  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.
