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            <h1 id="seo-header">生存分析的Cox比例风险回归模型</h1>
            
            
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                <p>如果只研究患者的中位生存时间或限制平均生存时间，或比较某一变量的限制平均生存时间，可以采用<a target="_blank" rel="noopener" href="https://occdn.limour.top/1949.html">生存分析</a>。如果自变量有多个，需要从中寻找主要的影响因素，则可以采用Cox回归模型进行分析。若某一变量的βj&#x3D;0，则称其对风险函数无贡献。对风险函数无贡献的变量可以从模型中剔除，然后重现计算新的Cox模型，称为用Cox回归分析的<strong>逐步回归方法</strong>对变量进行筛选。（《卫生统计学》赵耐青，下同）</p>
<p>多个自变量之间有可能存在交互作用，比如催化剂的单独效应为零，与其他因素配合却能较大地提高效应。在回归分析中，若，X1、X2之间存在交互作用，最常用的方法是在回归模型中增加这两个变量的乘积项X1X2作为新的自变量，称为<strong>交互作用项</strong>。交互作用项的引入主要根据研究的背景知识。</p>
<p><a target="_blank" rel="noopener" href="https://occdn.limour.top/2099.html">Logisitic回归</a>和Cox回归均基于大样本的假定，因此所需要的样本含量多于多重线性回归，需要达到<strong>模型自变量个数的15~20倍</strong>。如果样本含量较小，则难以得到稳定可靠的结论。</p>
<p><img src="https://img-cdn.limour.top/2022/07/17/62d3463eb5034.png" srcset="https://jscdn.limour.top/gh/Limour-dev/Sakurairo_Vision/load_svg/inload.svg" lazyload></p>
<h2 id="Cox回归的假设"><a href="#Cox回归的假设" class="headerlink" title="Cox回归的假设"></a>Cox回归的假设</h2><ul>
<li>HR不随时间变化，满足比例风险假定</li>
<li>无“过早死亡”的个体和“活得太久”的个体</li>
<li>连续自变量具有线性形式，自变量间无共线性</li>
</ul>
<p>参考1：<a target="_blank" rel="noopener" href="https://www.jianshu.com/p/97180e6cf884">JeremyL</a></p>
<h2 id="准备资料"><a href="#准备资料" class="headerlink" title="准备资料"></a>准备资料</h2><figure class="highlight r"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><code class="hljs R">group <span class="hljs-operator">&lt;-</span> t<span class="hljs-punctuation">(</span>readRDS<span class="hljs-punctuation">(</span><span class="hljs-string">&#x27;prad_tpm_Cu_death.rds&#x27;</span><span class="hljs-punctuation">)</span><span class="hljs-punctuation">)</span><br>clinical <span class="hljs-operator">&lt;-</span> read.csv<span class="hljs-punctuation">(</span><span class="hljs-string">&#x27;TCGA-PRAD_clinical.csv&#x27;</span><span class="hljs-punctuation">,</span> row.names <span class="hljs-operator">=</span> <span class="hljs-string">&#x27;bcr_patient_barcode&#x27;</span><span class="hljs-punctuation">)</span><br>mergeID <span class="hljs-operator">&lt;-</span> intersect<span class="hljs-punctuation">(</span>rownames<span class="hljs-punctuation">(</span>clinical<span class="hljs-punctuation">)</span><span class="hljs-punctuation">,</span> rownames<span class="hljs-punctuation">(</span>group<span class="hljs-punctuation">)</span><span class="hljs-punctuation">)</span><br>df <span class="hljs-operator">&lt;-</span> cbind<span class="hljs-punctuation">(</span>group<span class="hljs-punctuation">[</span>mergeID<span class="hljs-punctuation">,</span><span class="hljs-punctuation">]</span><span class="hljs-punctuation">,</span> clinical<span class="hljs-punctuation">[</span>mergeID<span class="hljs-punctuation">,</span> <span class="hljs-built_in">c</span><span class="hljs-punctuation">(</span><span class="hljs-string">&#x27;dcf_time&#x27;</span><span class="hljs-punctuation">,</span> <span class="hljs-string">&#x27;dcf_status&#x27;</span><span class="hljs-punctuation">,</span> <span class="hljs-string">&#x27;os_time&#x27;</span><span class="hljs-punctuation">,</span> <span class="hljs-string">&#x27;os_status&#x27;</span><span class="hljs-punctuation">)</span><span class="hljs-punctuation">]</span><span class="hljs-punctuation">)</span><br>df<span class="hljs-punctuation">[</span><span class="hljs-punctuation">,</span><span class="hljs-string">&#x27;dcf_status&#x27;</span><span class="hljs-punctuation">]</span> <span class="hljs-operator">=</span> ifelse<span class="hljs-punctuation">(</span>df<span class="hljs-punctuation">[</span><span class="hljs-punctuation">,</span><span class="hljs-string">&#x27;dcf_status&#x27;</span><span class="hljs-punctuation">]</span><span class="hljs-operator">==</span><span class="hljs-number">1</span><span class="hljs-punctuation">,</span><span class="hljs-number">0</span><span class="hljs-punctuation">,</span><span class="hljs-number">1</span><span class="hljs-punctuation">)</span><br>df<br></code></pre></td></tr></table></figure>

