使用持續時間資料進行中介分析¶
此筆記本示範當中介變數和結果變數為持續時間變數時，如何使用比例風險迴歸模型進行中介分析。這些範例基於模擬資料。
[1]:
import pandas as pd
import numpy as np
import statsmodels.api as sm
from statsmodels.stats.mediation import Mediation
使筆記本可重現。
[2]:
np.random.seed(3424)
指定樣本大小。
[3]:
n = 1000
產生暴露變數。
[4]:
exp = np.random.normal(size=n)
產生中介變數。
[5]:
def gen_mediator():
mn = np.exp(exp)
mtime0 = -mn * np.log(np.random.uniform(size=n))
ctime = -2 * mn * np.log(np.random.uniform(size=n))
mstatus = (ctime >= mtime0).astype(int)
mtime = np.where(mtime0 <= ctime, mtime0, ctime)
return mtime0, mtime, mstatus
產生結果變數。
[6]:
def gen_outcome(otype, mtime0):
if otype == "full":
lp = 0.5 * mtime0
elif otype == "no":
lp = exp
else:
lp = exp + mtime0
mn = np.exp(-lp)
ytime0 = -mn * np.log(np.random.uniform(size=n))
ctime = -2 * mn * np.log(np.random.uniform(size=n))
ystatus = (ctime >= ytime0).astype(int)
ytime = np.where(ytime0 <= ctime, ytime0, ctime)
return ytime, ystatus
建立包含所有相關變數的資料框架。
[7]:
def build_df(ytime, ystatus, mtime0, mtime, mstatus):
df = pd.DataFrame(
{
"ytime": ytime,
"ystatus": ystatus,
"mtime": mtime,
"mstatus": mstatus,
"exp": exp,
}
)
return df
在特定的中介母體結構下，執行完整的模擬和分析。
[8]:
def run(otype):
mtime0, mtime, mstatus = gen_mediator()
ytime, ystatus = gen_outcome(otype, mtime0)
df = build_df(ytime, ystatus, mtime0, mtime, mstatus)
outcome_model = sm.PHReg.from_formula(
"ytime ~ exp + mtime", status="ystatus", data=df
)
mediator_model = sm.PHReg.from_formula("mtime ~ exp", status="mstatus", data=df)
med = Mediation(
outcome_model,
mediator_model,
"exp",
"mtime",
outcome_predict_kwargs={"pred_only": True},
)
med_result = med.fit(n_rep=20)
print(med_result.summary())
執行具有完整中介作用的範例
[9]:
run("full")
Estimate Lower CI bound Upper CI bound P-value
ACME (control) 0.742427 0.643339 0.862745 0.0
ACME (treated) 0.742427 0.643339 0.862745 0.0
ADE (control) 0.073017 -0.016189 0.155321 0.1
ADE (treated) 0.073017 -0.016189 0.155321 0.1
Total effect 0.815444 0.675214 0.919580 0.0
Prop. mediated (control) 0.912695 0.814965 1.025747 0.0
Prop. mediated (treated) 0.912695 0.814965 1.025747 0.0
ACME (average) 0.742427 0.643339 0.862745 0.0
ADE (average) 0.073017 -0.016189 0.155321 0.1
Prop. mediated (average) 0.912695 0.814965 1.025747 0.0
執行具有部分中介作用的範例
[10]:
run("partial")
Estimate Lower CI bound Upper CI bound P-value
ACME (control) 0.987067 0.801560 1.192019 0.0
ACME (treated) 0.987067 0.801560 1.192019 0.0
ADE (control) 1.071734 0.964214 1.150352 0.0
ADE (treated) 1.071734 0.964214 1.150352 0.0
Total effect 2.058801 1.862231 2.288170 0.0
Prop. mediated (control) 0.481807 0.417501 0.533773 0.0
Prop. mediated (treated) 0.481807 0.417501 0.533773 0.0
ACME (average) 0.987067 0.801560 1.192019 0.0
ADE (average) 1.071734 0.964214 1.150352 0.0
Prop. mediated (average) 0.481807 0.417501 0.533773 0.0
執行沒有中介作用的範例
[11]:
run("no")
Estimate Lower CI bound Upper CI bound P-value
ACME (control) 0.010200 -0.039434 0.065176 1.0
ACME (treated) 0.010200 -0.039434 0.065176 1.0
ADE (control) 0.902295 0.824526 0.984934 0.0
ADE (treated) 0.902295 0.824526 0.984934 0.0
Total effect 0.912495 0.834728 1.009958 0.0
Prop. mediated (control) 0.003763 -0.044186 0.065520 1.0
Prop. mediated (treated) 0.003763 -0.044186 0.065520 1.0
ACME (average) 0.010200 -0.039434 0.065176 1.0
ADE (average) 0.902295 0.824526 0.984934 0.0
Prop. mediated (average) 0.003763 -0.044186 0.065520 1.0
上次更新：2024 年 10 月 03 日