[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85457-en":3,"doc-seo-85457-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85457,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Survival of the fittest Cox model: Pivotal variable selection for time-to-event data","Revisits Cox’s proportional hazards model to strengthen variable selection in survival analysis. A square-root transformation of the partial likelihood makes the choice of the regularization parameter pivotal, removing dependence on the unknown baseline hazard and the censoring mechanism. The derived selection criterion combines features of information criteria like BIC with penalized regression principles such as the lasso. Experiments on simulated and real datasets show substantial gains over state-of-the-art methods for support recovery.","arXiv :2510 . 19374v2 [ stat .ML] 13 Jul 2026  \nSurvival of the fittest Cox model: Pivotal variable selection for time-to-event data  \nMaxime van Cutsem  \nDepartment of Mathematics, University of Geneva [Maxime. Vancutsem@unige. ch](Maxime. Vancutsem@unige. ch)  \nSylvain Sardy  \nDepartment of Mathematics, University of Geneva [sylvain. sardy@unige. ch](sylvain. sardy@unige. ch)  \nJuly 14, 2026  \nAbstract  \nWe revisit Cox’s proportional hazards model to improve variable selection in survival analysis. A square-root transformation of the partial likelihood renders the selection of the regularization parameter pivotal, free of the unknown baseline hazard and censoring mechanism. The resulting criterion borrows from information criteria such as BIC and from penalized regression methods such as the lasso, taking the best of both. On simulated and real data, our method substantially improves upon state-of-the-art approaches used daily in support recovery.  \nKeywords: Cox model; Model selection; Pivotal detection boundary; Pivotal information criterion.  \n1 Introduction  \n1.1 Setting  \nWe consider the classical survival analysis setting. Survival analysis is concerned with the study of time-to-event data and censoring information. Such data arise in many fields, for example in medicine, where the event of interest may be the death of a patient, or in engineering, where the survival time may represent the lifetime of a machine component. At the time of analysis, the event of interest may not yet have been observed for every individual, a phenomenon known as censoring. In addition to event times and censoring indicators, survival studies often collect covariates that can influence the outcome. In a clinical oncology trial, for example, variables such as tumour stage, patient age, smoking status, or gene expression may have a substantial impact on survival. Identifying the most relevant covariates improves the interpretability of the model, reduces overfitting, and facilitates the detection of meaningful prognostic and predictive factors that can support clinical decision-making.  \nFormally, survival analysis assumes that two random variables underlie the data: the event time T and the censoring time C. Let (T1 , C1 ) ,...,(Tn , Cn ) be an independent sample from the joint distribution of (T, C) . The observed right-censored data consist of triplets (yi ,δi , xi)i=1 , ...,n where yi = min(ti , ci ), δi = I{ti ≤ ci } and xi ∈ Rp denotes the vector ofcovariates for the ith individual. We consider the non-informative censoring setting that Ti and Ci are conditionally independent given xi. We denote by X ∈ Rn×p , y ∈ Rn and δ ∈ Rn the vectorized form of the data. Let τ be the end of study time.  \nThe primary objective is to characterize the distribution of the event time T. A common quantity of interest is the survival function S(t|x) := P(T > t|x) which gives the probability that an individual with covariates x survives beyond time t and is commonly used for graphical representations. For model specification, however, it is often more convenient to  \nwork with the hazard function  \nf (t|x)   1   \nh (t|x) := = lim P (t ≤ T \u003C t + ∆t| T ≥ t, x) S (t|x) ∆t→0 ∆t  \nwhich describes the instantaneous risk of experiencing the event at time t, given survival up to that time. Here f (t|x) denotes the conditional density of T. While the survival function captures the long-term probability of survival, the hazard function captures the instantaneous failure rate. The two are tightly connected through  \nS (t|x) = exp 􀀒− Z0 t h (u|x)du􀀓 =: exp{−H(t|x)} .  \n1.2 The Cox model and Cox’s partial likelihood  \nThe proportional hazards model for survival data, also known as the Cox model [Cox, 1972], assumes that the hazard at time t depends on the covariates through  \nh (t|x) = h0 (t)exp(xTβ) ,  \nwhere h0 is the unknown baseline hazard function and β ∈ Rp is the regression coefficient vector. The associated linear predictor µβ (x) = xTβ = Ppj=1 βj xj has no int","cbCaivfF6MxW0Ghi","https://ap.wps.com/l/cbCaivfF6MxW0Ghi","pdf",401441,1,30,"English","en",105,"# Introduction\n## Setting\n## The Cox model and Cox’s partial likelihood\n## Model selection for survival analysis","[{\"question\":\"What problem does the paper address in Cox proportional hazards modeling?\",\"answer\":\"Improving variable selection for survival analysis by making the regularization choice more reliable.\"},{\"question\":\"How does the method avoid reliance on the unknown baseline hazard and censoring mechanism?\",\"answer\":\"A square-root transformation of the partial likelihood yields a pivotal selection of the regularization parameter that is free of those nuisance components.\"},{\"question\":\"What evidence is provided that the proposed selection criterion improves performance?\",\"answer\":\"The paper reports substantial improvements on both simulated and real datasets compared with state-of-the-art approaches for support recovery.\"}]",1784203690,76,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"survival-of-the-fittest-cox-model-pivotal-variable-selection-for-time-to-event-data","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/survival-of-the-fittest-cox-model-pivotal-variable-selection-for-time-to-event-data/85457/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address in Cox proportional hazards modeling?","Question",{"text":75,"@type":76},"Improving variable selection for survival analysis by making the regularization choice more reliable.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method avoid reliance on the unknown baseline hazard and censoring mechanism?",{"text":80,"@type":76},"A square-root transformation of the partial likelihood yields a pivotal selection of the regularization parameter that is free of those nuisance components.",{"name":82,"@type":73,"acceptedAnswer":83},"What evidence is provided that the proposed selection criterion improves performance?",{"text":84,"@type":76},"The paper reports substantial improvements on both simulated and real datasets compared with state-of-the-art approaches for support recovery.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":21,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]