Variable selection and shrinkage in the Cox proportional hazards model

Abstract

In this thesis, shrinkage and variable selection is used on one of the most famous models in survival analysis, the Cox proportional hazards model.
First, the Cox proportional hazards model is statistically observed, by deriving the so called partial likelihood. This likelihood type of function is used for maximum likelihood estimation of the model instead of using the normal likelihood function. The partial likelihood function is preferred over the normal likelihood function due to the appearance of the baseline hazard rate function in the normal likelihood function.
In the medical application, there are often so many explanatory variables involved, that the model becomes difficult to interpret and might become overparameterized. To prevent this, a model for variable selection and shrinkage, called the Least Absolute Shrinkage and Selection Operaor (LASSO) is used. For applying this method to the Cox proportional hazards model, several algorithms are used which can deal with the lack of differentiability of the LASSO method.
As a simulation study, this method is used on a dataset of breastcancer patients with 5 standard clinical and histological variables and 70 DNA based variables. The method of LASSO is used to see what variables have the biggest influence on the survival time of those patients.