Variable selection techniques for the Cox proportional hazardsmodel: A comparative study

In statistics different models are used to emulate real world processes. Variable selection refers to reduction of the number of parameters in the models in order to increase interpretability and model effectiveness. This thesis investigates performance of different variable selection methods for Cox proportional hazards models such as; all subset selection, backward elimination, best subset selections and least absolute shrinkage and selection operator. Data is simulated for 5 different models with coefficients reflecting large, moderate and small effects, with different sized data sets and simulations. The result are also partly compared to earlier reported results from \citet{Tibshirani1997, Fan2002, Zhang2007}. Our findings indicate that the best subset selection methods is faster than all subset selection but slower than least absolute shrinkage and selection operator. On the other hand best subset selection provide more accurate results than least absolute shrinkage and selection operator. We have been unable to verify all of the results reported by \citet{Tibshirani1997, Fan2002} and \citet{Zhang2007} probably because difference in the least absolute shrinkage and selection operator's tuning parameter