Statistical inference for Cox proportional hazards models with a diverging number of covariates

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions inverse Fisher information matrix. Such assumptions, however, are often violated under Cox proportion hazards models, leading to biased estimates under-coverage confidence intervals. We propose modified debiased lasso method, which solves series quadratic programming problems approximate matrix without posing sparse assumptions. establish asymptotic results for estimated coefficients when dimension covariates diverges sample size. As demonstrated by extensive simulations, our proposed method provides consistent and intervals nominal coverage probabilities. The utility is further assessing effects genetic markers patients' overall survival Boston Lung Cancer Survival Cohort, large-scale epidemiology study investigating mechanisms underlying lung cancer.