Math for Causal Inference
All simulators

Seeing vs Doing: the ICU

ICU patients die more often, yet admitting everyone saves lives: conditional versus interventional mortality.

Day 51: Interventions & the do-Operator
SeverityICUDeathseeing: P(death | ICU)0.176seeing: P(death | no ICU)0.030doing: P(death | do(ICU))0.058doing: P(death | do(no ICU))0.096
observed difference
0.146
P(D|ICU) − P(D|no ICU)
causal effect
-0.038
do(ICU) − do(no ICU)

Severity drives both ICU admission and death. Seeing compares patients who happened to be admitted with those who were not; doing sets admission for everyone, cutting the arrow from severity into ICU (the mutilated graph) and averaging over the population's severity mix.