Log-symmetric models with cure fraction with application to leprosy reactions data

Abstract

In this paper, we propose a log-symmetric survival model with cure fraction, considering that the distributions of lifetimes for susceptible individuals belong to the log-symmetric class of distributions. This class has continuous, strictly positive, and asymmetric distributions, including the log-normal, log-Student-t, Birnbaum–Saunders, log-logistic I, log-logistic II, contaminated log-normal, log-power-exponential, and log-slash distributions. The log-symmetric class is quite flexible and allows for including bimodal distributions and outliers. It has two parameters interpreted directly as location and scale, where the location is the median, which is a robust measure in the presence of outliers and quite informative in survival analysis. The proposed model includes explanatory variables through the parameter associated with the cure fraction. We evaluate the performance of such model through extensive simulation studies and consider a real data application to evaluate the effect of factors on the immunity to leprosy reactions in patients with Hansen’s disease.