Logistic-AFT Location-Scale Cure Models for the Relative Survival with an Application to HCV Mono-Infected Patients

Abstract

In population-based studies, relative survival is the ratio of the observed survival from a diseased group of individuals to the expected survival from a comparable group in the general population, and it provides a measure of the excess mortality rate of the disease under study based on the estimation of the observed mortality of the diseased group in comparison with the background mortality of the general population. Due to enhancement of medical diagnostic technology, patients may be diagnosed early and treated adequately with a better management of medical conditions, and then results in a cured fraction of the patients. In this case, cure occurs when the observed age-specific mortality of the diseased group returns to the same level as the background age-specific mortality of the general population. Equivalently, the relative survival tails off to a plateau such as the excess mortality rate approaches zero after some time point. It motivates us to extend the logistic-AFT location-scale mixture regression models (Chen et al., 2013) to estimate the relative survival with cure attributable to a disease for left truncated and interval censored data. Simulation studies were conducted to demonstrate the validity of the proposed estimation procedure. The method is applied to analyze the mortality of HCV infection patients in the Taiwan National Health Insurance Research Database as an illustration.