Negative Binomial Kumaraswamy-G Cure Rate Regression Model

Abstract

Abstract:In survival analysis, the presence of elements not susceptible to the event of interest is very common. These elements lead to what is called a fraction cure, cure rate, or even long-term survivors. In this paper, we propose a unified approach using the negative binomial distribution for modeling cure rates under the Kumaraswamy family of distributions. The estimation is made by maximum likelihood. We checked the maximum likelihood asymptotic properties through some simulation setups. Furthermore, we propose an estimation strategy based on the Negative Binomial Kumaraswamy-G generalized linear model. Finally, we illustrate the distributions proposed using a real data set related to health risk.

A Modified Cure Rate Model Based on a Piecewise Distribution with Application to Lobular Carcinoma Data

“…The pioneer model in this context was proposed by Berkson and Gage [2], which assumed the Bernoulli distribution for M. Almost fifty years later, in a cancer context, the causes were represented by carcinogenic cells and modeled according to the Poisson distribution by Chen et al [3]. Other important models in this context consider this approach, modifying the discrete distribution, including the negative binomial (NB) [4][5][6][7][8][9], zero-modified geometric [10], power series family [11], Conway-Maxwell-Poisson [12], weighted Poisson [13], modified power series (MPS) [14].…”

On a reparameterization of a flexible family of cure models

“…To model the heterogeneity among individuals, under the competing cause scenario of the BCH model, it can be assumed 55 that $$$ M $$$ follows a Poisson distribution with parameter $$$ Z\theta $$$, where $$$ Z $$$ is a non‐negative random variable (some other works are also of similar nature 56 ). As a consequence, considering a gamma distribution for $$$ Z $$$ with expected value equal to one, the next model has resulted $$$$ {S}_P(t)={\left(1+\gamma \theta F(t)\right)}^{-1/\gamma },\kern1em \theta >0,\kern0.3em \gamma \ge 0.\kern0.5em $$$$ Model () could also be derived by assuming that the number of competing causes, $$$ M $$$, follows a negative binomial distribution, with parameters $$$ 1/\gamma $$$ and $$$ \theta \gamma /\left(\theta \gamma +1\right) $$$ 57‐67 . Note also that a generalized negative binomial distribution for modeling the number of competing causes was also used 68,69 …”

A generalized Gompertz promotion time cure model and its fitness to cancer data

“…The readers are referred to Refs. [ [11] , [12] , [13] , [14] , [15] , [16] , [17] ] for other extensions of the cure models, the corresponding baseline distributions, and the estimation methods. Recent advances in the developments and applications of the cure rate models can be seen in Refs.…”