A Bayesian cure rate model using the Bell–Touchard distribution and Hamiltonian Monte Carlo methods

Manuel J. P. Barahona; Yolanda M. Gómez; Diego I. Gallardo; Manuel J. P. Barahona; Yolanda M. Gómez; Diego I. Gallardo

doi:10.3934/math.2026361

AIMS Mathematics

2026, Volume 11, Issue 3: 8792-8811. doi: 10.3934/math.2026361

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A Bayesian cure rate model using the Bell–Touchard distribution and Hamiltonian Monte Carlo methods

Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción, Chile

Received: 21 October 2025 Revised: 23 December 2025 Accepted: 06 January 2026 Published: 31 March 2026
MSC : 62F15, 62N01, 62N02, 62P10, 65C05

We proposed a novel cure rate model in which the number of competing causes follows a Bell–Touchard distribution. We derived its main mathematical properties and implemented Bayesian inference using the Hamiltonian Monte Carlo algorithm. A simulation study was conducted to assess the finite-sample performance of the estimators. The model's applicability was demonstrated using two real datasets: patients with melanoma and patients with cardiovascular disease. In the latter dataset, diabetic patients exhibited higher estimated cure and survival probabilities than non-diabetic individuals, potentially reflecting phenomena such as "reverse epidemiology" or intensified clinical management.
- Bell-Touchard distribution,
- long-term survival model,
- Hamiltonian Monte Carlo,
- reparameterization
Citation: Manuel J. P. Barahona, Yolanda M. Gómez, Diego I. Gallardo. A Bayesian cure rate model using the Bell–Touchard distribution and Hamiltonian Monte Carlo methods[J]. AIMS Mathematics, 2026, 11(3): 8792-8811. doi: 10.3934/math.2026361

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Abstract

We proposed a novel cure rate model in which the number of competing causes follows a Bell–Touchard distribution. We derived its main mathematical properties and implemented Bayesian inference using the Hamiltonian Monte Carlo algorithm. A simulation study was conducted to assess the finite-sample performance of the estimators. The model's applicability was demonstrated using two real datasets: patients with melanoma and patients with cardiovascular disease. In the latter dataset, diabetic patients exhibited higher estimated cure and survival probabilities than non-diabetic individuals, potentially reflecting phenomena such as "reverse epidemiology" or intensified clinical management.

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