TABLE 3.

Treatment Effect (Trt) and Standard Error (SE) Estimates in the Case Study (Trt(SE))

Method	Stratification	Opt. Matching	Regression	Weighting
Propensity score methods
BMA-Approx+Bayes
Occam’s window on	2.23(.75)	2.56(.86)	2.51(.78)	NA
Occam’s window off	2.23(.75)	2.52(.83)	2.51(.78)	NA
BMA-Approx+OLS
Occam’s window on	2.25(.78)	2.55(.83)	2.51(.79)	2.52(.76)
Occam’s window off	2.25(.78)	2.48(.86)	2.51(.79)	2.52(.76)
BMA-MCMC+Bayes
Occam’s window on	2.08(.81)	2.42(.87)	2.47(.81)	NA
BMA-MCMC+OLS
Occam’s window on	2.09(.84)	2.42(.86)	2.47(.82)	2.57(.84)
Two-step BPSA	2.02(.83)	2.22(.95)	2.23(.84)	NA
Other methods	Estimate(S.E.)
Bayes unadjusted regression	1.74(.77)
Bayes covariate-adjusted regression	2.30(.72)

Note. BPSA = Bayesian propensity score analysis; BMA-Approx+OLS = Approximate Bayesian model averaging with ordinary least squares outcome model; BMA-Approx+Bayes = Approximate Bayesian model averaging with Bayesian outcome model; BMA-MCMC+OLS = Fully Bayesian model averaging with OLS outcome model; BMA-MCMC+Bayes = Fully Bayesian model averaging with Bayesian outcome model.