<!DOCTYPE article
PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20190208//EN"
       "JATS-journalpublishing1.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" article-type="research-article" dtd-version="1.4" xml:lang="en">
 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Intellectual Technologies on Transport</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Intellectual Technologies on Transport</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Интеллектуальные технологии на транспорте</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="online">2413-2527</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">95717</article-id>
   <article-id pub-id-type="doi">10.20295/2413-2527-2025-242-58-70</article-id>
   <article-id pub-id-type="edn">wccnbo</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ И СИСТЕМНЫЙ АНАЛИЗ</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>MATHEMATICAL MODELLING AND SYSTEM ANALYSIS</subject>
    </subj-group>
    <subj-group>
     <subject>МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ И СИСТЕМНЫЙ АНАЛИЗ</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Comparative Analysis of the Predictive Ability of the Extended Cox Model</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>О прогностической способности расширенной модели Кокса: сравнительный анализ</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Микулик</surname>
       <given-names>Илья Игоревич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Mikulik</surname>
       <given-names>Ilya Igorevich</given-names>
      </name>
     </name-alternatives>
     <email>mikulik.ilia@gmail.com</email>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Благовещенская</surname>
       <given-names>Екатерина Анатольевна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Blagoveschenskaya</surname>
       <given-names>Ekaterina Anatol'evna</given-names>
      </name>
     </name-alternatives>
     <email>kblag2002@yahoo.com</email>
     <bio xml:lang="ru">
      <p>доктор физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Петербургский государственный университет путей сообщения Императора Александра I</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Emperor Alexander I St. Petersburg State Transport University</institution>
     <city>Saint Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Петербургский государственный университет путей сообщения Императора Александра I</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Emperor Alexander I St. Petersburg State Transport University</institution>
     <city>Saint-Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2025-06-26T00:00:00+03:00">
    <day>26</day>
    <month>06</month>
    <year>2025</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-06-26T00:00:00+03:00">
    <day>26</day>
    <month>06</month>
    <year>2025</year>
   </pub-date>
   <issue>2</issue>
   <fpage>58</fpage>
   <lpage>70</lpage>
   <history>
    <date date-type="received" iso-8601-date="2025-03-03T00:00:00+03:00">
     <day>03</day>
     <month>03</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2025-03-07T00:00:00+03:00">
     <day>07</day>
     <month>03</month>
     <year>2025</year>
    </date>
   </history>
   <self-uri xlink:href="https://atjournal.ru/en/nauka/article/95717/view">https://atjournal.ru/en/nauka/article/95717/view</self-uri>
   <abstract xml:lang="ru">
