Python自动进行logistic回归并绘制关于OR的森林图
首先定义如下函数：
import pandas as pd
import statsmodels.formula.api as smf
import statsmodels.api as sm
from scipy.stats import norm
import numpy as np
from plotnine import *
"""因变量y必须是int：0或1"""
def logistic_regression(y,x,df):
model = smf.glm(formula = f'{y} ~ {x}',
data = df,
family=sm.families.Binomial()).fit()
print(model.summary(), end='\n\n\n')
stat = pd.DataFrame({'p': model.pvalues, # series：每个β的p值
# 'beta': model.params, # series：β
# 'beta_lower_ci': model.conf_int().iloc[:, 0], #df：β的95%CI
# 'beta_upper_ci': model.conf_int().iloc[:, 1], #df：β的95%CI
'OR': np.exp(model.params), # series：OR
'OR_lower_ci': np.exp(model.params - norm.ppf(0.975)*model.bse),
'OR_upper_ci': np.exp(model.params + norm.ppf(0.975)*model.bse)})
stat['sig'] = stat.apply(lambda x : "*" if x['p']<0.05 else "no_sig",axis=1)
stat= stat.sort_values('OR', ascending=True)
print(stat)
"""绘制森林图：OR"""
forest_df = stat.drop("Intercept")\
.reset_index()\
.rename(columns={'index': 'independent_var'})\
.sort_values('OR', ascending=False)
print(ggplot(forest_df , aes(y='independent_var', x='OR')) + # y轴（自变量x）为连续变量或二分类变量
geom_point(aes(color='sig'),size=2) +
geom_errorbarh(aes(xmin='OR_lower_ci',
xmax='OR_upper_ci',
color ='sig'), height=0.1) +
scale_color_manual(values = ["red","black"]) +
scale_y_discrete(limits= forest_df["independent_var"]) +
guides(color=guide_legend(reverse=True))+
labs(title='logistic Regression', x='OR', y='variable')+
geom_vline(xintercept=1, linetype='dashed', color='black')+
theme_minimal()+
theme(plot_title=element_text(hjust=0.5)))以上函数logistic_regression(y,x,df)单独放在logistic_regression.py文件中，参考http://t.csdn.cn/ovlRZ
即可实现统计自动化。
准备待分析数据集df：
id age sex group T2DM HBP glucose
0 1 12 0 ctrl 0 0 15
1 2 40 0 ctrl 0 0 22
2 3 45 0 ctrl 0 0 24
3 4 67 0 ctrl 0 0 23
4 5 87 0 ctrl 1 0 26
5 6 65 0 disease 1 0 15
6 7 34 0 disease 1 0 23
7 8 67 0 disease 1 1 20
8 9 32 0 disease 1 1 19
9 10 59 0 disease 1 1 24
10 11 29 0 disease 1 1 23
11 12 48 0 disease 1 1 28
12 13 31 1 disease 0 1 22
13 14 32 1 disease 0 1 21
14 15 98 1 disease 0 1 24
15 16 99 1 disease 1 1 27
16 17 100 1 disease 1 1 28
17 18 101 1 disease 1 1 28
18 19 102 1 disease 0 1 30
19 20 103 1 disease 0 1 12
20 21 104 1 treat 0 1 13
21 22 105 1 treat 0 0 14
22 23 106 1 treat 0 0 15
23 24 107 1 treat 0 0 16
24 25 108 1 treat 0 0 17
25 26 109 1 treat 0 0 18
26 27 110 1 treat 0 0 19
27 28 111 1 treat 0 0 20
28 29 112 1 treat 1 0 21
29 30 113 1 treat 1 0 22
30 31 114 1 treat 1 1 23
31 32 115 1 treat 1 1 24
32 33 116 1 treat 1 1 25
33 34 117 1 treat 1 1 26
34 35 118 0 treat 0 1 27
35 36 119 0 treat 0 1 28
36 37 120 0 treat 0 1 29
37 38 121 0 treat 0 1 30
38 39 122 0 treat 0 1 31
39 40 123 0 treat 0 1 32
40 41 124 0 treat 0 0 33
41 42 125 0 treat 1 0 34
42 43 126 0 treat 1 0 35
43 44 127 0 treat 1 0 36
44 45 128 0 treat 1 0 37其中
sex是二分类变量，取值为0（女性）、1（男性）
T2DM是二分类变量，取值为0（不是T2DM）、1（是T2DM）
HBP是二分类变量，取值为0（不是HBP）、1（是HBP）
group是三分类变量
连续变量有age、glucose
以T2DM为因变量，sex、HBP、age、glucose为自变量，进行logistic回归，并绘制关于OR的森林图：
logistic_regression(y="T2DM",x="sex+HBP+age+glucose",df=df)输出为：
Generalized Linear Model Regression Results
==============================================================================
Dep. Variable: T2DM No. Observations: 45
Model: GLM Df Residuals: 40
Model Family: Binomial Df Model: 4
Link Function: Logit Scale: 1.0000
Method: IRLS Log-Likelihood: -28.334
Date: Wed, 21 Jun 2023 Deviance: 56.667
Time: 15:07:31 Pearson chi2: 44.3
No. Iterations: 4 Pseudo R-squ. (CS): 0.1154
Covariance Type: nonrobust
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
Intercept -2.7383 1.649 -1.661 0.097 -5.970 0.494
sex 0.6012 0.841 0.715 0.474 -1.046 2.249
HBP -0.0543 0.675 -0.081 0.936 -1.377 1.268
age -0.0155 0.012 -1.265 0.206 -0.039 0.008
glucose 0.1556 0.078 2.002 0.045 0.003 0.308
==============================================================================
p OR OR_lower_ci OR_upper_ci sig
Intercept 0.096803 0.064683 0.002554 1.638410 no_sig
HBP 0.935832 0.947133 0.252432 3.553680 no_sig
age 0.206003 0.984665 0.961363 1.008533 no_sig
glucose 0.045250 1.168346 1.003297 1.360547 *
sex 0.474470 1.824240 0.351258 9.474088 no_sig
结果显示glucose是T2DM的危险因素。