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href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=zh.wikipedia.org&uselang=zh"><span>资助维基百科</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E9%A3%8E%E9%99%A9%E6%AF%94" title="我们推荐您创建账号并登录，但这不是强制性的"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E9%A3%8E%E9%99%A9%E6%AF%94" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-定义" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#定义"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>定义</span> </div> </a> <ul id="toc-定义-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-应用" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#应用"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>应用</span> </div> </a> <ul id="toc-应用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>参考文献</span> </div> </a> <ul id="toc-参考文献-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="目录" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">开关目录</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">风险比</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。8种语言可用" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-8" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">8种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B3%D8%A8%D8%A9_%D8%A7%D9%84%D8%AE%D8%B7%D8%B1" title="نسبة الخطر – 阿拉伯语" lang="ar" hreflang="ar" data-title="نسبة الخطر" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Hazard_ratio" title="Hazard ratio – 英语" lang="en" hreflang="en" data-title="Hazard ratio" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rapporto_di_rischio" title="Rapporto di rischio – 意大利语" lang="it" hreflang="it" data-title="Rapporto di rischio" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%8F%E3%82%B6%E3%83%BC%E3%83%89%E6%AF%94" title="ハザード比 – 日语" lang="ja" hreflang="ja" data-title="ハザード比" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wsp%C3%B3%C5%82czynnik_ryzyka" title="Współczynnik ryzyka – 波兰语" lang="pl" hreflang="pl" data-title="Współczynnik ryzyka" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Raz%C3%A3o_de_risco" title="Razão de risco – 葡萄牙语" lang="pt" hreflang="pt" data-title="Razão de risco" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D1%82%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%B8%D0%B5_%D1%80%D0%B8%D1%81%D0%BA%D0%BE%D0%B2" title="Отношение рисков – 俄语" lang="ru" hreflang="ru" data-title="Отношение рисков" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Rasio_bencana" title="Rasio bencana – 巽他语" lang="su" hreflang="su" data-title="Rasio bencana" data-language-autonym="Sunda" data-language-local-name="巽他语" class="interlanguage-link-target"><span>Sunda</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q3930246#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="命名空间"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E9%A3%8E%E9%99%A9%E6%AF%94" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E9%A3%8E%E9%99%A9%E6%AF%94" rel="discussion" title="关于此页面的讨论[t]" accesskey="t"><span>讨论</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="更改语言变体" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">不转换</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-zh mw-list-item"><a href="/zh/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh" hreflang="zh"><span>不转换</span></a></li><li id="ca-varlang-1" class="ca-variants-zh-Hans mw-list-item"><a href="/zh-hans/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh-Hans" hreflang="zh-Hans"><span>简体</span></a></li><li id="ca-varlang-2" class="ca-variants-zh-Hant mw-list-item"><a href="/zh-hant/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh-Hant" hreflang="zh-Hant"><span>繁體</span></a></li><li