Table 2.

Percent Reduction (Increase) in Sample Mean Difference (Treated–Untreated) from PS Methods for the Measured Covariate X_M, and the Independent Portions of the Unmeasured Covariates Affecting Treatment Choice R₁, R₃, and R₄

	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6	Scenario 7	Scenario 8
XM
Binning*	95.5%	95.7%	93.5%	94.9%	91.1%	n/a	n/a	n/a
Matching†	85.7	95.4	98.9	97.7	99.1	99.2%	99.0%	98.4%
Weighting	100.8	101.3	122.6	100.0	61.3	22.7	16.8	15.0
R1
Binning*	−4.4	−20.0	−81.5	−42.0	−157.4	n/a	n/a	n/a
Matching†	−3.9	−19.6	−76.1	−40.0	−130.2	−323.5	−720.0	−2,200.0
Weighting	−4.6	−21.9	−117.9	−53.3	−88.6	−75.0	−33.3	−66.7
R3
Binning*	−4.5	−20.3	−82.8	−41.5	−155.1	n/a	n/a	n/a
Matching†	−3.8	−19.7	−75.6	−28.0	−134.9	−343.8	−730.0	−2,300.0
Weighting	−4.6	−21.4	−111.0	−51.6	−101.2	−71.9	−70.0	−40.0
R4
Binning*	−4.2	−19.9	−83.3	−41.3	−155.3	n/a	n/a	n/a
Matching†	−4.2	−18.5	−74.4	−38.5	−131.4	−334.4	−740.0	−2,500.0
Weighting	−4.9	−21.6	−111.3	−53.8	−95.3	−68.8	−60.0	−70.0

^*Average across 5 PS-quintile “bins,” n/a when not all five bins contained patients.

^†For match tolerance value = 0.01 (for matched portion of total sample only).