## CURE RATE MODELS – A PARTIAL REVIEW WITH AN APPLICATION TO RECURRENT EVENT OR COUNT DATA

### by Sumathi K and Aruna Rao K.

**Abstract:**
Cure rate models are survival models consisting of a cured fraction and an uncured fraction. These models are being widely used in analyzing data from cancer clinical trials. A model to estimate the cure fraction was first developed by Boag in 1949 and later developed by Berkson and Gage in 1952 . It was called the mixture model. It is also known as the standard cure rate model. Yakovlev et.al. in 1993 developed an alternative to the mixture model. This model is known as the bounded cumulative hazard (BCH) model. It was developed by considering the number of metastasis competent tumor cells which were left active even after the initial treatment for a cancer patient. The model could overcome some of the drawbacks of the standard cure rate model. Parametric and semi-parametric versions of the two models have been extensively studied. The bivariate extension of the univariate cure rate models include the joint modeling of times to relapse of the disease at two different organs, times to relapse of disease and death, times to occurrence of primary and secondary complications of a disease and joint modeling of time-to-event data and longitudinal data. These extensions involve the use of copulas and frailties. Although some results and applications have been reported, there is a necessity of further work some of which are identified. A cure rate model for count data is proposed and its application has been illustrated in estimating the proportion of people who do not have any dental problems at a given point of time.
**Key Words: **
cure rate models, mixture model, bounded cumulative hazard (BCH) model, copulas, count data

**Authors:**

Sumathi K, chaitra_udipi@yahoo.com

Aruna Rao K, arunaraomu@yahoo.com

**Editor:**
Ke Weiming, Weiming.Ke@sdstate.edu

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