Mixture and non-mixture cure models with GeTNH distribution for the application to cancer data

Mixture and non-mixture cure rate models are usually used to analyze lifetime data in medical studies and clinical trials. In this article, based on generalized truncated Nadarajah-Haghighi distribution (GeTNH) for the lifetime data, we introduce mixture and non-mixture cure rate models. Estimations of parameters of the proposed model are derived based on mixture and non-mixture cure rate models, right-censored data, and covariates using the maximum likelihood estimation (MLE) and Bayesian estimation methods. We also apply importance sampling to carry out Bayesian estimation procedures. We discuss two applications using oropharynx and melanoma cancer data to assess the usefulness and flexibility of the proposed model.