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<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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Ekologiya cheloveka (Human Ecology)</journal-id><journal-title-group><journal-title xml:lang="en">Ekologiya cheloveka (Human Ecology)</journal-title><trans-title-group xml:lang="ru"><trans-title>Экология человека</trans-title></trans-title-group></journal-title-group><issn publication-format="print">1728-0869</issn><issn publication-format="electronic">2949-1444</issn><publisher><publisher-name xml:lang="en">Eco-Vector</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">642576</article-id><article-id pub-id-type="doi">10.17816/humeco642576</article-id><article-id pub-id-type="edn">XXYJJP</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>ORIGINAL STUDY ARTICLES</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>ОРИГИНАЛЬНЫЕ ИССЛЕДОВАНИЯ</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Application of logistic regression in epidemiology: primary data, stratification and moving average</article-title><trans-title-group xml:lang="ru"><trans-title>Применение логистической регрессии в эпидемиологии: первичные данные, стратификация и скользящее среднее</trans-title></trans-title-group><trans-title-group xml:lang="zh"><trans-title>流行病学中的逻辑回归应用：原始数据、分层和移动平均数</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2689-3006</contrib-id><contrib-id contrib-id-type="spin">9910-2326</contrib-id><name-alternatives><name xml:lang="en"><surname>Varaksin</surname><given-names>Anatoly N.</given-names></name><name xml:lang="ru"><surname>Вараксин</surname><given-names>Анатолий Николаевич</given-names></name><name xml:lang="zh"><surname>Varaksin</surname><given-names>Anatoly N.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Dr. Sci. (Physics and Mathematics), Professor</p></bio><bio xml:lang="ru"><p>д-р физ.-мат. наук, профессор</p></bio><bio xml:lang="zh"><p>Dr. Sci. (Physics and Mathematics), Professor</p></bio><email>varaksin@ecko.uran.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-0173-6293</contrib-id><contrib-id contrib-id-type="spin">3163-6856</contrib-id><name-alternatives><name xml:lang="en"><surname>Shalaumova</surname><given-names>Yulia V.</given-names></name><name xml:lang="ru"><surname>Шалаумова</surname><given-names>Юлия Валерьевна</given-names></name><name xml:lang="zh"><surname>Shalaumova</surname><given-names>Yulia V.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Cand. Sci. (Engineering)</p></bio><bio xml:lang="ru"><p>канд. техн. наук</p></bio><bio xml:lang="zh"><p>Cand. Sci. (Engineering)</p></bio><email>jvshalaumova@gmail.com</email><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6642-9027</contrib-id><contrib-id contrib-id-type="spin">3233-7652</contrib-id><name-alternatives><name xml:lang="en"><surname>Maslakova</surname><given-names>Tatyana A.</given-names></name><name xml:lang="ru"><surname>Маслакова</surname><given-names>Татьяна Анатольевна</given-names></name><name xml:lang="zh"><surname>Maslakova</surname><given-names>Tatyana A.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Cand. Sci. (Physics and Mathematics)</p></bio><bio xml:lang="ru"><p>канд. физ.-мат. наук</p></bio><bio xml:lang="zh"><p>Cand. Sci. (Physics and Mathematics)</p></bio><email>t9126141139@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Institute of Industrial Ecology, Ural Branch of the Russian Academy of Sciences</institution></aff><aff><institution xml:lang="ru">Институт промышленной экологии Уральского отделения Российской академии наук</institution></aff><aff><institution xml:lang="zh">Institute of Industrial Ecology, Ural Branch of the Russian Academy of Sciences</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Institute of Plant and Animal Ecology, Ural Branch of the Russian Academy of Sciences</institution></aff><aff><institution xml:lang="ru">Институт промышленной экологии Уральского отделения Российской академии наук</institution></aff><aff><institution xml:lang="zh">Institute of Plant and Animal Ecology, Ural Branch of the Russian Academy of Sciences</institution></aff></aff-alternatives><pub-date date-type="preprint" iso-8601-date="2025-03-23" publication-format="electronic"><day>23</day><month>03</month><year>2025</year></pub-date><pub-date date-type="pub" iso-8601-date="2025-04-08" publication-format="electronic"><day>08</day><month>04</month><year>2025</year></pub-date><volume>31</volume><issue>9</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><issue-title xml:lang="zh"/><fpage>678</fpage><lpage>691</lpage><history><date date-type="received" iso-8601-date="2024-12-05"><day>05</day><month>12</month><year>2024</year></date><date date-type="accepted" iso-8601-date="2025-02-18"><day>18</day><month>02</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Eco-Vector</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Эко-Вектор</copyright-statement><copyright-statement xml:lang="zh">Copyright ©; 2025,</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Eco-Vector</copyright-holder><copyright-holder xml:lang="ru">Эко-Вектор</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc-nd/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://hum-ecol.ru/1728-0869/article/view/642576">https://hum-ecol.ru/1728-0869/article/view/642576</self-uri><abstract xml:lang="en"><p><bold>Background:<italic> </italic></bold>Logistic regression is the most commonly used method for establishing statistical relationships between quantitative predictors X and a dichotomous response Y (Y=0 or Y=1). Therefore, it is relevant to develop new approaches to the analysis of relationships between X and Y of this type.