    <p>Представлено исследование, посвященное сравнительному анализу расширенной модели Кокса с современными методами анализа выживаемости. Цель: проведение сравнительного анализа прогностических способностей расширенной модели Кокса с актуальными моделями и методами анализа выживаемости. Для достижения цели использованы методы машинного обучения (случайный лес выживаемости, градиентный бустинг, метод опорных векторов) и классические статистические подходы (модели Вейбулла, логлогистическая и логнормальная модели). Методы: анализ трех наборов данных: пациентов с раком предстательной железы, данных о рецидивах преступлений и пациентов с раком молочной железы. Результаты: демонстрируют, что расширенная модель Кокса превосходит или сопоставима по точности с современными методами машинного обучения, сохраняя при этом высокую интерпретируемость. Практическая значимость: заключается в возможности применения расширенной модели Кокса в медицине, социальных науках и других областях, где важны как точность прогнозирования, так и понимание влияния факторов на риск наступления события. Научная новизна работы заключается в проведении первого сравнительного анализа расширенной модели Кокса с другими методами анализа выживаемости, что открывает новые возможности для улучшения и адаптации модели в будущих исследованиях. Исследование имеет важное значение для развития методов анализа выживаемости и их применения в прикладных задачах, способствуя повышению точности прогнозов и улучшению интерпретируемости результатов.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>A study presents a comparative analysis of the extended Cox model with modern survival analysis methods. Purpose: to evaluate the predictive abilities of the extended Cox model in comparison with the current survival analysis models and techniques. To achieve this goal, machine learning methods (survival random forest, gradient boosting, support vector machines) and classical statistical approaches (Weibull, log-logistic, and log-normal models) were used. Methods: analyzing three datasets, that is prostate cancer patients, data on their recurrent admissions, and breast cancer patients. Results: To demonstrate that the extended Cox model outperforms or is comparable in accuracy to modern machine learning methods while maintaining high interpretability. Practical significance: the applicability of the extended Cox model in medicine, social sciences, and other fields where both prediction accuracy and understanding of the factors affecting the risk of an event are crucial. The scientific novelty of this study lies in conducting a first comparative analysis of the extended Cox model with other survival analysis methods opening new opportunities for improving and adapting the model in future research. The study will be of great importance for the development of survival analysis methods and their application in practical tasks contributing to increased prediction accuracy and improved interpretability of results.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>анализ выживаемости</kwd>
    <kwd>модель Кокса</kwd>
    <kwd>метаэвристические алгоритмы</kwd>
    <kwd>муравьиный алгоритм</kwd>
    <kwd>оптимизация</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>survival analysis</kwd>
    <kwd>Cox model</kwd>
    <kwd>metaheuristic algorithms</kwd>
    <kwd>ant colony algorithm</kwd>
    <kwd>optimization</kwd>
   </kwd-group>
  </article-meta>
 </front>
 <body>
  <p></p>
 </body>
 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Летчиков А. В., Матвеев Р. Ю., Широбокова М. А. Решение проблемы цензурированных данных при моделировании оценки индивидуального кредитного риска // Вестник Удмуртского университета. Серия «Экономика и право». 2019. Т. 29, Вып. 1. С. 34–41.</mixed-citation>
     <mixed-citation xml:lang="en">Letchikov A. V., Matveev R. Yu., Shirobokova M. A. Reshenie problemy tsenzurirovannykh dannykh pri modelirovanii otsenki individualnogo kreditnogo riska [Solving the Problem of Censored Data in Modeling the Individual Credit Risk Estimation], Vestnik Udmurtskogo universiteta. Seriya “Ekonomika i parvo” [The Bulletin of Udmurt University. Series Economics and Law], 2019, Vol. 29, Iss. 1, Pp. 34–41. (In Russian)</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Heterogeneous Datasets for Federated Survival Analysis Simulation / A. Archetti, E. Lomurno, F. Lattari [et al.] // ICPE ‘23 Companion: Companion of the ACM/SPEC International Conference on Performance Engineering (Coimbra, Portugal, 15–19 April 2023). New York (NY): Association for Computing Machinery, 2023. Pp. 173–180. DOI: 10.1145/3578245.3584935.</mixed-citation>
