混合效应模型 MMRM¶

方法简介¶

Mixed Model Repeated Measures (MMRM) 是验证性临床试验分析的金标准方法。它利用所有可用数据，在 MAR 假设下给出有效推断。

代码实现¶

RSASPython

library(lme4)
library(lmerTest)

m1 <- lmer(chg ~ treatment * visit + baseline + (1 | subject), 
           data = adqs)
summary(m1)

# ANCOVA-type tests
anova(m1, ddf = "Kenward-Roger")

proc mixed data=adqs;
    class subject treatment visit;
    model chg = treatment visit treatment*visit baseline / ddfm=kr;
    repeated visit / subject=subject type=un;
    lsmeans treatment*visit / slice=visit diff;
run;

import statsmodels.api as sm
from statsmodels.formula.api import mixedlm

model = mixedlm(
    "chg ~ C(treatment) * C(visit) + baseline",
    data=df,
    groups=df["subject"],
    re_formula="~1"
)
result = model.fit()
print(result.summary())

关键参数¶

协方差结构: UN (非结构化) — 金标准；CS (复合对称) — 简化假设
自由度校正: Kenward-Roger (KR) 或 Satterthwaite
固定效应: treatment, visit, treatment×visit, baseline

相关可视化¶