Long-Term Dagum-PVF Frailty Regression Model: Application in Health Studies

Survival models incorporating cure fractions, commonly known as cure fraction models or long-term survival models, are widely employed in epidemiological studies to account for both immune and susceptible patients in relation to the failure event of interest under investigation. In such studies, there is also a need to estimate the unobservable heterogeneity caused by prognostic factors that cannot be observed. Moreover, the hazard function may exhibit a non-monotonic form, specifically, an unimodal hazard function. In this article, we propose a long-term survival model based on the defective version of the Dagum distribution, with a power variance function (PVF) frailty term introduced in the hazard function to control for unobservable heterogeneity in patient populations, which is useful for accommodating survival data in the presence of a cure fraction and with a non-monotone hazard function. The distribution is conveniently reparameterized in terms of the cure fraction, and then associated with the covariates via a logit link function, enabling direct interpretation of the covariate effects on the cure fraction, which is not usual in the defective approach. It is also proven a result that generates defective models induced by PVF frailty distribution. We discuss maximum likelihood estimation for model parameters and evaluate its performance through Monte Carlo simulation studies. Finally, the practicality and benefits of our model are demonstrated through two health-related datasets, focusing on severe cases of COVID-19 in pregnant and postpartum women and on patients with malignant skin neoplasms.