Table 2.

Summary of Parameters for Simulation Group 1. In each of the 4 scenarios considered, we generate data as follows: (1) $C_1,\dots ,C_5\stackrel{iid}{~}N(0,1)$; (2) X ~ Bernoulli(p = expit(Cα^ps)); and (3) Y ~ N(βX + Cα^om, σ²) with β = 1 and σ² = 4. All effects of confounders are linear on both the treatment and outcome.

Scenario	Description	αps (PS model)	αom (Outcome model)
1	No confounding	(0.4,0.3,0.2,0.1,0)	(0,0,0,0,0)
2	Moderate confounding	(0.5,0.5,0.1,0,0)	(0.5,0,1,0.5,0)
3	Strong predictors of outcome, weak predictors of treatment	(0.1,0.1,1,1,1)	(2,2,0,0,0)
4	Strong confounding	(0.5,0.4,0.3,0.2,0.1)	(0.5,1,1.5,2,2.5)