<h2 id="Cox回归"><a href="#Cox回归" class="headerlink" title="Cox回归"></a>Cox回归</h2><figure class="highlight r"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br></pre></td><td class="code"><pre><code class="hljs R">library<span class="hljs-punctuation">(</span><span class="hljs-string">&quot;survival&quot;</span><span class="hljs-punctuation">)</span><br>library<span class="hljs-punctuation">(</span><span class="hljs-string">&quot;survminer&quot;</span><span class="hljs-punctuation">)</span><br>coxmf <span class="hljs-operator">&lt;-</span> paste0<span class="hljs-punctuation">(</span><span class="hljs-string">&quot;Surv(dcf_time/365, dcf_status==0)~&quot;</span><span class="hljs-punctuation">,</span> paste<span class="hljs-punctuation">(</span>colnames<span class="hljs-punctuation">(</span>df<span class="hljs-punctuation">)</span><span class="hljs-punctuation">[</span><span class="hljs-number">1</span><span class="hljs-operator">:</span><span class="hljs-number">10</span><span class="hljs-punctuation">]</span><span class="hljs-punctuation">,</span> collapse <span class="hljs-operator">=</span> <span class="hljs-string">&#x27;+&#x27;</span><span class="hljs-punctuation">)</span><span class="hljs-punctuation">)</span><br>coxmf<br>res.cox <span class="hljs-operator">&lt;-</span> coxph<span class="hljs-punctuation">(</span>formula<span class="hljs-punctuation">(</span>coxmf<span class="hljs-punctuation">)</span><span class="hljs-punctuation">,</span> data <span class="hljs-operator">=</span>  df<span class="hljs-punctuation">)</span><br>res.cox<br>tmp_res <span class="hljs-operator">&lt;-</span> summary<span class="hljs-punctuation">(</span>res.cox<span class="hljs-punctuation">)</span><br>res <span class="hljs-operator">&lt;-</span> as.data.frame<span class="hljs-punctuation">(</span>tmp_res<span class="hljs-operator">$</span>conf.int<span class="hljs-punctuation">)</span><br>res <span class="hljs-operator">&lt;-</span> res<span class="hljs-punctuation">[</span><span class="hljs-punctuation">,</span><span class="hljs-built_in">c</span><span class="hljs-punctuation">(</span><span class="hljs-number">1</span><span class="hljs-punctuation">,</span><span class="hljs-number">3</span><span class="hljs-punctuation">,</span><span class="hljs-number">4</span><span class="hljs-punctuation">)</span><span class="hljs-punctuation">]</span><br>colnames<span class="hljs-punctuation">(</span>res<span class="hljs-punctuation">)</span> <span class="hljs-operator">&lt;-</span> <span class="hljs-built_in">c</span><span class="hljs-punctuation">(</span><span class="hljs-string">&#x27;mean&#x27;</span><span class="hljs-punctuation">,</span> <span class="hljs-string">&#x27;lower&#x27;</span><span class="hljs-punctuation">,</span> <span class="hljs-string">&#x27;upper&#x27;</span><span class="hljs-punctuation">)</span><br>res<span class="hljs-punctuation">[[</span><span class="hljs-string">&#x27;Pvalue&#x27;</span><span class="hljs-punctuation">]</span><span class="hljs-punctuation">]</span> <span class="hljs-operator">&lt;-</span> tmp_res<span class="hljs-operator">$</span>coefficients<span class="hljs-punctuation">[</span><span class="hljs-punctuation">,</span><span class="hljs-string">&#x27;Pr(&gt;z)&#x27;</span><span class="hljs-punctuation">]</span><br>res<span class="hljs-punctuation">[[</span><span class="hljs-string">&#x27;VarName&#x27;</span><span class="hljs-punctuation">]</span><span class="hljs-punctuation">]</span> <span class="hljs-operator">&lt;-</span> rownames<span class="hljs-punctuation">(</span>res<span class="hljs-punctuation">)</span><br>res<br>saveRDS<span class="hljs-punctuation">(</span>res<span class="hljs-punctuation">,</span> <span class="hljs-string">&#x27;Cox_res.rds&#x27;</span><span class="hljs-punctuation">)</span><br></code></pre></td></tr></table></figure>

