TABLE 4.

Results for ordinal outcome and MW estimand in the hospitalized population

n	Estimator type	Effect	P(reject H 0)	MSE	Bias	Variance	Rel. Eff.
100	Unadjusted	0.500	0.054	0.263	−0.014	0.263	1.000
100	Adjusted	0.500	0.050	0.234	−0.017	0.234	0.890
100	Unadjusted	0.585	0.389	0.226	−0.010	0.226	1.000
100	Adjusted	0.585	0.431	0.208	−0.011	0.208	0.919
100	Unadjusted	0.609	0.625	0.205	−0.009	0.205	1.000
100	Adjusted	0.609	0.670	0.194	−0.006	0.194	0.944
200	Unadjusted	0.500	0.053	0.264	0.010	0.264	1.000
200	Adjusted	0.500	0.056	0.236	0.014	0.236	0.895
200	Unadjusted	0.587	0.720	0.232	−0.006	0.232	1.000
200	Adjusted	0.587	0.776	0.205	−0.001	0.206	0.886
200	Unadjusted	0.612	0.924	0.217	0.008	0.217	1.000
200	Adjusted	0.612	0.953	0.190	0.021	0.190	0.879
500	Unadjusted	0.500	0.063	0.271	−0.018	0.271	1.000
500	Adjusted	0.500	0.044	0.230	−0.020	0.230	0.848
500	Unadjusted	0.556	0.710	0.262	−0.001	0.262	1.000
500	Adjusted	0.556	0.749	0.231	−0.008	0.231	0.882
500	Unadjusted	0.576	0.935	0.249	0.000	0.250	1.000
500	Adjusted	0.576	0.958	0.224	−0.002	0.224	0.897
1000	Unadjusted	0.500	0.039	0.255	−0.004	0.255	1.000
1000	Adjusted	0.500	0.040	0.227	−0.007	0.228	0.894
1000	Unadjusted	0.540	0.722	0.243	−0.005	0.243	1.000
1000	Adjusted	0.540	0.745	0.220	−0.013	0.220	0.906
1000	Unadjusted	0.556	0.956	0.234	−0.003	0.234	1.000
1000	Adjusted	0.556	0.970	0.214	−0.009	0.214	0.915

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 six rows, the first two rows involve no treatment effect and the last four rows involve a benefit from treatment. MSE and variance are scaled by n; bias is scaled by $n^{1/2}$.