | Diego I. Gallardo Yolanda M. Gómez Héctor J. Gómez María José Gallardo-Nelson Marcelo Bourguignon |
| author_facet | Diego I. Gallardo Yolanda M. Gómez Héctor J. Gómez María José Gallardo-Nelson Marcelo Bourguignon |
| author_sort | Diego I. Gallardo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T09:35:37Z |
| format | Article |
| id | doaj.art-742fc7de393742ff8992df5f3a1f0b24 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:35:37Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-742fc7de393742ff8992df5f3a1f0b242023-11-16T17:20:44ZengMDPI AGMathematics2227-73902023-01-0111351810.3390/math11030518The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow TransplantationDiego I. Gallardo0Yolanda M. Gómez1Héctor J. Gómez2María José Gallardo-Nelson3Marcelo Bourguignon4Mathematics Department, Faculty of Engineering, University of Atacama, Copiapó 1530000, ChileMathematics Department, Faculty of Engineering, University of Atacama, Copiapó 1530000, ChileDepartment of Mathematical and Physical Sciences, Faculty of Engineering, Catholic University of Temuco, Temuco 4780000, ChileMedicine Department, Faculty of Medicine, University of Atacama, Copiapó 1530000, ChileStatistics Department, Federal University of Rio Grande do Norte, Natal 59078-970, BrazilThis 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.https://www.mdpi.com/2227-7390/11/3/518half-normal distributionkurtosispower seriesblood and marrow transplantation |
| spellingShingle | Diego I. Gallardo Yolanda M. Gómez Héctor J. Gómez María José Gallardo-Nelson Marcelo Bourguignon The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation Mathematics half-normal distribution kurtosis power series blood and marrow transplantation |
| title | The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation |
| title_full | The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation |
| title_fullStr | The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation |
| title_full_unstemmed | The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation |
| title_short | The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation |
| title_sort | slash half normal distribution applied to a cure rate model with application to bone marrow transplantation |
| topic | half-normal distribution kurtosis power series blood and marrow transplantation |
| url | https://www.mdpi.com/2227-7390/11/3/518 |
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