id="ca-varlang-3" class="ca-variants-zh-Hans-CN mw-list-item"><a href="/zh-cn/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh-Hans-CN" hreflang="zh-Hans-CN"><span>大陆简体</span></a></li><li id="ca-varlang-4" class="ca-variants-zh-Hant-HK mw-list-item"><a href="/zh-hk/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh-Hant-HK" hreflang="zh-Hant-HK"><span>香港繁體</span></a></li><li id="ca-varlang-5" class="ca-variants-zh-Hant-MO mw-list-item"><a href="/zh-mo/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh-Hant-MO" hreflang="zh-Hant-MO"><span>澳門繁體</span></a></li><li id="ca-varlang-6" class="ca-variants-zh-Hans-MY mw-list-item"><a href="/zh-my/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh-Hans-MY" hreflang="zh-Hans-MY"><span>大马简体</span></a></li><li id="ca-varlang-7" class="ca-variants-zh-Hans-SG mw-list-item"><a href="/zh-sg/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh-Hans-SG" hreflang="zh-Hans-SG"><span>新加坡简体</span></a></li><li id="ca-varlang-8" class="ca-variants-zh-Hant-TW mw-list-item"><a href="/zh-tw/%E9%A3%8E%E9%99%A9%E6%AF%94" lang="zh-Hant-TW" hreflang="zh-Hant-TW"><span>臺灣正體</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="查看"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E9%A3%8E%E9%99%A9%E6%AF%94"><span>阅读</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E9%A3%8E%E9%99%A9%E6%AF%94&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E9%A3%8E%E9%99%A9%E6%AF%94&action=history" title="本页面的早前版本。[h]" accesskey="h"><span>查看历史</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="工具" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">工具</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">工具</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">隐藏</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="更多选项" > <div class="vector-menu-heading"> 操作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E9%A3%8E%E9%99%A9%E6%AF%94"><span>阅读</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E9%A3%8E%E9%99%A9%E6%AF%94&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E9%A3%8E%E9%99%A9%E6%AF%94&action=history"><span>查看历史</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 常规 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%85%A5%E9%A1%B5%E9%9D%A2/%E9%A3%8E%E9%99%A9%E6%AF%94" title="列出所有与本页相链的页面[j]" accesskey="j"><span>链入页面</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%87%BA%E6%9B%B4%E6%94%B9/%E9%A3%8E%E9%99%A9%E6%AF%94" rel="nofollow" title="页面链出所有页面的更改[k]" accesskey="k"><span>相关更改</span></a></li><li id="t-upload" class="mw-list-item"><a href="//zh.wikipedia.org/wiki/Project:上传" title="上传图像或多媒体文件[u]" accesskey="u"><span>上传文件</span></a></li><li id="t-permalink" 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</div> <div id="p-electronpdfservice-sidebar-portlet-heading" class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 打印/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E9%A3%8E%E9%99%A9%E6%AF%94&action=show-download-screen"><span>下载为PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p"><span>打印页面</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 在其他项目中 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a 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class="vector-pinnable-header-label">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><p><b>风险比率</b>，正式的英文名称是<a href="/wiki/Hazard_Ratio" class="mw-redirect" title="Hazard Ratio">Hazard Ratio</a>。风险比率是两个<a href="/w/index.php?title=%E9%A3%8E%E9%99%A9%E7%8E%87&action=edit&redlink=1" class="new" title="风险率（页面不存在）">风险率</a>（<span class="ilh-all" data-orig-title="Hazard Rates" data-lang-code="en" data-lang-name="英语" data-foreign-title="Hazard Rates"><span class="ilh-page"><a href="/w/index.php?title=Hazard_Rates&action=edit&redlink=1" class="new" title="Hazard Rates（页面不存在）">Hazard Rates</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Hazard_Rates" class="extiw" title="en:Hazard Rates"><span lang="en" dir="auto">Hazard Rates</span></a></span><span class="ilh-paren">）</span></span></span>）的比值。