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1. Combining dosiomics and machine learning methods for predicting severe cardiac diseases in childhood cancer survivors: the French Childhood Cancer Survivor Study

Author

Mahmoud Bentriou, Véronique Letort, Stefania Chounta, Brice Fresneau, Duyen Do, Nadia Haddy, Ibrahima Diallo, Neige Journy, Monia Zidane, Thibaud Charrier, Naila Aba, Claire Ducos, Vincent S. Zossou, Florent de Vathaire, Rodrigue S. Allodji, and Sarah Lemler

Subjects
survival analysis, dosiomics, cardiac disease, childhood cancer, machine learning, FCCSS, Neoplasms. Tumors. Oncology. Including cancer and carcinogens, RC254-282
Abstract

BackgroundCardiac disease (CD) is a primary long-term diagnosed pathology among childhood cancer survivors. Dosiomics (radiomics extracted from the dose distribution) have received attention in the past few years to assess better the induced risk of radiotherapy (RT) than standard dosimetric features such as dose-volume indicators. Hence, using the spatial information contained in the dosiomics features with machine learning methods may improve the prediction of CD.MethodsWe considered the 7670 5-year survivors of the French Childhood Cancer Survivors Study (FCCSS). Dose-volume and dosiomics features are extracted from the radiation dose distribution of 3943 patients treated with RT. Survival analysis is performed considering several groups of features and several models [Cox Proportional Hazard with Lasso penalty, Cox with Bootstrap Lasso selection, Random Survival Forests (RSF)]. We establish the performance of dosiomics compared to baseline models by estimating C-index and Integrated Brier Score (IBS) metrics with 5-fold stratified cross-validation and compare their time-dependent error curves.ResultsAn RSF model adjusted on the first-order dosiomics predictors extracted from the whole heart performed best regarding the C-index (0.792 ± 0.049), and an RSF model adjusted on the first-order dosiomics predictors extracted from the heart’s subparts performed best regarding the IBS (0.069 ± 0.05). However, the difference is not statistically significant with the standard models (C-index of Cox PH adjusted on dose-volume indicators: 0.791 ± 0.044; IBS of Cox PH adjusted on the mean dose to the heart: 0.074 ± 0.056).ConclusionIn this study, dosiomics models have slightly better performance metrics but they do not outperform the standard models significantly. Quantiles of the dose distribution may contain enough information to estimate the risk of late radio-induced high-grade CD in childhood cancer survivors.

Published
2024
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2. Comprehensive landscape of immune-checkpoints uncovered in clear cell renal cell carcinoma reveals new and emerging therapeutic targets

Author

Mathilde Sautreuil, Diana Tronik-Le Roux, Sarah Lemler, Maria Belén Palma, Jérôme Verine, François Desgrandchamps, Paul-Henry Cournède, Edgardo D. Carosella, Joel LeMaoult, Marina Daouya, Fatiha Bouhidel, Mahmoud Bentriou, CEA/DSV, Commissariat à L'Energie Atomique Et Aux Energies Alternatives (CEA), Direction de La Recherche Fondamentale (DRF), Service de Recherche en Hémato-Immunologie (SRHI), Hôpital Saint-Louis, Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec-Université Paris-Saclay, Gvh et Gvl : Physiopathologie Chez l'Homme et Chez l'Animal, Incidence et Role Therapeutique, Université Paris Diderot - Paris 7 (UPD7)-Institut National de la Santé et de la Recherche Médicale (INSERM), Cátedra de Citología, Histología Y Embriología A, Facultad de Ciencias Médicas, UNLP, Service de Recherche en Hémato-Immunologie (SRHI - UMR_E 05), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7), Service d'Urologie [CHU Saint-Louis], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Paris Diderot - Paris 7 (UPD7)-Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), and Université Paris Diderot - Paris 7 (UPD7)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Groupe Hospitalier Saint Louis - Lariboisière - Fernand Widal [Paris]

Subjects
Male, Cancer Research, LAG3, [SDV]Life Sciences [q-bio], HLA-G, Immune-checkpoints, Transcriptome, Leukocyte Immunoglobulin-like Receptor B1, 0302 clinical medicine, Renal cell carcinoma, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Immunology and Allergy, Receptors, Immunologic, CD70, Aged, 80 and over, Membrane Glycoproteins, Middle Aged, Prognosis, RNAseq, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], Kidney Neoplasms, 3. Good health, Oncology, Immunohistochemistry, Female, Adult, Immunology, [SDV.CAN]Life Sciences [q-bio]/Cancer, Biology, 03 medical and health sciences, Antigens, CD, Biomarkers, Tumor, medicine, Humans, Carcinoma, Renal Cell, Aged, Retrospective Studies, HLA-G Antigens, CD86, Gene Expression Profiling, ccRCC, Cancer, TCGA, medicine.disease, Clear cell renal cell carcinoma, Case-Control Studies, Cancer research, Follow-Up Studies, 030215 immunology
Abstract

