A comparative study of mixture cure model

Abstract

In survival analysis, there are two types of model, parametric and nonparametric. For parametric models the survival data is described by a known non negative distribution. Exponential, weibull, log-normal and log-logistic distributions are the popular distributions used in survival analysis. Most of the time, distributions with two parameters are used as it allowed for more flexibility than one parameter distribution. There are cases where a fraction of individual who are not at risk in the event of interest. This fraction of individual is known as cure fraction. Survival models that take into account the existing of a cure fraction are called as cure model. Cure model separates the target population into two subgroups, long-term and short-term survivor. The survival time of the short-term survivor is described by a proper survival function, such as exponential, weibull, and log-normal survival functions. Weibull cure model is the most popular cure model used in survival analysis However, in some cases weibull distribution is not able to describe the survival data well. As an alternative distribution with two parameters Log-normal cure model is discussed in this study. Weibull cure model and log-normal cure models are compared in term of consistency. Survival data with different sample sizes and cure fractions are simulated. These data are then analyzed using the two cure models.