风险率是单位时间内发生的事件数占<a href="/wiki/%E8%A2%AB%E8%AF%95" class="mw-redirect" title="被试">被试</a>总体的百分比。<a href="/w/index.php?title=%E7%9E%AC%E6%97%B6&action=edit&redlink=1" class="new" title="瞬时（页面不存在）">瞬时</a>风险率就是当时间间隔趋近于0时的风险率，公式如下： </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h(t)=\lim _{\Delta t\rightarrow 0}{\frac {\mathrm {observed\;events\;in\;interval} [t,t+\Delta t]/N(t)}{\Delta t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">d</mi> <mspace width="thickmathspace" /> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">s</mi> <mspace width="thickmathspace" /> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mspace width="thickmathspace" /> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> <mo stretchy="false">[</mo> <mi>t</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>N</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h(t)=\lim _{\Delta t\rightarrow 0}{\frac {\mathrm {observed\;events\;in\;interval} [t,t+\Delta t]/N(t)}{\Delta t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd1c3caec5b45693a610f3a23f2792486e793fa5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:55.208ex; height:6.009ex;" alt="{\displaystyle h(t)=\lim _{\Delta t\rightarrow 0}{\frac {\mathrm {observed\;events\;in\;interval} [t,t+\Delta t]/N(t)}{\Delta t}}}"></span></dd></dl></dd></dl> <p>举例来说，在一个药物实验中，如果在单位时间内，被试组的死亡人数是参照组的两倍，那么风险比率就是2。风险比率与相对风险（<a href="/wiki/Relative_risk" class="mw-redirect" title="Relative risk">relative risk</a>）有联系也有区别。风险比率反映了单位时间内的相对风险，是相对风险在单位时间内的一种反映<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。但是相对风险反映的是整个实验的累积风险，而风险比率能够反映每个时间点上的瞬时风险。相比较而言，风险比率更能避免<a href="/w/index.php?title=%E9%80%89%E6%8B%A9%E5%81%8F%E5%B7%AE&action=edit&redlink=1" class="new" title="选择偏差（页面不存在）">选择偏差</a>（<span class="ilh-all" data-orig-title="Selection bias" data-lang-code="en" data-lang-name="英语" data-foreign-title="selection bias"><span class="ilh-page"><a href="/w/index.php?title=Selection_bias&action=edit&redlink=1" class="new" title="Selection bias（页面不存在）">Selection bias</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/selection_bias" class="extiw" title="en:selection bias"><span lang="en" dir="auto">selection bias</span></a></span><span class="ilh-paren">）</span></span></span>）：假设在上例中死亡是集中发生的，如果将计算相对风险的<a href="/w/index.php?title=%E6%97%B6%E9%97%B4%E7%BB%93%E7%82%B9&action=edit&redlink=1" class="new" title="时间结点（页面不存在）">时间结点</a>选在集中死亡发生之前，那么相对风险就不能客观反映这个药物的效果，但是风险比率能够客观反映这个药物在每个时间点上的风险。 </p> <div class="mw-heading mw-heading2"><h2 id="定义"><span id=".E5.AE.9A.E4.B9.89"></span>定义</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%A3%8E%E9%99%A9%E6%AF%94&action=edit&section=1" title="编辑章节：定义"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>风险比率是两个风险率的比值。风险比率反映了两个风险率之间的差别。这种差别是由各种外生变量引起的，比如<a href="/w/index.php?title=%E5%B9%B2%E9%A2%84%E7%B1%BB%E5%9E%8B&action=edit&redlink=1" class="new" title="干预类型（页面不存在）">干预类型</a>（<span class="ilh-all" data-orig-title="treatment" data-lang-code="en" data-lang-name="英语" data-foreign-title="treatment"><span class="ilh-page"><a href="/w/index.php?title=Treatment&action=edit&redlink=1" class="new" title="Treatment（页面不存在）">treatment</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/treatment" class="extiw" title="en:treatment"><span lang="en" dir="auto">treatment</span></a></span><span class="ilh-paren">）</span></span></span>）的不同（比如用药或者不用药）、性别的影响（男性或者女性）等等。