Table 4. Results for ordinal outcome and Mann Whitney (MW) estimand in the hospitalized population.

BCa bootstrap is used for confidence intervals and hypothesis testing. “Effect” denotes the true estimand value; “MSE” denotes mean squared error; “Rel. Eff.” denotes relative efficiency which we approximate as the ratio of the MSE of the estimator under consideration to the MSE of the unadjusted estimator. In each block of four rows, the first two rows involve no treatment effect and the last two rows involve a benefit from treatment.

n	Estimator Type	Effect	P(reject H0)	MSE	Bias	Variance	Rel. Eff.
100	Unadjusted	0.500	0.054	0.003	−0.002	0.003	1.000
100	Adjusted	0.500	0.055	0.002	−0.003	0.002	0.822
100	Unadjusted	0.627	0.688	0.002	−0.002	0.002	1.000
100	Adjusted	0.627	0.753	0.002	−0.002	0.002	0.852
200	Unadjusted	0.500	0.047	0.001	−0.001	0.001	1.000
200	Adjusted	0.500	0.036	0.001	−0.001	0.001	0.864
200	Unadjusted	0.627	0.940	0.001	−0.001	0.001	1.000
200	Adjusted	0.627	0.968	0.001	0.000	0.001	0.878
500	Unadjusted	0.500	0.055	0.001	0.000	0.001	1.000
500	Adjusted	0.500	0.052	0.000	0.000	0.000	0.843
500	Unadjusted	0.582	0.946	0.001	0.000	0.001	1.000
500	Adjusted	0.582	0.959	0.000	0.000	0.000	0.905
1000	Unadjusted	0.500	0.046	0.000	0.000	0.000	1.000
1000	Adjusted	0.500	0.046	0.000	0.000	0.000	0.844
1000	Unadjusted	0.557	0.936	0.000	0.000	0.000	1.000
1000	Adjusted	0.557	0.948	0.000	0.000	0.000	0.890