     <mixed-citation xml:lang="en">Archetti A., Lomurno E., Lattari F., et al. Heterogeneous Datasets for Federated Survival Analysis Simulation, ICPE ‘23 Companion: Companion of the ACM/SPEC International Conference on Performance Engineering (Coimbra, Portugal, April 15–19, 2023). New York (NY), Association for Computing Machinery, 2023, Pp. 173–180. DOI: 10.1145/3578245.3584935.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Микулик И. И., Жаринов Г. М., Кнеев А. Ю. Алгоритм построения функции риска расширенной модели Кокса и его применение на базе данных больных раком предстательной железы // Advanced Engineering Research (Rostov-on-Don). 2024. Т. 24, № 4. С. 413–423. DOI: 10.23947/2687-1653-2024-24-4-413-423.</mixed-citation>
     <mixed-citation xml:lang="en">Mikulik I. I., Zharinov G. M., Kneev A. Yu. Algorithm for Constructing the Hazard Function of the Extended Cox Model and Its Application to the Prostate Cancer Patient Database, Advanced Engineering Research (Rostov-on-Don), 2024, Vol. 24, No. 4, Pp. 413–423. DOI: 10.23947/2687-1653-2024-24-4-413-423.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Wang P., Li Y., Reddy C. K. Machine Learning for Survival Analysis: A Survey // ACM Computing Surveys. 2019. Vol. 51, Iss. 6. Art. No. 110. 36 p. DOI: 10.1145/3214306.</mixed-citation>
     <mixed-citation xml:lang="en">Wang P., Li Y., Reddy C. K. Machine Learning for Survival Analysis: A Survey, ACM Computing Surveys, 2019, Vol. 51, Iss. 6, Art. No. 110, 36 p. DOI: 10.1145/3214306.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Overview of Parametric Survival Analysis for Health-Economic Applications / K. J. Ishak, N. Kreif, A. Benedict, N. Muszbek // PharmacoEconomics. 2013. Vol. 31, Iss. 8. Pp. 663–675. DOI: 10.1007/s40273-013-0064-3.</mixed-citation>
     <mixed-citation xml:lang="en">Ishak K. J., Kreif N., Benedict A., Muszbek N. Overview of Parametric Survival Analysis for Health-Economic Applications, PharmacoEconomics, 2013, Vol. 31, Iss. 8, Pp. 663–675. DOI: 10.1007/s40273-013-0064-3.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Zhu S., Campanella O., Chen G. Estimation of Parameters in the Weibull Model from Microbial Survival Data Obtained Under Constant Conditions with Come-up Times // Journal of Food Engineering. 2021. Vol. 292. Art. No. 110364. 10 p. DOI: 10.1016/j.jfoodeng.2020.110364.</mixed-citation>
     <mixed-citation xml:lang="en">Zhu S., Campanella O., Chen G. Estimation of Parameters in the Weibull Model from Microbial Survival Data Obtained Under Constant Conditions with Come-up Times, Journal of Food Engineering, 2021, Vol. 292, Art. No. 110364, 10 p. DOI: 10.1016/j.jfoodeng.2020.110364.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Borges P. Estimating the Turning Point of the Log-Logistic Hazard Function in the Presence of Long-Term Survivors with an Application for Uterine Cervical Cancer Data // Journal of Applied Statistics. 2021. Vol. 48, Iss. 2. Pp. 203–213. DOI: 10.1080/02664763.2020.1720627.</mixed-citation>
     <mixed-citation xml:lang="en">Borges P. Estimating the Turning Point of the Log-Logistic Hazard Function in the Presence of Long-Term Survivors with an Application for Uterine Cervical Cancer Data, Journal of Applied Statistics, 2021, Vol. 48, Iss. 2, Pp. 203–213. DOI: 10.1080/02664763.2020.1720627.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Extrapolation of Survival Curves Using Standard Parametric Models and Flexible Parametric Spline Models: Comparisons in Large Registry Cohorts with Advanced Cancer / J. Gray, T. Sullivan, N. R. Latimer [et al.] // Medical Decision Making. 2021. Vol. 41, Iss. 2. Pp. 179–193. DOI: 10.1177/0272989X20978958.</mixed-citation>
