The Cox Model And Its Applications PDF Download

"Variable selection plays an important role in statistical modeling and prediction. It can discriminate between variables that are critical to predicting the outcome and the noise variables which are irrelevant or redundant for the purpose. Thus the "best" subset of variables can be identified for prediction. In addition, in a high-dimensional setting where the sample size is less than the number of covariates, variable selection can circumvent the identifiability issue by removing noise variables, and construct a valid predictive model. In practice, researchers often have knowledge of the relationships among covariates. For instance, an interaction is obtained from the product of two or more other variables (main terms). Taking such relationships into account in the implementation of variable selection can help to identify the relevant variable subsets and thus improve the prediction accuracy. My doctoral thesis establishes a general framework for incorporating these known relationships into variable selection, broadening its utility in applications and extending it to more types of data.In the first manuscript, I propose a novel framework by first introducing the mathematical language of expressing selection rules (dependencies among the selection of variables). Then, I show that the resulting combination of permissible sets of selected variables ("selection dictionary") can be derived. I also bridge the proposed framework to existing penalized regression by offering a condition that relates to the selection dictionary: a postulated grouping structure (i.e., how to group variables in penalized regression) respecting the imposed selection rule.The second manuscript involves an application of the theory and methods developed in the first one. The aim is to identify predictors of major bleeding among hospitalized hypertensive patients using oral anticoagulants for atrial fibrillation, where adherence and drug-drug interactions are considered. I illustrate how to use the framework in practice and provide a roadmap of how to identify the grouping structure to respect some common selection rules.In the third manuscript, I focus on a versatile (in terms of respecting selection rules) penalized regression, the overlapping group Lasso, and extend it to be used in the Cox model with time-dependent covariates. Technical details are presented in a more straightforward way to reach a broader audience. Simulation studies show that the proposed method is able to handle complex selection rules with the use of the framework. Furthermore, it can better identify the variables whose coefficients are non-zero, and is associated with a lower mean squared error as compared to the non-structured variable selection method.In summary, the proposed framework highlights the importance of incorporating a priori knowledge of relationships among covariates into variable selection, advances the development of variable selection, and extends the use of existing methods"--