Treatment Choice With Trial Data: Statistical Decision Theory Should Supplant Hypothesis Testing

Figures & data

Table 1 Minimax-regret rules for small sample sizes

	N = 0	N = 1	N = 2	N = 3	N = 4	N = 5	N = 6	N = 7	N = 8	N = 9	N = 10
n 0: threshold sample size
α = 0.10	0	0	0	0	0	0	0	0	0	1	1
α = 0.25	0	0	0	1	1	1	1	2	2	2	2
α = 0.50	0	1	1	2	2	3	3	4	4	5	5
α = 0.75	0	1	2	2	3	4	5	5	6	7	8
α = 0.90	0	1	2	3	4	5	6	7	8	8	9
λ: threshold allocation
α = 0.10	0.9	0.67	0.52	0.41	0.32	0.26	0.18	0.09	0	0.89	0.78
α = 0.25	0.75	0.36	0.17	0.93	0.67	0.42	0.18	0.93	0.67	0.43	0.18
α = 0.50	0.5	1	0.5	1	0.5	1	0.5	1	0.5	1	0.5
α = 0.75	0.25	0.64	0.83	0.07	0.33	0.58	0.82	0.07	0.33	0.57	0.82
α = 0.90	0.1	0.33	0.48	0.59	0.68	0.74	0.82	0.91	1	0.11	0.22
Minimax regret value
α = 0.10	0.09	0.067	0.052	0.041	0.033	0.027	0.022	0.019	0.017	0.017	0.017
α = 0.25	0.19	0.09	0.052	0.039	0.038	0.035	0.03	0.027	0.027	0.025	0.023
α = 0.50	0.25	0.063	0.063	0.044	0.044	0.035	0.035	0.03	0.03	0.027	0.027
α = 0.75	0.19	0.09	0.052	0.039	0.038	0.035	0.03	0.027	0.027	0.025	0.023
α = 0.90	0.09	0.067	0.052	0.041	0.033	0.027	0.022	0.019	0.017	0.017	0.016

Source: Manski (2007, Table 12.1).

Table 2 Minimum sample sizes per treatment enabling $\epsilon$-optimal treatment choice: binary outcomes, two treatments, balanced designs

ε	ES rule	One-sided 5% z-test	One-sided 1% z-test
0.0	145	3488	7963
0.03	17	382	879
0.05	6	138	310
0.10	2	33	79
0.15	1	16	35

Source: Manski and Tetenov (2016, Table 1).

Manski, C., and Tetenov, A. (2016), “Sufficient Trial Size to Inform Clinical Practice,” Proceedings of the National Academy of Sciences, 113, 10518–10523. DOI: 10.1073/pnas.1612174113.

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