Application of Logistic model combined with ROC curve and Bayes discriminant function in the diagnosis of severity of COVID-19
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摘要:
目的 使用两种统计方法（Logistic模型联合ROC曲线法和Bayes判别函数法）对新型冠状病毒肺炎（简称新冠肺炎，corona virus disease 2019，COVID-19）患者严重程度进行预测，以期辅助临床对于患者分型早期诊断。 方法 收集538名确诊病例的人口学相关信息、临床资料及流行病学调查资料等，计数资料使用例数（%）表示，采用Logistic回归分析模型进行单因素和多因素回归分析；采用ROC曲线法找到最佳临界值；采用Bayes判别法对研究对象进行分类。 结果 Logistic模型联合ROC曲线法的总体预测准确率分别为0.682，重症预测正确率为0.784，轻症预测正确率为0.662；Bayes判别法总体预测准确率分别为0.703，重症预测正确率为0.705，轻症预测正确率为0.702。 结论 Logistic模型联合ROC曲线法与Bayes判别分析在鉴别COVID-19临床严重程度诊断中均有较高的正确率，且各有优势，两种方法均有一定的应用价值。 -
关键词:
- 新型冠状病毒肺炎 /
- 临床严重程度 /
- Logistic回归分析模型 /
- ROC曲线 /
- Bayes函数
Abstract:Objective corona virus disease 2019(COVID-19) patients were predicted by two statistical methods (Logistic model combined with ROC curve and Bayes discriminant function), in order to assist the clinical classification of patients for early diagnosis. Methods Demography related information, clinical data and epidemiological investigation data of 538 confirmed cases was collected. Number of cases (%) was used to describe categorical data. Logistic model is used for single factor and multi factor regression analysis; ROC curve method is used to find the optimum critical point; Bayes discriminant method is used to classify the subjects. Results The overall prediction accuracy of the Logistic combined ROC curve method was 0.682, the prediction accuracy of severe symptoms cases was 0.784, and that of mild symptoms cases was 0.662. The overall prediction accuracy of Bayes discriminant method was 0.703, the prediction accuracy of severe symptoms cases was 0.705, and that of mild symptoms cases was 0.702. Conclusions Logistic regression analysis model combined ROC curve method and Bayes discriminant analysis both have high accuracy in the diagnosis of clinical severity of COVID-19, and each has its own advantages. Both of them have certain application value. -
Key words:
- COVID-19 /
- Clinical severity /
- Logistic regression analysis model /
- ROC curve /
- Bayes function
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图 1 多因素Logistic模型预测概率值的ROC曲线
Figure 1. The ROC curve of probability value predicted by multivariate Logistic model
表 1 变量赋值
Table 1. Variable assignment
指标 赋值 严重程度 1=重症，0=轻症 性别 1=男，2=女 年龄(岁) 连续型变量 发病到确诊时间(d) 连续型变量 病例来源 1=输入病例，2=本地病例 是否为无症状感染者 1=是，0=否 患基础性疾病 1=有，0=无 是否有相关临床症状 1=是，0=否 临床症状数量 连续型变量 注：相关临床症状包括：发热、咳嗽、肺炎、流鼻水、喉咙痛、腹泻等消化道症状、肌肉/关节酸痛、头痛/头晕、乏力、胸闷、畏寒/寒颤、咳痰。 
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表 2 以临床严重程度为因变量构建的单因素和多因素Logistic回归分析模型
Table 2. Univariate and multivariate Logistic models constructed with clinical severity as the dependent variable
变量 单因素分析 多因素分析 OR(95% CI)值 P值 OR(95% CI)值 P值 是否为无症状感染者 否 1.000 1.000 是 0.310 (0.109~0.875) 0.027 0.695 (0.199~2.423) 0.568 是否伴基础性疾病 否 1.000 1.000 是 3.231 (2.023~5.160) < 0.001 1.983 (1.165~3.374) 0.012 是否有发热症状 否 1.000 1.000 是 1.817 (1.126~2.930) 0.014 1.462 (0.775~2.757) 0.241 是否有咳嗽症状 否 1.000 1.000 是 2.068 (1.302~3.283) 0.002 1.51 (0.825~2.764) 0.182 是否有肺炎症状 否 1.000 1.000 是 1.662 (1.030~2.680) 0.037 1.091 (0.607~1.962) 0.770 年龄(岁) 1.060 (1.043~1.078) < 0.001 1.062 (1.042~1.083) < 0.001 发病到确诊时间(d) 1.066 (1.019~1.115) 0.005 1.042 (0.988~1.098) 0.130 临床症状数量 1.332 (1.154~1.538) < 0.001 1.240(0.976~1.577) 0.078
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表 3 单因素Bayes判别分析
Table 3. Single factor Bayes discriminant analysis
变量 Wilk's λ值 P值 年龄 0.898 < 0.001 发病到确诊时间 0.985 0.004 是否为无症状感染者 0.990 0.020 伴基础性疾病 0.971 < 0.001 是否有发热症状 0.989 0.013 是否有咳嗽症状 0.982 0.002 是否有肺炎症状 0.992 0.036 临床症状数量 0.970 < 0.001
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表 4 多因素Bayes判别函数系数
Table 4. Multivariate Bayes discriminant function coefficient
变量 临床症状 Wilk's λ值 P值 年龄 6.51 6.367 发病到确诊时间 0.289 -0.508 是否为无症状感染者 2.02 1.672 是否伴基础性疾病 1.006 0.593 是否有发热症状 0.526 0.480 是否有咳嗽症状 0.238 0.185 是否有肺炎症状 0.181 0.149 临床症状数量 1.488 1.276 常量 -11.667 -7.531
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表 5 两种预测方法预测准确度比较[n(%)]
Table 5. Comparison of prediction accuracy between the two prediction methods [n(%)]
预测结果 重症 轻症 P值 Logistic联合ROC曲线法 < 0.001 重症 69(78.4) 152(33.8) 轻症 19(21.6) 298(66.2) Bayes判别法 < 0.001 重症 62(70.5) 134(29.8) 轻症 26(29.5) 316(70.2)
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