International audience; Clear cell renal cell carcinoma (ccRCC) constitutes the most common renal cell carcinoma subtype and has long been recognized as an immunogenic cancer. As such, significant attention has been directed toward optimizing immune-checkpoints (IC)-based therapies. Despite proven benefits, a substantial number of patients remain unresponsive to treatment, suggesting that yet unreported, immunosuppressive mechanisms coexist within tumors and their microenvironment. Here, we comprehensively analyzed and ranked forty-four immune-checkpoints expressed in ccRCC on the basis of in-depth analysis of RNAseq data collected from the TCGA database and advanced statistical methods designed to obtain the group of checkpoints that best discriminates tumor from healthy tissues. Immunohistochemistry and flow cytometry confirmed and enlarged the bioinformatics results. In particular, by using the recursive feature elimination method, we show that HLA-G, B7H3, PDL-1 and ILT2 are the most relevant genes that characterize ccRCC. Notably, ILT2 expression was detected for the first time on tumor cells. The levels of other ligand-receptor pairs such as CD70:CD27; 4-1BB:4-1BBL; CD40:CD40L; CD86:CTLA4; MHC-II:Lag3; CD200:CD200R; CD244:CD48 were also found highly expressed in tumors compared to adjacent non-tumor tissues. Collectively, our approach provides a comprehensible classification of forty-four IC expressed in ccRCC, some of which were never reported before to be co-expressed in ccRCC. In addition, the algorithms used allowed identifying the most relevant group that best discriminates tumor from healthy tissues. The data can potentially assist on the choice of valuable immune-therapy targets which hold potential for the development of more effective anti-tumor treatments.

Published
2020
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3. Identifying clusters of health risk behaviors and their predictors in adult survivors of childhood cancer: A report from the French Childhood Cancer Survivor Study

Author

Joeffrey Marchi, Hubert C Hounsossou, François Pein, Odile Oberlin, Rodrigue S. Allodji, Vincent Souchard, Angela Jackson, Sandrine Pinto, Giao Vu-Bezin, Damien Drubay, Ibrahima Diallo, Véronique Letort, Charlotte Demoor-Goldschmidt, A. Mayet, Brice Fresneau, Sarah Lemler, Nadia Haddy, Carole Rubino, Imene Mansouri, Neige Journy, Florent de Vathaire, Agnès Dumas, Centre de recherche en épidémiologie et santé des populations (CESP), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Paul Brousse-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris-Saclay, Direction de la recherche clinique [Gustave Roussy], Institut Gustave Roussy (IGR), Centre d'épidémiologie et de santé publique des armées [Marseille] (CESPA), Service de Santé des Armées, CRLCC René Gauducheau, Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec-Université Paris-Saclay, Centre hospitalier universitaire de Nantes (CHU Nantes), Epidémiologie Clinique et Evaluation Economique Appliquées aux Populations Vulnérables (ECEVE (U1123 / UMR_S_1123)), Institut National de la Santé et de la Recherche Médicale (INSERM)-AP-HP Hôpital universitaire Robert-Debré [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Paris Cité (UPCité), Ligue Contre le Cancer Agence Nationale de la Recherche, ANR Fondation ARC pour la Recherche sur le Cancer, ARC, We thank the patients and all the clinicians and research staff who participated in the study. We are grateful to Françoise Terrier, Isao Kobayashi and Martine Labbé for their crucial contributions to this work. This study was partially supported by the INCa/ARC foundation with the CHART project, the French Agence Nationale Pour la Recherche Scientifique (Hope‐Epi project), the ARC foundation with the Pop‐HaRC project, Ligue Nationale Contre le Cancer, and Programme Hospitalier de Recherche Clinique. These funding agencies had no role in the design and conduct of the study, in the collection, management, analysis and interpretation of the data, or in the preparation, review, and approval of the manuscript., HAL UVSQ, Équipe, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université de Paris (UP), and Institut National de la Santé et de la Recherche Médicale (INSERM)-AP-HP Hôpital universitaire Robert-Debré [Paris]-Université de Paris (UP)

