On a new piecewise regression model with cure rate: Diagnostics and application to medical data

Abstract

In this article, we discuss an extension of the classical negative binomial cure rate model with piecewise exponential distribution of the time to event for concurrent causes, which enables the modeling of monotonic and non-monotonic hazard functions (ie, the shape of the hazard function is not assumed as in traditional parametric models). This approach produces a flexible cure rate model, depending on the choice of time partition. We discuss local influence on this negative binomial power piecewise exponential model. We report on Monte Carlo simulation studies and application of the model to real melanoma and leukemia datasets.

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

“…52 Furthermore, it has a continuous survival function, very desirable in inference-making. 38 Because of its flexibility it has been widely extended to incorporate several features, as we can see, for example, in Gamerman, 53 Huang et al, 54 Thiébaut et al, 55 Demarqui et al, 56 Han et al, 57 Gómez et al, 58 just to cite a few.…”

On a reparameterization of a flexible family of cure models

“…Model (4) could also be derived by assuming that the number of competing causes, M, follows a negative binomial distribution, with parameters 1∕𝛾 and 𝜃𝛾∕(𝜃𝛾 + 1). [57][58][59][60][61][62][63][64][65][66][67] Note also that a generalized negative binomial distribution for modeling the number of competing causes was also used. 68,69 Applying the Box-Cox transformation on the population survival function 70 we result in the next model (a similar approach, using the Box-Cox transformation, was also adopted in other works 71 )…”

“…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 two‐way flexible generalized gamma transformation cure rate model

“…13 Gómez et al extended the parametric negative binomial cure model by proposing a piecewise exponential approximation to the progression time of each competing risk. 14 Recently, researchers have developed alternate estimation algorithms for cure models and demonstrated the advantages of these newly proposed algorithms. [15][16][17] In this article, we propose a new two-way flexible cure rate model.…”

“…Leão et al proposed a new cure model with flexible zero‐modified geometric distribution to model the number of competing risks 13 . Gómez et al extended the parametric negative binomial cure model by proposing a piecewise exponential approximation to the progression time of each competing risk 14 . Recently, researchers have developed alternate estimation algorithms for cure models and demonstrated the advantages of these newly proposed algorithms 15‐17 …”