A new cure rate model with flexible competing causes with applications to melanoma and transplantation data

Abstract

In this article, we introduce a long-term survival model in which the number of competing causes of the event of interest follows the zero-modified geometric (ZMG) distribution. Such distribution accommodates equidispersion, underdispersion, and overdispersion and captures deflation or inflation of zeros in the number of lesions or initiated cells after the treatment. The ZMG distribution is also an appropriate alternative for modeling clustered samples when the number of competing causes of the event of interest consists of two subpopulations, one containing only zeros (cure proportion), while in the other (noncure proportion) the number of competing causes of the event of interest follows a geometric distribution. The advantage of this assumption is that we can measure the cure proportion in the initiated cells. Furthermore, the proposed model can yield greater or lower cure proportion than that of the geometric distribution when modeling the number of competing causes. In this article, we present some statistical properties of the proposed model and use the maximum likelihood method to estimate the model parameters. We also conduct a Monte Carlo simulation study to evaluate the performance of the estimators. We present and discuss two applications using real-world medical data to assess the practical usefulness of the proposed model.

Discrete Bilal distribution with right-censored data

“…Moreover, the model can be easily implemented in computational programs as R, as showed in the Appendix. Currently, we find many examples of application of cure rate models to medical data (Gallardo et al, 2021;Leão, 2020;Rafati et al, 2020), which makes these models attractive to be assumed in lifetime data analysis. The methods introduced in this paper could be very helpful to researchers dealing with discrete survival data.…”

A two‐way flexible generalized gamma transformation cure rate model

“…where f (⋅) is the density function corresponding to F(⋅). We now turn our attention to flexible modeling of f (⋅) or, equivalently, F(⋅) = 1 − S(⋅) in Equations ( 9) and (13). For this purpose, we consider a fully parametric setup and assume f (⋅) in Equation ( 13) to follow a wider class of generalized gamma distribution with the density and survival functions respectively given by…”

“…12 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.…”

“…Balakrishnan et al proposed a piecewise linear approximation to model the hazard functions of competing risks in the context of mixture and promotion time cure rate models 12 . 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 .…”

Bivariate distributions based on copulas functions: developments and applications in medical studies

“…Other approaches to model data with cure rate can be found in Peng et al (1998) Rodrigues et al (2009, Rodrigues et al (2011), Gallardo et al (2018, Pescim et al (2019), Amico et al (2019) and Leão et al (2020).…”