The Long Term Fr\'echet distribution: Estimation, Properties and its Application

TL;DR

This paper introduces the long-term Fréchet distribution for modeling data with a cured or non-susceptible subpopulation, detailing its properties, estimation methods, and application to leukemia survival data.

Contribution

It proposes a new long-term survival distribution, analyzes its mathematical properties, derives maximum likelihood estimators, and demonstrates its application in clinical survival analysis.

Findings

Distribution fits leukemia-free survival data well

MLEs perform reliably in simulations

Mathematical properties support practical use

Abstract

In this paper a new long-term survival distribution is proposed. The so called long term Fr\'echet distribution allows us to fit data where a part of the population is not susceptible to the event of interest. This model may be used, for example, in clinical studies where a portion of the population can be cured during a treatment. It is shown an account of mathematical properties of the new distribution such as its moments and survival properties. As well is presented the maximum likelihood estimators (MLEs) for the parameters. A numerical simulation is carried out in order to verify the performance of the MLEs. Finally, an important application related to the leukemia free-survival times for transplant patients are discussed to illustrates our proposed distribution