     <mixed-citation xml:lang="en">Gray J., Sullivan T., Latimer N. R., et al. Extrapolation of Survival Curves Using Standard Parametric Models and Flexible Parametric Spline Models: Comparisons in Large Registry Cohorts with Advanced Cancer, Medical Decision Making, 2021, Vol. 41, Iss. 2, Pp. 179–193. DOI: 10.1177/0272989X20978958.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Decision Tree for Competing Risks Survival Probability in Breast Cancer Study / N. A. Ibrahim, A. Kudus, I. Daud, M. R. Abu Bakar // International Journal of Biological and Medical Sciences. 2008. Vol. 3, Iss. 1. Pp. 25–29.</mixed-citation>
     <mixed-citation xml:lang="en">Ibrahim N. A., Kudus A., Daud I., Abu Bakar M. R. Decision Tree for Competing Risks Survival Probability in Breast Cancer Study, International Journal of Biological and Medical Sciences, 2008, Vol. 3, Iss. 1, Pp. 25–29.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Support Vector Machines for Survival Analysis / V. Van Belle, K. Pelckmans, J. A. K. Suykens, S. Van Huffel // Proceedings of the Third International Conference on Computational Intelligence in Medicine and Healthcare (CIMED2007), (Plymouth, United Kingdom, 25–27 July 2007). 8 p.</mixed-citation>
     <mixed-citation xml:lang="en">Van Belle V., Pelckmans K., Suykens J. A. K., Van Huffel S. Support Vector Machines for Survival Analysis, Proceedings of the Third International Conference on Computational Intelligence in Medicine and Healthcare (CIMED2007), Plymouth, United Kingdom, July 25–27, 2007). 8 p.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Shivaswamy P. K., Chu W., Jansche M. A Support Vector Approach to Censored Targets // Proceedings of the 7th IEEE International Conference on Data Mining (ICDM 2007) (Omaha, NE, USA, 28–31 October 2007). Institute of Electrical and Electronics Engineers, 2007. Pp. 655–660. DOI: 10.1109/ICDM.2007.93.</mixed-citation>
     <mixed-citation xml:lang="en">Shivaswamy P. K., Chu W., Jansche M. A Support Vector Approach to Censored Targets, Proceedings of the 7th IEEE International Conference on Data Mining (ICDM 2007), Omaha, NE, USA, October 28–31, 2007. Institute of Electrical and Electronics Engineers, 2007, Pp. 655–660. DOI: 10.1109/ICDM.2007.93.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Integrating Bioinformatics and Machine Learning Methods to Analyze Diagnostic Biomarkers for HBV-induced Hepatocellular Carcinoma / A. Yang, J. Liu, M. Li [et al.] // Diagnostic Pathology. 2024. Vol. 19, Iss. 1. Art. No. 105. 10 p. DOI: 10.1186/s13000-024-01528-8.</mixed-citation>
     <mixed-citation xml:lang="en">Yang A., Liu J., Li M., et al. Integrating Bioinformatics and Machine Learning Methods to Analyze Diagnostic Biomarkers for HBV-induced Hepatocellular Carcinoma, Diagnostic Pathology, 2024, Vol. 19, Iss. 1, Art. No. 105, 10 p. DOI: 10.1186/s13000-024-01528-8.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Deep Learning for Survival Analysis: A Review / S. Wiegrebe, P. Kopper, R. Sonabend [et al.] // Artificial Intelligence Review. 2024. Vol. 57, Iss. 3. Art. No. 65. 34 p. DOI: 10.1007/s10462-023-10681-3.</mixed-citation>
     <mixed-citation xml:lang="en">Wiegrebe S., Kopper P., Sonabend R., et al. Deep Learning for Survival Analysis: A Review, Artificial Intelligence Review, 2024, Vol. 57, Iss. 3, Art. No. 65, 34 p. DOI: 10.1007/s10462-023-10681-3.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kovalev M. S., Utkin L. V. A Robust Algorithm for Explaining Unreliable Machine Learning Survival Models Using the Kolmogorov — Smirnov Bounds // Neural Networks. 2020. Vol. 132. Pp. 1–18. DOI: 10.1016/j.neunet.2020.08.007.</mixed-citation>