Subjects
Adult, Male, Adolescent, Substance-Related Disorders, childhood cancer survivors, Psychological intervention, [SHS.PSY]Humanities and Social Sciences/Psychology, physical activity, Experimental and Cognitive Psychology, [SDV.CAN]Life Sciences [q-bio]/Cancer, Childhood Cancer Survivor Study, Motor Activity, smoking, 03 medical and health sciences, 0302 clinical medicine, Cancer Survivors, [SDV.CAN] Life Sciences [q-bio]/Cancer, Survivorship curve, Neoplasms, Surveys and Questionnaires, Medicine, Humans, 030212 general & internal medicine, Health risk, Child, radiotherapy, business.industry, fungi, health risk behaviors, Pediatric cancer, alcohol drinking, Latent class model, 3. Good health, cannabis use, Psychiatry and Mental health, [SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie, 030220 oncology & carcinogenesis, Cohort, oncology, Marital status, Female, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, France, business, survivorship, Demography, marital status
Abstract

International audience; Objective: Health risk behaviors (HRB) of childhood cancer survivors (CCS) are generally studied separately, despite the evidence suggesting that HRB are not independent. To our knowledge, few studies have examined HRB profiles in the former pediatric cancer patients. In this study, we identified HRB profiles and examined predictors engaging in unhealthy behaviors in CCS. Methods: We used data from a French cohort of CCS that includes five-year survivors diagnosed between 1945 and 2000 and treated before reaching age 18, in five centers in France. A total of 2961 adult CCS answered a self-reported questionnaire pertaining to HRB. Latent class analysis was used to identify HRB profiles combining physical activity, smoking, cannabis use, and alcohol drinking. Multinomial logistic analyses examined predictors for engaging in unhealthy behaviors. Results: Three HRB patterns emerged: “Low-risk” (n = 1846, 62.3%) included CCS who exhibited the highest frequency for usual physical activity and the lowest probabilities for current smoking or cannabis use, but most drank at least moderately; “Moderate-risk behaviors” (n = 291, 9.8%), and “High-risk behaviors” (n = 824, 27.8%) for CCS who exhibited the highest frequencies for current smoking, cannabis use, and heavy drinking. The multivariable regression revealed that male CCS, less educated or not married were significantly more likely to be in the high-risk behaviors group than the low-risk group. Conclusions: As CCS remain a vulnerable population, screening for HRB should be routinized in long-term follow-up care and interventions targeting multiple HRB simultaneously among survivors should be developed.

Published
2020
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4. Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process

Author

Sarah Lemler, Charlotte Dion, Sorbonne Université (SU), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), CentraleSupélec, Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), and CentraleSupélec-Université Paris-Saclay

Subjects
Statistics and Probability, FOS: Computer and information sciences, Nonparametric estimator Model selection Diffusion Hawkes process AMS Classification: 62G05, Context (language use), Nonparametric estimator, Mathematics - Statistics Theory, Statistics Theory (math.ST), Model selection, 01 natural sciences, Least squares, Statistics - Applications, Diffusion, 010104 statistics & probability, 0502 economics and business, FOS: Mathematics, Applied mathematics, Applications (stat.AP), 0101 mathematics, Hawkes process, 050205 econometrics, Mathematics, 60J60, [STAT.AP]Statistics [stat]/Applications [stat.AP], 05 social sciences, Nonparametric statistics, Estimator, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Nonparametric regression, Diffusion process, 60J75, Subspace topology
Abstract

International audience; We consider a 1-dimensional diffusion process X with jumps. The particularity of this model relies in the jumps which are driven by a multidimensional Hawkes process denoted N. This article is dedicated to the study of a nonparametric estimator of the drift coefficient of this original process. We construct estimators based on discrete observations of the process X in a high frequency framework with a large horizon time and on the observations of the process N. The proposed nonparametric estimator is built from a least squares contrast procedure on subspace spanned by trigonometric basis vectors. We obtain adaptive results that are comparable with the one obtained in the nonparametric regression context. We finally conduct a simulation study in which we first focus on the implementation of the process and then on showing the good behavior of the estimator.

Published
2019
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5. Exponential ergodicity for diffusions with jumps driven by a Hawkes process

Author

Eva Löcherbach, Charlotte Dion, Sarah Lemler, Sorbonne Université (SU), Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), CentraleSupélec, Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec-Université Paris-Saclay, Université Paris 1 Panthéon-Sorbonne (UP1), and Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM)

Subjects
Statistics and Probability, Beta-mixing, Piecewise deterministic Markov processes (PDMP), β-mixing, 01 natural sciences, nonlinear Hawkes process, AMS Classification: 60J35, 010104 statistics & probability, Mixing (mathematics), Exponential growth, 60G55 Keywords: Diffusions with jumps, FOS: Mathematics, Applied mathematics, Ergodic theory, Piecewise-deterministic Markov process, 0101 mathematics, Mathematics, 010102 general mathematics, Ergodicity, Probability (math.PR), Diffusions with jumps, Exponential function, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, Foster-Lyapunov drift criteria, Diffusion process, Statistics, Probability and Uncertainty, 60H99, 60F99, Mathematics - Probability
Abstract

