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Motivated by a geometric projection principle, we propose a unified likelihood ratio inferential framework, including score, Wald and partial likelihood ratio statistics for hypothesis testing. Without assuming model selection consistency, we derive the asymptotic distributions of these test statistics, establish their semiparametric optimality and conduct power analysis under Pitman alternatives. We also develop new procedures to construct pointwise confidence intervals for the baseline hazard function and conditional hazard function. Simulation studies show that all tests proposed perform well in controlling type I errors. Moreover, the partial likelihood ratio test is empirically more powerful than the other tests. The methods proposed are illustrated by an example of a gene expression data set.<\/jats:p>","DOI":"10.1111\/rssb.12224","type":"journal-article","created":{"date-parts":[[2016,12,26]],"date-time":"2016-12-26T10:47:34Z","timestamp":1482749254000},"page":"1415-1437","source":"Crossref","is-referenced-by-count":56,"title":["Testing and Confidence Intervals for High Dimensional Proportional Hazards Models"],"prefix":"10.1093","volume":"79","author":[{"given":"Ethan X.","family":"Fang","sequence":"first","affiliation":[{"name":"Pennsylvania State University , University Park , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang","family":"Ning","sequence":"additional","affiliation":[{"name":"Cornell University , Ithaca , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Han","family":"Liu","sequence":"additional","affiliation":[{"name":"Princeton University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,12,26]]},"reference":[{"key":"2023022101103514300_rssb12224-cit-0001","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1038\/35000501","article-title":"Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling","volume":"403","author":"Alizadeh","year":"2000","journal-title":"Nature"},{"key":"2023022101103514300_rssb12224-cit-0002","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1182\/blood-2011-03-345272","article-title":"Prediction of survival in diffuse large B-cell lymphoma based on the expression of 2 genes reflecting tumor and microenvironment","volume":"118","author":"Alizadeh","year":"2011","journal-title":"Blood"},{"key":"2023022101103514300_rssb12224-cit-0003","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1214\/aos\/1176345976","article-title":"Cox's regression model for counting processes: a large sample study","volume":"10","author":"Andersen","year":"1982","journal-title":"Ann. 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