     <mixed-citation xml:lang="en">Kovalev M. S., Utkin L. V. A Robust Algorithm for Explaining Unreliable Machine Learning Survival Models Using the Kolmogorov — Smirnov Bounds, Neural Networks, 2020, Vol. 132, Pp. 1–18. DOI: 10.1016/j.neunet.2020.08.007.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Archetti A., Ieva F., Matteucci M. Scaling Survival Analysis in Healthcare with Federated Survival Forests: A Comparative Study on Heart Failure and Breast Cancer Genomics // Future Generation Computer Systems. 2023. Vol. 149. Pp. 343–358. DOI: 10.1016/j.future.2023.07.036.</mixed-citation>
     <mixed-citation xml:lang="en">Archetti A., Ieva F., Matteucci M. Scaling Survival Analysis in Healthcare with Federated Survival Forests: A Comparative Study on Heart Failure and Breast Cancer Genomics, Future Generation Computer Systems, 2023, Vol. 149, Pp. 343–358. DOI: 10.1016/j.future.2023.07.036.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B16">
    <label>16.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Powell J. L. Estimation of Semiparametric Models // Handbook of Econometrics. Volume IV / R. F. Engle, D. L. McFadden (eds.). Amsterdam: North-Holland Publishing, 1994. Pp. 2443–2521. DOI: 10.1016/S1573-4412(05)80010-8.</mixed-citation>
     <mixed-citation xml:lang="en">Powell J. L. Estimation of Semiparametric Models. In: Engle R. F., McFadden D. L. (eds.) Handbook of Econometrics. Volume IV. Amsterdam, North-Holland Publishing, 1994, Pp. 2443–2521. DOI: 10.1016/S1573-4412(05)80010-8.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B17">
    <label>17.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Assessing Performance and Clinical Usefulness in Prediction Models with Survival Outcomes: Practical Guidance for Cox Proportional Hazards Models / D. J. McLernon, D. Giardiello, B. Van Calster // Annals of Internal Medicine. 2023. Vol. 176, No. 1. Pp. 105–114. DOI: 10.7326/M22-0844.</mixed-citation>
     <mixed-citation xml:lang="en">McLernon D. J., Giardiello D., Van Calster B. Assessing Performance and Clinical Usefulness in Prediction Models with Survival Outcomes: Practical Guidance for Cox Proportional Hazards Models, Annals of Internal Medicine, 2023, Vol. 176, No. 1, Pp. 105–114. DOI: 10.7326/M22-0844.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B18">
    <label>18.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Tao X., Wang M., Ji Y. The Application of Graph-Structured Cox Model in Financial Risk Early Warning of Companies // Sustainability. 2023. Vol. 15, Iss. 14. Art. No. 10802. 16 p. DOI: 10.3390/su151410802.</mixed-citation>
     <mixed-citation xml:lang="en">Tao X., Wang M., Ji Y. The Application of Graph-Structured Cox Model in Financial Risk Early Warning of Companies, Sustainability, 2023, Vol. 15, Iss. 14, Art. No. 10802, 16 p. DOI: 10.3390/su151410802.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B19">
    <label>19.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Gomez-Gonzalez J. E., Uribe J. M., Valencia O. M. Does Economic Complexity Reduce the Probability of a Fiscal Crisis? // World Development. 2023. Vol. 168. Art. No. 106250. 17 p. DOI: 10.1016/j.worlddev.2023.106250.</mixed-citation>
     <mixed-citation xml:lang="en">Gomez-Gonzalez J. E., Uribe J. M., Valencia O. M. Does Economic Complexity Reduce the Probability of a Fiscal Crisis? World Development, 2023, Vol. 168, Art. No. 106250, 17 p. DOI: 10.1016/j.worlddev.2023.106250.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B20">
    <label>20.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Viral Kinetics in Sylvatic Yellow Fever Cases / V. I. Avelino-Silva, M. V. Thomazella, M. P. Marmorato [et al.] // The Journal of Infectious Diseases. 2023. Vol. 227, Iss. 9. Pp. 1097–1103. DOI: 10.1093/infdis/jiac435.</mixed-citation>
     <mixed-citation xml:lang="en">Avelino-Silva V. I., Thomazella M. V., Marmorato M. P., et al. Viral Kinetics in Sylvatic Yellow Fever Cases, The Journal of Infectious Diseases, 2023, Vol. 227, Iss. 9, Pp. 1097–1103. DOI: 10.1093/infdis/jiac435.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B21">