International audience; In this paper, we introduce a new class of processes which are diffusions with jumps driven by a multivariate nonlinear Hawkes process. Our goal is to study their long-time behavior. In the case of exponential memory kernels for the underlying Hawkes process we establish conditions for the positive Harris recurrence of the couple (X, Y), where X denotes the diffusion process and Y the piecewise deterministic Markov process (PDMP) defining the stochastic intensity of the driving Hawkes. As a direct consequence of the Harris recurrence, we obtain the ergodic theorem for X. Furthermore, we provide sufficient conditions under which the process is exponentially β−mixing.

Published
2019
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6. Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates

Author

Agathe Guilloux, Marie-Luce Taupin, Sarah Lemler, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec, Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), INRA - Mathématiques et Informatique Appliquées (Unité MIAJ), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de Mathématiques et Modélisation d'Evry, Polytechnique - X - Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS) - Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de mathématiques et informatique pour la complexité et les systèmes (Châtenay-Malabry, Hauts de Seine), and Unité MaIAGE

Subjects
FOS: Computer and information sciences, Statistics and Probability, Statistics::Theory, Kernel density estimation, [MATH] Mathematics [math], 010103 numerical & computational mathematics, Semi-parametric model, Statistics - Applications, Counting process, 01 natural sciences, Non-asymptotic oracle inequality, Methodology (stat.ME), 010104 statistics & probability, Minimum-variance unbiased estimator, [STAT.AP] Statistics [stat]/Applications [stat.AP], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics, Consistent estimator, Applications (stat.AP), [MATH]Mathematics [math], 0101 mathematics, Statistics - Methodology, ComputingMilieux_MISCELLANEOUS, Goldenshluger and Lepski method, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], Numerical Analysis, [STAT.ME] Statistics [stat]/Methodology [stat.ME], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Estimator, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Survival analysis, Kernel estimation, Efficient estimator, Variable kernel density estimation, Statistics, Probability and Uncertainty, Minimax estimator, [STAT.ME]Statistics [stat]/Methodology [stat.ME], Invariant estimator, Conditional hazard rate function
Abstract

The aim of this article is to propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a Lasso procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Breslow estimator of the cumulative baseline function. We propose and study an adaptive procedure for selecting the bandwidth, in the spirit of Gold-enshluger and Lepski (2011). We state non-asymptotic oracle inequalities for the final estimator, which reveal the reduction of the rates of convergence when the dimension of the covariates grows.

Published
2016
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7. High-dimensional time-varying Aalen and Cox models

Author

Alaya, Mokhtar Z., Sarah Lemler, Agathe Guilloux, Thibault Allart, Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC), CentraleSupélec, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Centre d'études et de recherche en informatique et communications (CEDRIC), Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)-Conservatoire National des Arts et Métiers [CNAM] (CNAM), Ubisoft, Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), and Guilloux, Agathe

Subjects
[STAT]Statistics [stat], Time- varying coefficients, [STAT.AP]Statistics [stat]/Applications [stat.AP], [STAT.ME] Statistics [stat]/Methodology [stat.ME], [STAT.AP] Statistics [stat]/Applications [stat.AP], Oracle inequalities, 62N01, Dynamic regression, Total-variation, [STAT.ME]Statistics [stat]/Methodology [stat.ME], [STAT] Statistics [stat], 2010 MSC: 62G08, Time-dependent covariates
Abstract

We consider the problem of estimating the intensity of a counting process in high-dimensional time-varying Aalen and Cox models. We introduce a covariate-specific weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We provide theoretical guaranties for the convergence of our estimators and present a proximal algorithm to solve the convex studied problems. The practical use and effectiveness of the proposed method are demonstrated by simulation studies and real data example.

