Table 5 (for Appendix 1).

Simulated power for different models in three-wave simulation

Scenario		Simulated power for first follow-up $Y_1$, by model		Simulated power for second follow-up $Y_2$, by model
Delayed Effect	Sample Size	$Y_1$ Only	$Y_1$ Adjusted for $Y_0$	$Y_2$ Only	$Y_2$ Adjust ed for $Y_0$	$Y_2$ Adjusted for $Y_0$ and $Y_1$
						(Indep.)	(AR-1)	(Exch.)
No	300	0.962	0.997	0.651	0.715	0.651	0.726	0.699
No	500	0.998	1.000	0.859	0.907	0.859	0.909	0.893
Yes	300	0.961	0.997	0.515	0.517	0.515	0.540	0.521
Yes	500	0.998	1.000	0.744	0.746	0.744	0.757	0.737

Notes. In all of these conditions, the average estimated odds ratio for the effect of $A_1$ was set to 3.0 for $Y_1$ and 2.0 for $Y_2$, in terms of the pairwise comparison of ($+$, $-$) to ($-$, $-$) adaptive interventions, which is equivalent here to the effect of $A_1$. For simplicity of interpretation, $A_2$ and the $A_1\times A_2$ interaction were set to have no effect. The conditions differ in the relationship of the simulated late follow-up $Y_2$ to the baseline assessment $Y_0$ and initial treatment $A_1$. The simulated decay in effect size over time between $Y_1$ and $Y_2$ is intended to be analogous to that found in many real-world clinical trials.