<h2 id="Cox模型进行预测"><a href="#Cox模型进行预测" class="headerlink" title="Cox模型进行预测"></a>Cox模型进行预测</h2><p>想要评估GLS对估计生存概率的影响。在本例中，构造了一个有两行的新数据，每一行代表一个GLS值;其他自变量设置为它们的平均值(如果是连续变量)或最低水平(如果是离散变量)。对于一个哑变量，平均值是数据集中编码为1的比例。（<a target="_blank" rel="noopener" href="https://www.jianshu.com/p/3f53255f8b60">JeremyL</a>）</p>
<figure class="highlight r"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><code class="hljs R">gls_df <span class="hljs-operator">&lt;-</span> as.data.frame<span class="hljs-punctuation">(</span>rbind<span class="hljs-punctuation">(</span>colMeans<span class="hljs-punctuation">(</span>df<span class="hljs-punctuation">[</span><span class="hljs-number">1</span><span class="hljs-operator">:</span><span class="hljs-number">10</span><span class="hljs-punctuation">]</span><span class="hljs-punctuation">)</span><span class="hljs-punctuation">,</span>colMeans<span class="hljs-punctuation">(</span>df<span class="hljs-punctuation">[</span><span class="hljs-number">1</span><span class="hljs-operator">:</span><span class="hljs-number">10</span><span class="hljs-punctuation">]</span><span class="hljs-punctuation">)</span><span class="hljs-punctuation">)</span><span class="hljs-punctuation">)</span><br>gls_df<span class="hljs-punctuation">[[</span><span class="hljs-string">&#x27;GLS&#x27;</span><span class="hljs-punctuation">]</span><span class="hljs-punctuation">]</span> <span class="hljs-operator">&lt;-</span> with<span class="hljs-punctuation">(</span>df<span class="hljs-punctuation">,</span><span class="hljs-built_in">c</span><span class="hljs-punctuation">(</span><span class="hljs-built_in">min</span><span class="hljs-punctuation">(</span>GLS<span class="hljs-punctuation">)</span><span class="hljs-punctuation">,</span><span class="hljs-built_in">max</span><span class="hljs-punctuation">(</span>GLS<span class="hljs-punctuation">)</span><span class="hljs-punctuation">)</span><span class="hljs-punctuation">)</span><br>gls_df<br>ggsurvplot<span class="hljs-punctuation">(</span>survfit<span class="hljs-punctuation">(</span>res.cox<span class="hljs-punctuation">,</span> newdata <span class="hljs-operator">=</span> gls_df<span class="hljs-punctuation">)</span><span class="hljs-punctuation">,</span> conf.int <span class="hljs-operator">=</span> <span class="hljs-literal">TRUE</span><span class="hljs-punctuation">,</span><span class="hljs-punctuation">,</span>data <span class="hljs-operator">=</span> df<span class="hljs-punctuation">)</span><br></code></pre></td></tr></table></figure>

<h2 id="检测是否满足假设"><a href="#检测是否满足假设" class="headerlink" title="检测是否满足假设"></a><a target="_blank" rel="noopener" href="https://www.jianshu.com/p/97180e6cf884">检测是否满足假设</a></h2><ul>
<li><p>比例风险假设</p>
</li>
<li><p>test.ph &lt;- cox.zph(res.cox)</p>
</li>
<li><p>ggcoxzph(test.ph)</p>
</li>
<li><p>p无统计学意义表示满足假设</p>
</li>
<li><p>无离群值</p>
</li>
<li><p>ggcoxdiagnostics(res.cox, type &#x3D; “dfbeta”, linear.predictions &#x3D; F)</p>
</li>
<li><p>ggcoxdiagnostics(res.cox, type &#x3D; “deviance”, linear.predictions &#x3D; F)</p>
</li>
<li><p>线性假设</p>
</li>
<li><p>ggcoxfunctional(Surv(dcf_time&#x2F;365, dcf_status&#x3D;&#x3D;0) ~ GLS + log(GLS) + sqrt(GLS), data &#x3D; df)</p>
</li>
<li><p>ggcoxfunctional(formula(coxmf), data &#x3D; df)</p>
</li>
<li><p>拟合线应该是线性的表示满足Cox比例风险模型的假设</p>
</li>
</ul>

                
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