생존분석모형에서 변수선택 및 응용

Abstract

Determining relevant variables for a regression model is very important in regression analysis. In ordinary regression models, there are a variety of classical techniques for variable selection such as forward selection, backward elimination and stepwise selection. However, these classical methods can be computationally intensive for a large number of covariates and often suffer from high variability. Recently, variable selection methods using a penalized likelihood with various penalty functions (e.g. LASSO, SCAD) have been widely studied in simple statistical models such as linear models and generalized linear models. The main advantage of these methods is that they select important variables and estimate the regression coefficients, simultaneously. Thus, they delete insignificant variables by estimating their coefficients as zero. In this thesis we study how to select proper variables based on the penalized hierarchical likelihood (HL) in survival-hazards models including Cox's proportional hazards models and semi-parametric frailty models. For this purpose we allows three penality functions, LASSO, SCAD and HL. The computations are based on the R packages including “frailtyHL”. Our methods are illustrated with clinical-trial data sets from Korea and Europe. We compare the results from three variable-selection methods, and also discuss their advantages and disadvantages.

key words : Frailty models, H-likelihood, LASSO, SCAD, Variable selection