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-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Cox · Survival.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">Survival.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../getting_started/">Getting Started</a></li><li><a class="tocitem" href="../events/">Event Times</a></li><li><a class="tocitem" href="../km/">Kaplan-Meier</a></li><li><a class="tocitem" href="../na/">Nelson-Aalen</a></li><li class="is-active"><a class="tocitem" href>Cox</a><ul class="internal"><li><a class="tocitem" href="#API"><span>API</span></a></li><li><a class="tocitem" href="#References"><span>References</span></a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Cox</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Cox</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaStats/Survival.jl/blob/main/docs/src/cox.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Cox-Proportional-Hazards-Model"><a class="docs-heading-anchor" href="#Cox-Proportional-Hazards-Model">Cox Proportional Hazards Model</a><a id="Cox-Proportional-Hazards-Model-1"></a><a class="docs-heading-anchor-permalink" href="#Cox-Proportional-Hazards-Model" title="Permalink"></a></h1><p>The <a href="https://en.wikipedia.org/wiki/Proportional_hazards_model">Cox proportional hazards model</a> is a semiparametric regression model used to fit survival models without knowing the distribution. It is based on the assumption that covariates affect the hazard function multiplicatively. That is,</p><p class="math-container">\[\lambda(t | X_i) = \lambda_0(t) \exp(X_i \cdot \beta)\]</p><p>where <span>$\lambda(t|X_i)$</span> is the estimated hazard for sample <span>$i$</span>, <span>$\lambda_0$</span> is the baseline hazard, <span>$X_i$</span> is the vector of covariates for sample <span>$i$</span>, and <span>$\beta$</span> is the vector of coefficients in the model.</p><h2 id="API"><a class="docs-heading-anchor" href="#API">API</a><a id="API-1"></a><a class="docs-heading-anchor-permalink" href="#API" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="StatsAPI.fit-Tuple{Type{CoxModel}, AbstractMatrix, AbstractVector}" href="#StatsAPI.fit-Tuple{Type{CoxModel}, AbstractMatrix, AbstractVector}"><code>StatsAPI.fit</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">fit(::Type{CoxModel}, M::AbstractMatrix, y::AbstractVector; kwargs...)</code></pre><p>Given a matrix <code>M</code> of predictors and a corresponding vector of events, compute the Cox proportional hazard model estimate of coefficients. Returns a <code>CoxModel</code> object.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaStats/Survival.jl/blob/cb9bb8c715ee7ddafaa64c7c7aad4e13c79f408d/src/cox.jl#L219-L225">source</a></section></article><h2 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h2><ul><li>Cox, D. R. (1972). <em>Regression models and life tables (with discussion)</em>. Journal of the Royal Statistical Society, Series B, 34:187–220.</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../na/">« Nelson-Aalen</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.24 on <span class="colophon-date" title="Wednesday 28 June 2023 18:58">Wednesday 28 June 2023</span>. Using Julia version 1.9.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Cox · Survival.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">Survival.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../getting_started/">Getting Started</a></li><li><a class="tocitem" href="../events/">Event Times</a></li><li><a class="tocitem" href="../km/">Kaplan-Meier</a></li><li><a class="tocitem" href="../na/">Nelson-Aalen</a></li><li class="is-active"><a class="tocitem" href>Cox</a><ul class="internal"><li><a class="tocitem" href="#API"><span>API</span></a></li><li><a class="tocitem" href="#References"><span>References</span></a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Cox</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Cox</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaStats/Survival.jl/blob/main/docs/src/cox.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Cox-Proportional-Hazards-Model"><a class="docs-heading-anchor" href="#Cox-Proportional-Hazards-Model">Cox Proportional Hazards Model</a><a id="Cox-Proportional-Hazards-Model-1"></a><a class="docs-heading-anchor-permalink" href="#Cox-Proportional-Hazards-Model" title="Permalink"></a></h1><p>The <a href="https://en.wikipedia.org/wiki/Proportional_hazards_model">Cox proportional hazards model</a> is a semiparametric regression model used to fit survival models without knowing the distribution. It is based on the assumption that covariates affect the hazard function multiplicatively. That is,</p><p class="math-container">\[\lambda(t | X_i) = \lambda_0(t) \exp(X_i \cdot \beta)\]</p><p>where <span>$\lambda(t|X_i)$</span> is the estimated hazard for sample <span>$i$</span>, <span>$\lambda_0$</span> is the baseline hazard, <span>$X_i$</span> is the vector of covariates for sample <span>$i$</span>, and <span>$\beta$</span> is the vector of coefficients in the model.</p><h2 id="API"><a class="docs-heading-anchor" href="#API">API</a><a id="API-1"></a><a class="docs-heading-anchor-permalink" href="#API" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="StatsAPI.fit-Tuple{Type{CoxModel}, AbstractMatrix, AbstractVector}" href="#StatsAPI.fit-Tuple{Type{CoxModel}, AbstractMatrix, AbstractVector}"><code>StatsAPI.fit</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">fit(::Type{CoxModel}, M::AbstractMatrix, y::AbstractVector; kwargs...)</code></pre><p>Given a matrix <code>M</code> of predictors and a corresponding vector of events, compute the Cox proportional hazard model estimate of coefficients. Returns a <code>CoxModel</code> object.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaStats/Survival.jl/blob/9d4319f4a356bfefd22cf98386878de9b7f45f91/src/cox.jl#L219-L225">source</a></section></article><h2 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h2><ul><li>Cox, D. R. (1972). <em>Regression models and life tables (with discussion)</em>. Journal of the Royal Statistical Society, Series B, 34:187–220.</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../na/">« Nelson-Aalen</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 8 April 2024 15:57">Monday 8 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>