Table 3

Empirical proportion of trials that randomize in the wrong direction

Scenario	Efficacy of group			Probability (group_i is larger than group_j)
Scenario	Group 2	Group 3	Group 4	Group 2 > group3	Group 2 > group4	Group 3 > group4
1	Neutral	Neutral	Neutral	0.50	0.50	0.50
2	Inferior	Neutral	Neutral	0.06	0.06	0.50
3	Neutral	Neutral	Superior	0.50	0.16	0.16
4	Inferior	Neutral	Superior	0.07	0.00	0.16
5	Neutral	Superior	Superior	0.18	0.18	0.49
6	Inferior	Superior	Superior	0.02	0.02	0.48
7	Superior	Superior	Superior	0.48	0.48	0.48
8	Neutral	Neutral	Superior	0.50	0.33	0.33
9	Inferior	Neutral	Superior	0.04	0.01	0.39

Note: Neutral—no treatment effect; superior—superior to control; inferior—inferior to control. This table summarizes the proportion of trials in which a worse arm was allocated more patients than a better arm. For example, in scenario 4, group 2 (inferior to control) is allocated more patients than group 3 (no treatment effect) in 7% of trials but never allocated more patients than group 4 (superior to control). Also group 3 is allocated more patients than group 4 in 16% of trials.