    <label>21.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Survival Analysis of Productive Life in Florida Dairy Goats Using a Cox Proportional Hazards Model / C. Ziadi, J. P. Sánchez, M. Sánchez [et al.] // Journal of Animal Breeding and Genetics. 2023. Vol. 140, Iss. 4. Pp. 431–439. DOI: 10.1111/jbg.12769.</mixed-citation>
     <mixed-citation xml:lang="en">Ziadi C., Sánchez J. P., Sánchez M., et al. Survival Analysis of Productive Life in Florida Dairy Goats Using a Cox Proportional Hazards Model, Journal of Animal Breeding and Genetics, 2023, Vol. 140, Iss. 4, Pp. 431–439. DOI: 10.1111/jbg.12769.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B22">
    <label>22.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">High Social Risk and Mortality. A Prospective Study in Community-Dwelling Older Adults Living in a Rural Ecuadorian Village / O. H. Del Brutto, R. M. Mera, D. A. Rumbea [et al.] // Preventive Medicine Reports. 2023. Vol. 32. Art. No. 102146. 4 p. DOI: 10.1016/j.pmedr.2023.102146.</mixed-citation>
     <mixed-citation xml:lang="en">Del Brutto O. H., Mera R. M., Rumbea D. A., et al. High Social Risk and Mortality. A Prospective Study in Community-Dwelling Older Adults Living in a Rural Ecuadorian Village, Preventive Medicine Reports, 2023, Vol. 32, Art. No. 102146, 4 p. DOI: 10.1016/j.pmedr.2023.102146.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B23">
    <label>23.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Papathanasiou D., Demertzis K., Tziritas N. Machine Failure Prediction Using Survival Analysis // Future Internet. 2023. Vol. 15, Iss. 5. Art. No. 153. 26 p. DOI: 10.3390/fi15050153.</mixed-citation>
     <mixed-citation xml:lang="en">Papathanasiou D., Demertzis K., Tziritas N. Machine Failure Prediction Using Survival Analysis, Future Internet, 2023, Vol. 15, Iss. 5, Art. No. 153, 26 p. DOI: 10.3390/fi15050153.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B24">
    <label>24.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Evaluating the Yield of Medical Tests / F. E. Harrell Jr., R. M. Califf, D. B. Pryor [et al.] // JAMA: The Journal of the American Medical Association. 1982. Vol. 247, No. 18. Pp. 2543–2546. DOI: 10.1001/jama.1982.03320430047030.</mixed-citation>
     <mixed-citation xml:lang="en">Harrell Jr. F. E., Califf R. M., Pryor D. B., et al. Evaluating the Yield of Medical Tests, JAMA: The Journal of the American Medical Association, 1982, Vol. 247, No. 18, Pp. 2543–2546. DOI: 10.1001/jama.1982.03320430047030.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B25">
    <label>25.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">The Concordance Index Decomposition: A Measure for a Deeper Understanding of Survival Prediction Models / A. Alabdallah, M. Ohlsson, S. Pashami, T. Rögnvaldsson // Artificial Intelligence in Medicine. 2024. Vol. 148. Art. No. 102781. 10 p. DOI: 10.1016/j.artmed.2024.102781.</mixed-citation>
     <mixed-citation xml:lang="en">Alabdallah A., Ohlsson M., Pashami S., Rögnvaldsson T. The Concordance Index Decomposition: A Measure for a Deeper Understanding of Survival Prediction Models, Artificial Intelligence in Medicine, 2024, Vol. 148, Art. No. 102781, 10 p. DOI: 10.1016/j.artmed.2024.102781.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B26">
    <label>26.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Pitfalls of the Concordance Index for Survival Outcomes / N. Hartman, S. Kim, K. He, J. D. Kalbfleisch // Statistics in Medicine. 2023. Vol. 42, Iss. 13. Pp. 2179–2190. DOI: 10.1002/sim.9717.</mixed-citation>
     <mixed-citation xml:lang="en">Hartman N., Kim S., He K., Kalbfleisch J. D. Pitfalls of the Concordance Index for Survival Outcomes, Statistics in Medicine, 2023, Vol. 42, Iss. 13, Pp. 2179–2190. DOI: 10.1002/sim.9717.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B27">
