假设我有一个简单的 DAG,表示混杂变量 X = 吸烟、治疗 T 和结果 Y = 死亡,这样:
T ~ X
Y ~ T + X
是否可以生成一个包含 1m 个观察值的合成数据集,该数据集遵循一些指定的条件概率:
# Pr(smoking):
smoking <- data.frame(
smoking = c(0, 1),
proba = c(0.7, 0.3)
)
# Pr(treatment | smoking):
treatment <- expand.grid(
smoking = c(0, 1),
treatment = c(0, 1)
) %>% arrange(smoking, treatment)
treatment$proba <- c(0.8, 0.2, 0.45, 0.55)
# Pr(death | treatment, smoking):
death <- expand.grid(
treatment = c(0, 1),
smoking = c(0,1),
dead = c(0,1)
) %>%
arrange(treatment, smoking, dead)
death$proba <- c(0.9, 0.1, 0.2, 0.8, 0.89, 0.11, 0.5, 0.5)
我可以在这里手动执行此操作,因为它是一个非常基本的 DAG,但我想知道它是否可以以另一种更具可扩展性的方式完成,例如使用bnlearn
.
当前解决方案:
db <- data.frame(
smoking = rbinom(n = 1000000, size = 1, prob = 0.3)
)
db$treatment[db$smoking == 0] <- rbinom(n = sum(db$smoking == 0), size = 1, prob = 0.2)
db$treatment[db$smoking == 1] <- rbinom(n = sum(db$smoking == 1), size = 1, prob = 0.55)
db$dead[db$treatment == 0 & db$smoking == 0] <- rbinom(
n = sum(db$treatment == 0 & db$smoking == 0),
size = 1, prob = 0.1
)
db$dead[db$treatment == 0 & db$smoking == 1] <- rbinom(
n = sum(db$treatment == 0 & db$smoking == 1),
size = 1, prob = 0.8
)
db$dead[db$treatment == 1 & db$smoking == 0] <- rbinom(
n = sum(db$treatment == 1 & db$smoking == 0),
size = 1, prob = 0.11
)
db$dead[db$treatment == 1 & db$smoking == 1] <- rbinom(
n = sum(db$treatment == 1 & db$smoking == 1),
size = 1, prob = 0.5
)