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从0开始学习R语言--Day53--AFT模型

news 2025/7/23 21:50:00

在分析医疗数据时，尽管用cox回归可以分析一切因素对风险的影响，但是有时候因素的影响是非常直接的，比如对于癌症患者的生存风险，治疗手段（如化疗），会直接让肿瘤的生长速度减半，也就相当于延长了患者的生存时间，这个时候如果还要去用cox回归去分析单位时间内风险的概率，就有点本末倒置了，直接用AFT模型分析对生存时间的影响就能得到结果，毕竟在这个背景下，我们用析的最终目的是为了得知因素的效果。

以下是一个例子：

# 加载必要的包
library(survival)
library(ggplot2)# 1. 生成模拟数据集
set.seed(123)
n <- 200  # 样本量# 生成协变量
age <- rnorm(n, mean = 50, sd = 10)
treatment <- sample(0:1, n, replace = TRUE)
severity <- rnorm(n, mean = 5, sd = 2)# 生成生存时间（Weibull分布）
true_time <- exp(2 + 0.05*age - 0.8*treatment - 0.3*severity + rweibull(n, shape = 1.5, scale = 1))# 生成删失时间（随机删失）
censor_time <- runif(n, min = 0, max = max(true_time)*1.5)# 构造最终的时间和事件指示变量
time <- pmin(true_time, censor_time)
status <- as.numeric(true_time <= censor_time)# 创建数据框
surv_data <- data.frame(time = time,status = status,age = age,treatment = factor(treatment, labels = c("Control", "Treatment")),severity = severity
)# 查看前几行数据
head(surv_data)# 2. 拟合AFT模型（Weibull分布）
aft_weibull <- survreg(Surv(time, status) ~ age + treatment + severity, data = surv_data, dist = "weibull")
summary(aft_weibull)# 3. 拟合AFT模型（对数正态分布）
aft_lognormal <- survreg(Surv(time, status) ~ age + treatment + severity, data = surv_data, dist = "lognormal")
summary(aft_lognormal)# 4. 比较模型
AIC(aft_weibull, aft_lognormal)# 5. 解释结果（以Weibull模型为例）
# 正系数表示延长生存时间，负系数表示缩短生存时间
# 例如，treatmentTreatment的系数为0.72，表示治疗组比对照组的生存时间更长# 6. 预测生存时间
new_data <- data.frame(age = c(45, 45),treatment = factor(c("Control", "Treatment")),severity = c(4, 4)
)pred_time <- predict(aft_weibull, newdata = new_data, type = "response")
pred_time# 7. 可视化生存曲线
# 创建预测数据集
pred_grid <- expand.grid(age = seq(30, 70, by = 10),treatment = levels(surv_data$treatment),severity = mean(surv_data$severity)
)# 预测生存时间
pred_grid$pred_time <- predict(aft_weibull, newdata = pred_grid, type = "response")# 绘制预测生存时间
ggplot(pred_grid, aes(x = age, y = pred_time, color = treatment)) +geom_line(linewidth = 1) +  # 将size改为linewidthlabs(title = "AFT模型预测生存时间",x = "年龄",y = "预测生存时间",color = "治疗组") +theme_minimal()

输出：

Call:
survreg(formula = Surv(time, status) ~ age + treatment + severity, data = surv_data, dist = "weibull")Value Std. Error      z       p
(Intercept)         4.28068    0.28790  14.87 < 2e-16
age                 0.03353    0.00491   6.83 8.7e-12
treatmentTreatment -0.92151    0.09536  -9.66 < 2e-16
severity           -0.34059    0.02463 -13.83 < 2e-16
Log(scale)         -0.45295    0.04899  -9.25 < 2e-16Scale= 0.636 Weibull distribution
Loglik(model)= -828.1   Loglik(intercept only)= -936.9Chisq= 217.62 on 3 degrees of freedom, p= 6.6e-47 
Number of Newton-Raphson Iterations: 6 
n= 200 
Call:
survreg(formula = Surv(time, status) ~ age + treatment + severity, data = surv_data, dist = "lognormal")Value Std. Error     z      p
(Intercept)         3.33903    0.24058  13.9 <2e-16
age                 0.04375    0.00417  10.5 <2e-16
treatmentTreatment -0.79381    0.07826 -10.1 <2e-16
severity           -0.32634    0.01969 -16.6 <2e-16
Log(scale)         -0.61917    0.05181 -11.9 <2e-16Scale= 0.538 Log Normal distribution
Loglik(model)= -788   Loglik(intercept only)= -913.5Chisq= 251.07 on 3 degrees of freedom, p= 3.8e-54 
Number of Newton-Raphson Iterations: 6 
n= 200 df      AIC
aft_weibull    5 1666.161
aft_lognormal  5 1585.9131        2 
83.67537 33.29607