Kidney cancer, a potentially life-threatening malignancy affecting the kidneys, demands early detection and proactive intervention to enhance prognosis and survival. Advancements in medical and health sciences and the emergence of novel treatments are expected to lead to a favorable response in a subset of patients. This, in turn, is anticipated to enhance overall survival and disease-free survival rates. Cure fraction models have become essential for estimating the proportion of individuals considered cured, free from adverse events. This article presents a novel piecewise power-law cure fraction model with a piecewise decreasing hazard function, deviating from the traditional piecewise constant hazard assumption. Through the analysis of real medical data, we evaluate various factors to explain the survival of individuals. Consistently positive outcomes are observed, affirming the significant potential of our approach. Furthermore, we employ a local influence analysis to detect potentially influential individuals and perform a post-deletion analysis to analyze their impact on our inferences.

We introduce two new approaches to clustering categorical and mixed data: Condorcet clustering with a fixed number of groups, denoted $$\alpha$$-Condorcet and Mixed-Condorcet respectively. As k-modes, this approach is essentially based on similarity and dissimilarity measures. The presentation is divided into three parts: first, we propose a new Condorcet criterion, with a fixed number of groups (to select cases into clusters). In the second part, we propose a heuristic algorithm to carry out the task. In the third part, we compare $$\alpha$$ -Condorcet clustering with k-modes clustering and Mixed-Condorcet with k-prototypes. The comparison is made with a quality’s index, accuracy of a measurement, and a within-cluster sum-of-squares index.

Our findings are illustrated using real datasets: the feline dataset, the US Census 1990 dataset and other data.

Generating censored random samples while controlling the desired percentage of censorship is a critical task when assessing the performance of our model in corresponding simulation studies. In this presentation, we will explore an approach to aboard this challenge, particularly when dealing with random censorship. This method is implemented in the recently available 'rcens' package on CRAN, which also offers functionalities to control the censorship percentage in generated samples with different types of censorship (Types I, II, and III), providing researchers and professionals with a straightforward tool to simulate datasets according to desired distributional needs. Lastly, we will discuss a potential scheme for generating interval censorship also implemented in 'rcens'.