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.

Crohn's disease is a chronic inflammatory disease that manifests itself mainly in the intestinal region, if left untreated, the disease can progress to more serious conditions such as surgery to remove all or part of the colon or intestine. As it is a chronic disease, studying the risk factors that can worsen the patient's clinical condition can help improve the quality of people who have received such diagnoses and need to live with Crohn's for the rest of their lives. Survival models are commonly used to find an association between information on patients' lifestyle and health habits and the progression of these diseases. However, conventional survival models presuppose that, for sufficiently long times, all individuals will have suffered the event of interest, otherwise they will be censored. In addition, these models do not fit individuals with zero survival times. Thus, patients who have surgery on the same day they receive the diagnosis or patients who will never undergo surgery are not considered in these models. In case studies with patients diagnosed with Crohn's, both characteristics may be present and, for this reason, it is necessary to use a model that fits zero inflation and long-term data. This dissertation proposes a survival model called the Long Term Zero Inflated Weibull model or W-ZICR, which can correctly estimate the proportions of cured individuals and the proportions of individuals with times equal to zero. The model was applied to assess the risk and survival of patients diagnosed with Crohn's disease who were followed up at the Hospital das Clínicas in Ribeirão Preto. In general, it was concluded that patients who used steroids, smokers, patients with B2 or B3 Montreal B-category and patients with L3 or L4 Montreal L-category have a lower survival rate and a higher risk of undergoing surgery when compared to the others. In addition, the proposed model adjusted well to zero-inflated data and proved to be an excellent tool for studying patients diagnosed with Crohn's disease.

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