一般我们首先确定一个基准的风险率，然后通过<a href="/w/index.php?title=%E5%9B%9E%E5%BD%92%E6%96%B9%E7%A8%8B&action=edit&redlink=1" class="new" title="回归方程（页面不存在）">回归方程</a>来测算各种外生变量对于风险比率的影响。 </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log h(t)=f(h_{0}(t),\alpha +\beta _{1}X_{1}+\cdots +\beta _{k}X_{k}).\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> <mo>⁡</mo> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>α</mi> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log h(t)=f(h_{0}(t),\alpha +\beta _{1}X_{1}+\cdots +\beta _{k}X_{k}).\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5057142b3c1c32685d11e2d10dfb7b3331763781" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.141ex; height:2.843ex;" alt="{\displaystyle \log h(t)=f(h_{0}(t),\alpha +\beta _{1}X_{1}+\cdots +\beta _{k}X_{k}).\,}"></span></dd></dl></dd></dl> <p>这类方程通常被称作<a href="/w/index.php?title=%E6%AF%94%E7%8E%87%E9%A3%8E%E9%99%A9%E5%9B%9E%E5%BD%92%E6%A8%A1%E5%9E%8B&action=edit&redlink=1" class="new" title="比率风险回归模型（页面不存在）">比率风险回归模型</a>（<span class="ilh-all" data-orig-title="proportional hazards regression model" data-lang-code="en" data-lang-name="英语" data-foreign-title="Proportional hazards models"><span class="ilh-page"><a href="/w/index.php?title=Proportional_hazards_regression_model&action=edit&redlink=1" class="new" title="Proportional hazards regression model（页面不存在）">proportional hazards regression model</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Proportional_hazards_models" class="extiw" title="en:Proportional hazards models"><span lang="en" dir="auto">Proportional hazards models</span></a></span><span class="ilh-paren">）</span></span></span>）。著名的此类方程有<a href="/w/index.php?title=Cox&action=edit&redlink=1" class="new" title="Cox（页面不存在）">Cox</a> <span class="ilh-all" data-orig-title="semiparametric proportional hazards model" data-lang-code="en" data-lang-name="英语" data-foreign-title="Proportional hazards models"><span class="ilh-page"><a href="/w/index.php?title=Semiparametric_proportional_hazards_model&action=edit&redlink=1" class="new" title="Semiparametric proportional hazards model（页面不存在）">semiparametric proportional hazards model</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Proportional_hazards_models" class="extiw" title="en:Proportional hazards models"><span lang="en" dir="auto">Proportional hazards models</span></a></span><span class="ilh-paren">）</span></span></span> <sup id="cite_ref-Cox_2-0" class="reference"><a href="#cite_note-Cox-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>和<a href="/wiki/%E5%B9%82" class="mw-redirect" title="幂">幂</a>指数类型的<a href="/wiki/Gompertz" class="mw-redirect" title="Gompertz">Gompertz</a> and <span class="ilh-all" data-orig-title="Weibull" data-lang-code="en" data-lang-name="英语" data-foreign-title="Waloddi Weibull"><span class="ilh-page"><a href="/w/index.php?title=Weibull&action=edit&redlink=1" class="new" title="Weibull（页面不存在）">Weibull</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Waloddi_Weibull" class="extiw" title="en:Waloddi Weibull"><span lang="en" dir="auto">Waloddi Weibull</span></a></span><span class="ilh-paren">）</span></span></span> <span class="ilh-all" data-orig-title="parametric model" data-lang-code="en" data-lang-name="英语" data-foreign-title="Parametric model"><span class="ilh-page"><a href="/w/index.php?title=Parametric_model&action=edit&redlink=1" class="new" title="Parametric model（页面不存在）">parametric model</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Parametric_model" class="extiw" title="en:Parametric model"><span lang="en" dir="auto">Parametric model</span></a></span><span class="ilh-paren">）</span></span></span>。