Published
2018

8. Limit theorems and inequalities via martingale methods

Author

Jean-René Chazottes, Xiequan Fan, Jérôme Dedecker, Christophe Cuny, and Sarah Lemler

Subjects
Statistics::Theory, T57-57.97, Applied mathematics. Quantitative methods, Inequality, media_common.quotation_subject, QA1-939, Martingale (probability theory), Mathematical economics, Mathematics, media_common
Abstract

In these notes, we first give a brief overwiew of martingales methods, from Paul Levy (1935) untill now, to explain why these methods have become a central tool in probability, statistics and ergodic theory. Next, we present some recent results for/or based on martingales: exponential bounds for super-martingales, concentration inequalities for Lipschitz functionals of dynamical systems, oracle inequalities for the Cox model in a high dimensional setting, and invariance principles for stationary sequences. Resume. Dans ces notes, nous faisons d'abord un rapide survol des methodes de martingales, depuis Paul Levy (1935) jusqu'a nos nos jours, afin d'expliquer pourquoi ces methodes sont devenues centrales en probabilite, statistique et theorie ergodique. Ensuite, nous presentons des resultats recents sur/ou fondes sur les martingales : des inegalites exponentielles pour les sur-martingales, des inegalites de concentration pour les fonctionnelles lipschitziennes de systemes dynamiques, des inegalites oracle pour le modele de Cox en grande dimension, et des principes d'invariances pour les suites stationnaires.

Published
2014

9. Oracle inequalities for the Lasso in the high-dimensional Aalen multiplicative intensity model

Author

Sarah Lemler, Laboratoire Statistique et Génome (SG), and Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Intensity, Non-parametric model, Mathematics - Statistics Theory, 02 engineering and technology, High dimensional, Statistics Theory (math.ST), 01 natural sciences, Non-asymptotic oracle inequalities, Combinatorics, 010104 statistics & probability, Lasso (statistics), [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 62N02, 62G08, Statistics, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, 62G05, High-dimensional covariates, 0101 mathematics, Empirical Bernstein’s inequality, Oracle inequality, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], Cox proportional hazards model, Multiplicative function, 020206 networking & telecommunications, Right-censored data, Nonparametric model, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Survival analysis, Semiparametric model, Empirical Bernstein's inequality, Statistics, Probability and Uncertainty, Lasso, 60E15
Abstract

Dans le cadre general d’un processus de comptage, nous interessons a la facon d’obtenir un pronostic sur la duree de survie en fonction des covariables en grande dimension. Pour ce faire, nous construisons un estimateur de l’intensite conditionnelle. Nous l’estimons par le meilleur modele de Cox etant donne deux dictionnaires de fonctions. Le premier dictionnaire est utilise pour construire le logarithme du risque de base et le second, pour approximer le risque relatif. Nous introduisons une nouvelle procedure Lasso pondere avec une ponderation basee sur les donnees pour estimer les parametres inconnus du meilleur modele de Cox approximant l’intensite. Nous etablissons une inegalite oracle non-asymptotique en divergence de Kullback empirique, qui est la fonction de perte la plus appropriee a notre procedure. Nos resultats reposent sur une inegalite de Bernstein pour les martingales a sauts et sur des proprietes des fonctions self-concordantes.

Published
2016

10. Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates

Author

Agathe Guilloux, Sarah Lemler, Marie-Luce Taupin, Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université Pierre et Marie Curie - Paris 6 (UPMC), Laboratoire de Mathématiques et Modélisation d'Evry, Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA), Institut National de la Recherche Agronomique (INRA) - Université d'Evry-Val d'Essonne - ENSIIE - Centre National de la Recherche Scientifique (CNRS), INRA - Mathématiques et Informatique Appliquées (Unité MIAJ), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), ENSIIE-Université d'Évry-Val-d'Essonne (UEVE)-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS), Unité MaIAGE, and INRAE

Subjects
FOS: Computer and information sciences, Statistics and Probability, Statistics::Theory, Mathematics - Statistics Theory, Statistics Theory (math.ST), 02 engineering and technology, Semi-parametric model, Model selection, Statistics - Applications, 01 natural sciences, Non-asymptotic oracle inequalities, 010104 statistics & probability, Statistics::Machine Learning, Lasso (statistics), [STAT.AP] Statistics [stat]/Applications [stat.AP], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Covariate, Statistics, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Statistics::Methodology, Applications (stat.AP), High-dimensional covariates, 0101 mathematics, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], ComputingMilieux_MISCELLANEOUS, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], Proportional hazards model, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Applied Mathematics, Estimator, Contrast (statistics), 020206 networking & telecommunications, Right-censored data, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Cox's proportional hazards model, Nonparametric model, Survival analysis, Regression, Statistics::Computation, Adaptive estimator, Concentration inequalities, Statistics, Probability and Uncertainty, Conditional hazard rate function
Abstract

International audience; The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model selection procedure to obtain an adaptive penalized contrast estimator of the baseline function. Using non-asymptotic estimation results stated for the Lasso estimator of the regression parameter , we establish a non-asymptotic oracle inequality for this penalized contrast estimator of the baseline function, which highlights the discrepancy of the rate of convergence when the dimension of the covariates increases.

Published
2016
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