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A Contribution to Variable Selection for the Cox Proportional Hazards Model with High-Dimensional Predictors
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The aim of this thesis is to develop a variable selection framework with the spike-and-slab prior distribution via the hazard function of the Cox model. Specifically, we consider the transformation of the score and information functions for the partial likelihood function evaluated at the given data from the parameter space into thespace generated by the logarithm of the hazard ratio. Thereby, we reduce the nonlinear complexity of the estimation equation for the Cox model and allow the utilization of a wider variety of stable variable selection methods. Then, we use a stochastic variable search Gibbs sampling approach via the spike-and-slab prior distribution to obtain the sparsity structure of the covariates associated with the survival outcome. To demonstrate the efficiency and accuracy of the proposed method in both low-dimensional and high-dimensional settings, we conduct numerical simulations to evaluate the finite-sample performance of the proposed method. Finally, we apply this novel framework within biological contexts on real world data sets such as primary biliary cirrhosis and lung adenocarcinoma data to find important variables associated with decreased survival in subjects with the aforementioned diseases