    <label>27.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Румянцева Е. В., Фурманов К. К. Использование вневыборочных остатков Кокса — Снелл при прогнозировании наступления событий // Бизнес-информатика. 2021. T. 15, № 1. С. 7–18. DOI: 10.17323/2587-814X.2021.1.7.18.</mixed-citation>
     <mixed-citation xml:lang="en">Rumyantseva E. V., Furmanov K. K. Using Out-of-Sample Cox — Snell Residuals in Time-to-Event Forecasting, Business Informatics, 2021, Vol. 15, No. 1, Pp. 7–18. DOI: 10.17323/2587-814X.2021.1.7.18.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B28">
    <label>28.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Longato E., Vettoretti M., Di Camillo B. A Practical Perspective on the Concordance Index for the Evaluation and Selection of Prognostic Time-to-Event Models // Journal of Biomedical Informatics. 2020. Vol. 108. Art. No. 103496. 9 p. DOI: 10.1016/j.jbi.2020.103496.</mixed-citation>
     <mixed-citation xml:lang="en">Longato E., Vettoretti M., Di Camillo B. A Practical Perspective on the Concordance Index for the Evaluation and Selection of Prognostic Time-to-Event Models, Journal of Biomedical Informatics, 2020, Vol. 108, Art. No. 103496, 9 p. DOI: 10.1016/j.jbi.2020.103496.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B29">
    <label>29.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Pencina M. J., D’Agostino R. B. Overall C as a Measure of Discrimination in Survival Analysis: Model Specific Population Value and Confidence Interval Estimation // Statistics in Medicine. 2004. Vol. 23, Iss. 13. Pp. 2109–2123. DOI: 10.1002/sim.1802.</mixed-citation>
     <mixed-citation xml:lang="en">Pencina M. J., D’Agostino R. B. Overall C as a Measure of Discrimination in Survival Analysis: Model Specific Population Value and Confidence Interval Estimation, Statistics in Medicine, 2004, Vol. 23, Iss. 13, Pp. 2109–2123. DOI: 10.1002/sim.1802.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B30">
    <label>30.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">A Convolutional Neural Network Model for Survival Prediction Based on Prognosis-Related Cascaded Wx Feature Selection / Q. Yin, W. Chen, C. Zhang, Z. Wei // Laboratory Investigation. 2022. Vol. 102, Iss. 10. Pp. 1064–1074. DOI: 10.1038/s41374-022-00801-y.</mixed-citation>
     <mixed-citation xml:lang="en">Yin Q., Chen W., Zhang C., Wei Z. A Convolutional Neural Network Model for Survival Prediction Based on Prognosis-Related Cascaded Wx Feature Selection, Laboratory Investigation, 2022, Vol. 102, Iss. 10, Pp. 1064–1074. DOI: 10.1038/s41374-022-00801-y.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B31">
    <label>31.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Свидетельство о государственной регистрации базы данных № 2016620331 Российская Федерация. База данных больных раком предстательной железы: опубл. 20.04.2016 / Г. М. Жаринов.</mixed-citation>
     <mixed-citation xml:lang="en">Zharinov G. M. Baza dannykh bolnykh rakom predstatelnoy zhelezy [Prostate cancer patient database]. Certificate of State registration of the database RU No. 2016620331, published at April 20, 2016. (In Russian)</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B32">
    <label>32.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Rossi P. H., Berk R. A., Lenihan K. J. Money, Work, and Crime: Experimental Evidence. New York: Academic Press, 1980. 260 p.</mixed-citation>
     <mixed-citation xml:lang="en">Rossi P. H., Berk R. A., Lenihan K. J. Money, Work, and Crime: Experimental Evidence. New York, Academic Press, 1980. 260 p.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B33">
    <label>33.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Teng J. SEER Breast Cancer Data // IEEE Dataport. Last update 18.01.2019. DOI: 10.21227/a9qy-ph35.</mixed-citation>
     <mixed-citation xml:lang="en">Teng J. SEER Breast Cancer Data, IEEE Dataport. Last update January 18, 2019. DOI: 10.21227/a9qy-ph35.</mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
