Table 1.

Distribution of L, Exposure A, and Potential Outcome Y^a for 4 Different Hypothetical Scenarios of a Confounded Exposure-Outcome Relationship, Along With the Marginal Probability of Exposure and the ATT

Scenario	L	Logit{P(A = 1|L = l)}	E(Ya|L = l)	p 1 a	ATT
1	Bern(0.5)b			0.16	−0.78
2	Bern(0.3)b			0.74	1.15
3	N(0, 1)c			0.73	0.96
4	N(1, 1)c			0.50	0.71

Abbreviation: ATT, average treatment effect in the treated.

^a = Pr(A = 1).

^b Bern() = Bernoulli distribution with expectation .

^c N = normal distribution with mean μ and variance 1.