Table 3:

Predicted and Simulated Power for Fixed Effect Sizes

Scenario		One Wave			Two Wave
		Predicted Power		Simulated Power	Predicted Power		Simulated Power
Odds Ratio	Sample Size	MPB	CPB		MPB	CPB
Pre-post correlation 0.06
1.5	300	0.298	0.298	0.296	0.299	0.313	0.298
1.5	500	0.455	0.454	0.457	0.456	0.476	0.458
2	300	0.665	0.664	0.667	0.666	0.692	0.667
2	500	0.869	0.868	0.876	0.870	0.888	0.878
3	300	0.956	0.955	0.961	0.956	0.966	0.962
3	500	0.997	0.997	0.999	0.997	0.998	0.998
Pre-post correlation 0.3
1.5	300	0.286	0.286	0.279	0.312	0.324	0.305
1.5	500	0.437	0.437	0.449	0.475	0.493	0.484
2	300	0.672	0.671	0.677	0.716	0.737	0.722
2	500	0.874	0.874	0.880	0.904	0.917	0.908
3	300	0.957	0.957	0.963	0.971	0.977	0.976
3	500	0.997	0.997	0.999	0.999	0.999	0.999
Pre-post correlation 0.6
1.5	300	0.290	0.290	0.291	0.423	0.431	0.427
1.5	500	0.442	0.442	0.450	0.627	0.637	0.641
2	300	0.649	0.649	0.652	0.831	0.840	0.848
2	500	0.856	0.857	0.861	0.965	0.968	0.968
3	300	0.955	0.956	0.962	0.994	0.995	0.996
3	500	0.997	0.997	0.998	1.000	1.000	1.000

Notes. “MPB” = marginal-probabilities-based (expression 3); “CPB” = conditional-probabilities-based (expression 5), In all conditions, the proportion of responders was set to approximately 0.565 given $A_1=+1$ and 0.336 given $A_1=-1$; this difference is the reason why the pre-post correlation $\text{Cor}(Y_0,Y_1)$ could not be set to exactly zero. The odds ratio shown is for 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 on $Y_1$. The simulated power shown for the two-wave model uses the covariate adjustment approach (pretest as covariate); the repeated measures approach had approximately the same power, or in some conditions about 0.005% higher.