</p> <p><bold>Aim:<italic> </italic></bold>To demonstrate the specific characteristics of the application of stratification, moving average and cumulative probability function methods in the construction and analysis of logistic regression models in the context of health risk assessment.</p> <p><bold>Materials and methods:<italic> </italic></bold>The analysis of logistic regression models employs a range of statistical methods, including the stratification, moving average, cumulative probability function, goodness-of-fit tests, and proportion comparison tests.</p> <p><bold>Results:<italic> </italic></bold>It is shown that the standard stratification methods are not sufficient for exploring the nature of the relationships between dichotomous Y and quantitative X. Additional methods, including moving average and cumulative likelihood function, facilitate the identification of features characterizing these relationships. The utility of graphical representations of logistic regression results in elucidating the statistical relationships between variables X and Y is demonstrated. The efficacy of the stratification, moving average and cumulative probability function methods is illustrated by examples from the field of epidemiology.</p> <p><bold>Conclusion:</bold> The combination of moving average and cumulative probability function methods with stratification enables the reliable identification of the nature of the relationship between dichotomous Y and quantitative X, as well as the potential for deviations from the conditions of applicability of logistic regression models.</p></abstract><trans-abstract xml:lang="ru"><p><bold>Обоснование.</bold> Методы логистической регрессии являются наиболее используемыми для установления статистических связей между количественными предикторами <italic>Х</italic> и дихотомическим откликом <italic>Y</italic> (<italic>Y</italic>=0 или <italic>Y</italic>=1). Именно поэтому разработка новых подходов к анализу связей между <italic>Х</italic> и <italic>Y</italic> такого типа является актуальной.</p> <p><bold>Цель.</bold> Показать особенности применения методов стратификации, скользящего среднего и функции кумулятивной вероятности при построении и анализе моделей логистической регрессии в задачах оценки риска здоровью.</p> <p><bold>Материалы и методы.</bold> Для анализа моделей логистической регрессии используются методы стратификации, скользящего среднего, функции кумулятивной вероятности, а также критерии согласия и методы сравнения долей.</p> <p><bold>Результаты.</bold> Показано, что стандартные методы стратификации недостаточны для оценки характера связей между дихотомическим <italic>Y</italic> и количественным <italic>Х</italic>. Дополнительные методы (скользящее среднее и функция кумулятивной вероятности) позволяют выявить особенности этих связей. Показана роль графического представления результатов логистической регрессии для понимания статистических связей между переменными <italic>Х</italic> и <italic>Y</italic>. Результаты применения методов стратификации, скользящего среднего и функции кумулятивной вероятности иллюстрируются примерами из области эпидемиологии.</p> <p><bold>Заключение.</bold> Методы скользящего среднего и функции кумулятивной вероятности в сочетании со стратификацией позволяют надёжно идентифицировать характер связи между дихотомическим <italic>Y</italic> и количественным <italic>Х</italic> и выявить возможные отклонения от условий применимости моделей логистической регрессии.</p></trans-abstract><trans-abstract xml:lang="zh"><p>论证。逻辑回归法是建立定量预测因子X与二元响应变量Y（Y=0或Y=1）之间统计关系的最常用方法。这就是开发新的方法来分析X和Y之间的关系变得如此迫切的原因。</p> <p>目的。说明在健康风险评估任务中构建和分析逻辑回归模型时应用分层、移动平均数和累积概率函数方法的特殊性。</p> <p>材料和方法。使用分层、移动平均数、累积概率函数，以及拟合优度准则和份额比较方法来分析逻辑回归模型。</p> <p>结果。结果表明，标准的分层方法不足以评估二元变量Y与定量X之间关系的性质。其他方法（移动平均数和累积概率函数）可以确定这些关系的特性。逻辑回归结果的图形表示法在理解变量X和 Y之间的统计关系方面的作用显而易见。以流行病学领域的实例说明了分层法、移动平均数和累积概率函数法的应用结果。</p> <p>结论。移动平均数和累积概率函数法与分层相结合，能够可靠地确定二元变量Y与定量X之间关系的性质，并确定逻辑回归模型适用条件的可能偏差。</p></trans-abstract><kwd-group xml:lang="en"><kwd>logistic models</kwd><kwd>model adequacy</kwd><kwd>statistical significance</kwd><kwd>stratification</kwd><kwd>moving average</kwd><kwd>cumulative probability function</kwd><kwd>cardiovascular diseases</kwd><kwd>thyroid diseases</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>модели логистической регрессии</kwd><kwd>адекватность модели</kwd><kwd>статистическая значимость</kwd><kwd>стратификация</kwd><kwd>скользящее среднее</kwd><kwd>функция кумулятивной вероятности</kwd><kwd>сердечно-сосудистые заболевания</kwd><kwd>заболевания щитовидной железы</kwd></kwd-group><kwd-group xml:lang="zh"><kwd>逻辑回归模型</kwd><kwd>模型充分性</kwd><kwd>统计意义</kwd><kwd>分层</kwd><kwd>移动平均数</kwd><kwd>累积概率函数</kwd><kwd>心血管疾病</kwd><kwd>甲状腺疾病</kwd></kwd-group><funding-group><award-group><funding-source><institution-wrap><institution xml:lang="en">Ministry of Science and Higher Education of the Russian Federation</institution></institution-wrap><institution-wrap><institution xml:lang="ru">Министерство образования и науки Российской Федерации</institution></institution-wrap><institution-wrap><institution xml:lang="zh">Ministry of Science and Higher Education of the Russian Federation</institution></institution-wrap></funding-source><award-id>AAAA-A19-119111990097-4</award-id></award-group></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Ayvazyan SA, Yenyukov IS, Meshalkin LD. 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