通常我们可以通过固定所有其他变量，比如<a href="/wiki/%E6%80%A7%E5%88%AB" title="性别">性别</a>、<a href="/wiki/%E5%B9%B4%E9%BE%84" title="年龄">年龄</a>、<a href="/wiki/%E7%8E%AF%E5%A2%83" class="mw-disambig" title="环境">环境</a>、<a href="/w/index.php?title=%E5%9C%B0%E7%82%B9&action=edit&redlink=1" class="new" title="地点（页面不存在）">地点</a>等等，来集中研究干预类型对于风险的影响，比如将使用某种特定药物的实验组与使用<a href="/wiki/%E5%AE%89%E6%85%B0%E5%89%82" class="mw-redirect" title="安慰剂">安慰剂</a>的对照组进行比较。如果有一些无法被固定的混杂因素，那么就采用<a href="/wiki/%E9%9A%8F%E6%9C%BA%E5%AF%B9%E7%85%A7%E8%AF%95%E9%AA%8C" title="随机对照试验">随机对照试验</a>的方法，来抵消这些<a href="/w/index.php?title=%E6%B7%B7%E6%9D%82%E5%9B%A0%E7%B4%A0&action=edit&redlink=1" class="new" title="混杂因素（页面不存在）">混杂因素</a>的影响，但是前提必须是研究对象数量要充足。 </p> <div class="mw-heading mw-heading2"><h2 id="应用"><span id=".E5.BA.94.E7.94.A8"></span>应用</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%A3%8E%E9%99%A9%E6%AF%94&action=edit&section=2" title="编辑章节：应用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Kaplan-Meier_curve_Tumor_Volume_Size.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Kaplan-Meier_curve_Tumor_Volume_Size.png/220px-Kaplan-Meier_curve_Tumor_Volume_Size.png" decoding="async" width="220" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Kaplan-Meier_curve_Tumor_Volume_Size.png/330px-Kaplan-Meier_curve_Tumor_Volume_Size.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Kaplan-Meier_curve_Tumor_Volume_Size.png/440px-Kaplan-Meier_curve_Tumor_Volume_Size.png 2x" data-file-width="512" data-file-height="584" /></a><figcaption><span class="ilh-all" data-orig-title="Kaplan-Meier curve" data-lang-code="en" data-lang-name="英语" data-foreign-title="Kaplan–Meier estimator"><span class="ilh-page"><a href="/w/index.php?title=Kaplan-Meier_curve&action=edit&redlink=1" class="new" title="Kaplan-Meier curve（页面不存在）">Kaplan-Meier curve</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator" class="extiw" title="en:Kaplan–Meier estimator"><span lang="en" dir="auto">Kaplan–Meier estimator</span></a></span><span class="ilh-paren">）</span></span></span> 表示脑部<a href="/wiki/%E8%82%BF%E7%98%A4" class="mw-redirect" title="肿瘤">肿瘤</a>转移程度对于生存率的影响 Elaimy et al. (2011)<sup id="cite_ref-Elaimy_3-0" class="reference"><a href="#cite_note-Elaimy-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>在<a href="/wiki/%E5%8C%BB%E5%AD%A6" title="医学">医学</a>和<a href="/wiki/%E5%85%AC%E5%85%B1%E5%8D%AB%E7%94%9F" title="公共卫生">公共卫生</a>研究中，常常使用风险比率来表示实验组与对照组之间的风险差别。<a href="/w/index.php?title=%E5%8D%A1%E6%99%AE%E5%85%B0-%E6%A2%85%E8%80%B6%E7%94%9F%E5%AD%98%E6%9B%B2%E7%BA%BF&action=edit&redlink=1" class="new" title="卡普兰-梅耶生存曲线（页面不存在）">卡普兰-梅耶生存曲线</a>（<span class="ilh-all" data-orig-title="Kaplan-Meier curve" data-lang-code="en" data-lang-name="英语" data-foreign-title="Kaplan–Meier estimator"><span class="ilh-page"><a href="/w/index.php?title=Kaplan-Meier_curve&action=edit&redlink=1" class="new" title="Kaplan-Meier curve（页面不存在）">Kaplan-Meier curve</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator" class="extiw" title="en:Kaplan–Meier estimator"><span lang="en" dir="auto">Kaplan–Meier estimator</span></a></span><span class="ilh-paren">）</span></span></span>）能够直观表示风险率。曲线上的点表示此时存活人数占全组人数的比值，即生存率。生存率与风险率之<a href="/wiki/%E5%92%8C" class="mw-disambig" title="和">和</a>为1.图中在任意一个时间点上，两个组的风险率之<a href="/wiki/%E6%AF%94" title="比">比</a>，就是风险比率。 </p> <div class="mw-heading mw-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%A3%8E%E9%99%A9%E6%AF%94&action=edit&section=3" title="编辑章节：参考文献"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation journal">Spruance,S.L. <a rel="nofollow" class="external text" href="http://aac.asm.org/content/48/8/2787.full.pdf+html"><i>Hazard ratio in clinical trials</i></a> <span style="font-size:85%;">(PDF)</span>. Antimicrobial Agents and Chemotherapy. 