Table 4:

Illustrating the TMLE procedure under $(Q_0,g_n^{★})$-adaptive sampling scheme. This table illustrates how the TMLE procedure behaves (on a simulated trajectory) as the sample size increases. We report, at each sample size n_i, the updated adapted design $g_n^{★}=G^{★}({\theta }_n(O_{n_7}^1(n)))$ (columns two to four), current TMLE ${\psi }_n^{*}(O_{n_7}^1(n))$ (column five) and 95% confidence interval I_n,1 as in (28) with $s_n^{*}(O_{n_7}^1(n))$ substituted to s_n. The true risk difference ψ₀ = ≃ 1.264 belongs to all confidence intervals. See also Fig. 7.5.

Sample size	Allocation probabilities			TMLE	Confidence interval
n	$g_n^{★}(1|1)$	$g_n^{★}(1|2)$	$g_n^{★}(1|3)$	${\psi }_n^{*}$	$[{\psi }_n^{*}\pm s_n^{*}{\xi }_{1-0.05/2}/\sqrt{n}]$
n1	0.589	0.764	0.766	1.252	[0.722;1.783]
n2	0.624	0.775	0.707	1.388	[0.974;1.802]
n3	0.679	0.767	0.795	1.361	[1.037;1.685]
n4	0.677	0.757	0.813	1.341	[1.068;1.615]
n5	0.670	0.760	0.806	1.250	[1.012;1.488]
n6	0.677	0.788	0.835	1.288	[1.126;1.451]
n7	0.694	0.793	0.834	1.273	[1.157;1.389]