Table 1.

Selected covariates for adjustment

Method	Treatment	Covariates
cv(Lasso+OLS)	Treated	Age, p_death, age$\cdot$ age, age:p_death
cv(Lasso+OLS)	Control	Age, p_death, age$\mathrm{\cdot }$ age, age:p_death, p_death:mech_vent
cv(Lasso)	Treated	Pac_rate, age, p_death, age$\cdot$ age, p_death$\cdot$ p_death, region:im_score, region:systemnew,
		pac_rate:age, pac_rate:p_death, pac_rate:systemnew, im_score:interactnew, age:p_death,
		age:glasgow, age:systemnew, interactnew:systemnew, pac_rate:creatinine, age:mech_vent,
		age:respiratory, age:creatinine, interactnew:mech_vent, interactnew:male,
		glasgow:organ_failure, p_death:mech_vent, systemnew:male
cv(Lasso)	Control	Age, p_death, age$\mathrm{\cdot }$ age, unitsize:p_death, pac_rate:systemnew, age:p_death,
		interactnew:mech_vent, p_death:mech_vent*

^*Covariate definitions: age, patient’s age; p_death, baseline probability of death; mech_vent, mechanical ventilation at admission; region, geographic region; pac_rate, PAC rate in unit; creatinine, respiratory, glasgow, interactnew, organ_failure, systemnew, and im_score, various physiological indicators.