TABLE 1.

Treatment (Trt) Effect and Standard Error (SE) Estimates in Simulation Study 1 (Avg. Trt Effect(SD of Trt Effect Estimates)/Avg. SE(SD of SE Estimates))

Method	Stratification	Opt. Matching	Regression	Weighting
BMA-Approx+OLS
Occam’s window on	4.93(.19)/.23(.03)	4.98(.18)/.21(.02)	4.99(.17)/.20(.01)	4.92(.21)/.18(.01)
Occam’s window off	4.94(.20)/.23(.03)	4.99(.17)/.21(.02)	4.99(.17)/.20(.01)	4.91(.21)/.18(.01)
BMA-Approx+Bayes
Occam’s window on	4.93(.19)/.23(.03)	4.99(.18)/.21(.02)	4.99(.17)/.19(.01)	NA
Occam’s window off	4.93(.20)/.23(.03)	4.99(.18)/.21(.02)	4.99(.17)/.19(.01)	NA
BMA-MCMC+OLS (Noninformative)
Top 50%	4.89(.19)/.25(.04)	4.92(.17)/.24(.02)	4.93(.17)/.21(.02)	4.99(.24)/.25(.06)
Top 70%	4.88(.18)/.26(.04)	4.92(.17)/.24(.02)	4.93(.17)/.22(.02)	4.97(.23)/.25(.06)
Top 90%	4.88(.18)/.26(.04)	4.92(.17)/.24(.02)	4.92(.17)/.22(.02)	4.97(.23)/.25(.06)
BMA-MCMC+Bayes (Noninformative, 50%)	4.88(.18)/.25(.04)	4.93(.17)/.24(.02)	4.93(.17)/.21(.02)	NA
BMA-MCMC+OLS (Informative)
Top 50%	4.89(.18)/.26(.04)	4.93(.17)/.24(.02)	4.93(.17)/.22(.02)	4.98(.23)/.25(.06)
Top 70%	4.88(.18)/.26(.04)	4.92(.17)/.24(.02)	4.93(.17)/.22(.02)	4.97(.23)/.25(.06)
Top 90%	4.88(.18)/.26(.04)	4.92(.17)/.24(.02)	4.92(.17)/.22(.02)	4.97(.23)/.25(.06)
Two-step BPSA	4.88(.18)/.26(.04)	4.93(.17)/.25(.02)	4.93(.17)/.22(.02)	NA

Note. The Bayesian propensity score weighting approach with Bayesian outcome model is not discussed here due to the absence of Bayesian weighted regression in the propensity score literature.

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.