Survival Curve for Cancer Patients Following Treatment

Fertility progression in Germany: An analysis using flexible nonparametric cure survival models

“…Two main families of models can be distinguished: the mixture and the non-mixture (also referred to as the promotion time model) cure models. The mixture cure model, first introduced by Berkson and Gage (1952) and extensively studied in the statistical literature afterward (see Peng and Dear 2000;Peng 2003;Lu 2010 among others), defines the population survival function as a mixture of contributions due to the susceptible and the non-susceptible sub-populations:…”

The generalized log-gamma mixture model with covariates: local influence and residual analysis

“…Cure rate models have been used for modeling time-to-event data for various types of cancers, including breast cancer, non-Hodgkins lymphoma, leukemia, prostate cancer and melanoma. Perhaps the most popular type of cure rate models is the mixture model introduced by Berkson and Gage (1952) and Maller and Zhou (1996). In this model, the population is divided into two subpopulations so that an individual either is cured with probability π , or has a proper survival function S(t), with probability 1 − π.…”

Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data

“…Boag (1949) developed the first cure rate model by introducing a component representing the proportion of cured patients in the population and a distribution representing the lifetime of the susceptibles, which in the literature is known as the mixture cure rate model. Three years later, this was modified by Berkson and Gage (1952). Farewell (1982) considered the mixture model and used a logistic regression for the mixture proportion and a Weibull regression for the latency.…”

“…The books by Maller and Zhou (1996) and Ibrahim et al (2001) serve as excellent references on cure rate models. More recently, Rodrigues (2009) developed a flexible family of cure rate models, in terms of dispersion, by unifying the long-term survival models proposed by Boag (1949), Berkson and Gage (1952) and Chen et al (1999). Rodrigues et al (2011) extended the proposal of Yakovlev and Tsodikov (1996) through a special case of the compound (destructive) weighted Poisson distribution.…”