The obesity paradox in critically ill patients: a causal learning approach to a casual finding

Table 4 Summary table of the traditional versus robust causal inference approach

Estimand	Method	Complete cases in A		Complete cases in (A, C)		Imputation for (A, C)
Estimand	Method	Estimate (95% CI)	P	Estimate (95% CI)	P	Estimate (95% CI)	P
Raw marginal risk difference (unadjusted)	Regression	− 1.06% (− 3.23 to 1.11)	0.337	− 2.25% (− 4.65 to 0.15)	0.067	− 1.03% (− 3.22 to 1.14)	0.354
Marginal causal risk difference (ATU)	Regression + G-computation	–	–	− 2.48% (− 4.80 to − 0.15)	0.037	− 1.46% (− 3.58 to 0.66)	0.178
Marginal causal risk difference (ATU)	TMLE + super learner	–	–	− 1.52% (− 3.85 to 0.81)	0.201	− 0.59% (− 2.77 to 1.60)	0.599

With A = obesity and C = age, sex, ethnicity, income, smoking status, alcohol consumption, physical activity, hypothyroidism, chronic glucocorticoid therapy, solid malignancy, hematological malignancy, dementia, human immunodeficiency virus/acquired immunodeficiency syndrome, calendar time
ATU average treatment effect in the untreated, CI confidence interval, TMLE targeted maximum likelihood estimation

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