Adaptive Multiple Comparison Sequential Design (AMCSD) for clinical trials

Figures & data

Table 1. Two doses, two looks, common control and normally distributed endpoint.

		Level 2 test	Level 2 test	Level 1 test
Look #	Information fraction	Cumulative alpha	Critical boundary	Critical boundary
1	0.5	0.001628664	3.143063	2.796510
2	1	0.024908965	2.222481	1.977431

Table 2. Critical boundary with two treatments and two looks, any distribution.

		Level 2 test	Level 2 test	Level 1 test
Look #	Information fraction	Cumulative alpha	Critical boundary	Critical boundary
1	0.5	0.001475915	3.179276	2.796510
2	1	0.024993234	2.248088	1.977431

Table 3. Type I error control with two doses and with two looks.

Normal distribution, common control		Survival analysis
(θ1, θ2)	Type I error	(HR1, HR2)	Type I error
(0,0)	0.02471	(1,1)	0.0236
(0,0.2)	0.00598	(1,0.9)	0.0091
(0, 0.5)	0.00023	(1, 0.8)	0.0048
(0,0.8)	0.00001	(1,0.7)	0.0013

Table 4. Point estimates and confidence interval coverage.

(θ1, θ2)	Coverage of ${\theta }_{\mathit{chosen}}$ by 2-sided CI	Median bias ${\hat{\theta }}_{\mathit{best}}-{\theta }_{\mathit{chosen}}$	Fraction of ${\theta }_{\mathit{chosen}}<{\theta }_{\mathit{LCL}}$	Fraction of ${\theta }_{\mathit{chosen}}>{\theta }_{\mathit{UCL}}$
(0,0)	0.97179	−0.0002246516	0.0233	0.00485
(0.05,0.2)	0.95619	−0.01690911	0.03229	0.01152
(0.15,0.33)	0.95908	−0.02318386	0.02719	0.01373
(0.3,0.45)	0.96271	−0.01839128	0.02612	0.01117

Figure 1. Scenario 1 illustration.

Figure 2. Scenario 2 illustration.