Statistical inference for Cox proportional hazards models with a diverging number of covariates
针对协变量数量随样本量增加而发散的Cox比例风险模型，提出一种修正的去偏lasso方法，无需稀疏矩阵假设即可进行一致估计和置信区间推断，并在肺癌生存数据中验证了其有效性。
For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often violated under Cox proportion hazards models, leading to biased estimates with under-coverage confidence intervals. We propose a modified debiased lasso method, which solves a series of quadratic programming problems to approximate the inverse information matrix without posing sparse matrix assumptions. We establish asymptotic results for the estimated regression coefficients when the dimension of covariates diverges with the sample size. As demonstrated by extensive simulations, our proposed method provides consistent estimates and confidence intervals with nominal coverage probabilities. The utility of the method is further demonstrated by assessing the effects of genetic markers on patients' overall survival with the Boston Lung Cancer Survival Cohort, a large-scale epidemiology study investigating mechanisms underlying the lung cancer.