@article{Barahona2026, 
author = {Manuel J. P. Barahona and Yolanda M. Gómez and Diego I. Gallardo},
title = {A Bayesian cure rate model using the Bell–Touchard distribution and Hamiltonian Monte Carlo methods},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {8792-8811},
keywords = {Bell-Touchard distribution, long-term survival model, Hamiltonian Monte Carlo, reparameterization},
url = {https://www.sciopen.com/article/10.3934/math.2026361},
doi = {10.3934/math.2026361},
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.}
}