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Cure fraction is not an easy task to be calculated relating probabilistic estimations to an event. For instance, cancer patients may abandon treatment, be cured, or die due to another illness, causing limitations regarding the information about the odds of cancer cure (related to the patient follow-up) and may mislead the researcher’s inference. In this paper, we overcame this limitation and proposed a risk assessment tool related to the lifetime of cancer patients to survival functions to help medical decision-making. Moreover, we proposed a new machine learning algorithm, so-called long-term generalized weighted Lindley (LGWL) distribution, solving the inferential limitation caused by the censored information. Regarding the robustness of this distribution, some mathematical properties are shown and inferential procedures discussed, under the maximum likelihood estimators’ perspective. Empirical results used TCGA lung cancer data (but not limited to this cancer type) showing the competitiveness of the proposed distribution to the medical field. The cure-rate is dynamic but quantifiable. For instance, after 14 years of development/spread of lung cancer, the group of patients under the age of 70 had a cure fraction of 32%, while the group of elderly patients presented a cure fraction of 22%, whereas those estimations using the traditional (long-term) Weibull distribution is 31% and 17%. The LGWL returned closer curves to the empirical distribution, then were better adjusted to the adopted data, elucidating the importance of cure-rate fraction in survival models. |