2004, <b>48</b> (8): pp. 2787–2792 <span class="reference-accessdate"> [<span class="nowrap">2013-08-09</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20180803201030/http://aac.asm.org/content/48/8/2787.full.pdf+html">存档</a> <span style="font-size:85%;">(PDF)</span>于2018-08-03）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%A3%8E%E9%99%A9%E6%AF%94&rft.atitle=Hazard+ratio+in+clinical+trials&rft.au=Spruance%2CS.L&rft.date=2004&rft.genre=article&rft.issue=8&rft.jtitle=Antimicrobial+Agents+and+Chemotherapy&rft.pages=pp.+2787-2792&rft.volume=48&rft_id=http%3A%2F%2Faac.asm.org%2Fcontent%2F48%2F8%2F2787.full.pdf%2Bhtml&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33"> 引文格式1维护：冗余文本 (<a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E5%86%97%E4%BD%99%E6%96%87%E6%9C%AC" title="Category:引文格式1维护：冗余文本">link</a>)</span> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20180803201030/http://aac.asm.org/content/48/8/2787.full.pdf+html">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</span> </li> <li id="cite_note-Cox-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cox_2-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Cox, D. R. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130620214140/http://hydra.usc.edu/pm518b/literature/cox-72.pdf">Regression-Models and Life-Tables</a> <span style="font-size:85%;">(PDF)</span>. Journal of the Royal Statistical Society. B (Methodological). 1972, <b>34</b> (2): 187–220 <span class="reference-accessdate"> [<span class="nowrap">5 December</span> 2012]</span>. （<a rel="nofollow" class="external text" href="http://hydra.usc.edu/pm518b/literature/cox-72.pdf">原始内容</a> <span style="font-size:85%;">(PDF)</span>存档于2013-06-20）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%A3%8E%E9%99%A9%E6%AF%94&rft.atitle=Regression-Models+and+Life-Tables&rft.aufirst=D.+R.&rft.aulast=Cox&rft.date=1972&rft.genre=article&rft.issue=2&rft.jtitle=Journal+of+the+Royal+Statistical+Society&rft.pages=187-220&rft.volume=34&rft_id=http%3A%2F%2Fhydra.usc.edu%2Fpm518b%2Fliterature%2Fcox-72.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20130620214140/http://hydra.usc.edu/pm518b/literature/cox-72.pdf">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</span> </li> <li id="cite_note-Elaimy-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Elaimy_3-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Elaimy, Ameer; Alexander R Mackay, Wayne T Lamoreaux, Robert K Fairbanks, John J Demakas, Barton S Cooke, Benjamin J Peressini, John T Holbrook, Christopher M Lee. <a rel="nofollow" class="external text" href="http://www.wjso.com/content/9/1/69">Multimodality treatment of brain metastases: an institutional survival analysis of 275 patients</a>. World Journal of Surgical Oncology. 5 July 2011, <b>9</b> (69) <span class="reference-accessdate"> [<span class="nowrap">2013-08-09</span>]</span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1186%2F1477-7819-9-69"><span title="數位物件識別號">doi:10.1186/1477-7819-9-69</span></a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20140227073512/http://www.wjso.com/content/9/1/69/">存档</a>于2014-02-27）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E9%A3%8E%E9%99%A9%E6%AF%94&rft.atitle=Multimodality+treatment+of+brain+metastases%3A+an+institutional+survival+analysis+of+275+patients&rft.aufirst=Ameer&rft.aulast=Elaimy&rft.date=2011-07-05&rft.genre=article&rft.issue=69&rft.jtitle=World+Journal+of+Surgical+Oncology&rft.volume=9&rft_id=http%3A%2F%2Fwww.wjso.com%2Fcontent%2F9%2F1%2F69&rft_id=info%3Adoi%2F10.1186%2F1477-7819-9-69&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span 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