VARIABLE SELECTION IN PROPORTIONAL HAZARDS MODEL:DETERMINING TUNING VARIABLE BY AUC
Hazard rate or failure rate is a basic quantity used in engineering reliability theory, biomedical research and many other scientific disciplines. The failure rate of a system at any time t depends on many parameters, or covariates, Z1,…,Zk. Advances in computing technology has led to a deluge of data. The number (k) of recorded covariates can be very large as in tens of thousands; some of these are truly covariates of the failure time, while others are superfluous. Very large k makes it difficult if not impossible to assess the significance of each covariate in the reliability analysis. A question arises as to how to extract pertinent information from the data and discard those superfluous covariables? In recent years, a variety of statistical methods have been developed that can be used for variable selection. One such method is presented in this paper. A stochastic model that takes into consideration the covariates is the proportional hazards model or the Cox regression model. This model is widely used in biostatistics for studying patient survival probability. In engineering, it can be applied to studying the reliability of a system. Tibshirani, who introduced the lasso method in 1966, applied the lasso in this model to determine how many and which covariates are needed for making accurate estimate of the reliability. Implementation of the lasso requires the determination of a tuning variable for which generalized cross-validation (GCV) criterion is commonly employed. Another criterion, investigated by Wang (2009), makes use of the area under the operating characteristic curve (AUC). Simulations show that the AUC and GCV criteria are comparable. But the AUC criterion gives a better interpretation of the failure data. A data set of patients with squamous cell cancer in the head and neck region is used for illustration.
Wen-Chyi Wang Grace Yang
Ventiv Clinical Solutions,224 Schilling Circle,Hunt Valley,MD 21031 USA Corresponding author,Department of Mathematics,University of Maryland,College Park,Maryland 20742 US
国际会议
厦门
英文
189-194
2011-10-28（万方平台首次上网日期，不代表论文的发表时间）