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

TL;DR

This paper introduces a flexible log-symmetric survival model with cure fraction, capable of handling asymmetric, bimodal, and outlier-prone data, applied to leprosy reaction analysis.

Contribution

It develops a novel survival model incorporating log-symmetric distributions with cure fraction, including multiple distribution types and covariates, with validation through simulations and real data.

Findings

Model effectively captures complex lifetime distributions.

Simulation studies demonstrate robust performance.

Application reveals factors influencing leprosy reactions.

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-$t$-Student, Birnbaum-Saunders, log-logistic I, log-logistic II, log-normal-contaminated, log-exponential-power, and log-slash distributions. The log-symmetric class is quite flexible and allows for including bimodal distributions and outliers. This includes explanatory variables through the parameter associated with the cure fraction. We evaluate the performance of the proposed 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.