Table 2:

Data-Generating Parameters for End-of-Study Binary Outcomes in Simulations

Scenario		Parameters of Data-Generating Model
Pretest– Posttest Corr.	Effect Size (Odds Ratio)	Conditional Regression Parameters in (6)			Marginal Expected Values
		${\beta }_0$	${\beta }_{Y_0}$	${\beta }_{A_1}$	(−, −)	(−, +)	(+, −)	(+, +)
0.06	1.5	−0.44	0.00	0.100	0.45	0.45	0.55	0.55
0.06	2	−0.44	0.00	0.250	0.42	0.42	0.59	0.59
0.06	3	−0.44	0.00	0.460	0.37	0.37	0.63	0.64
0.3	1.5	−0.90	1.20	0.115	0.45	0.45	0.55	0.55
0.3	2	−0.90	1.20	0.290	0.42	0.42	0.59	0.59
0.3	3	−0.90	1.20	0.520	0.37	0.37	0.64	0.64
0.6	1.5	−1.55	3.00	0.220	0.45	0.45	0.55	0.55
0.6	2	−1.55	3.00	0.450	0.41	0.41	0.58	0.58
0.6	3	−1.55	3.00	0.780	0.37	0.37	0.64	0.64

Note. The conditional regression parameters refer to Expression (6). For simplicity, ${\beta }_R$ is set to 1 and ${\beta }_{A_2}={\beta }_{A_1{A}_2}=0$. This leads to an average percentage of responders across arms of 45%, with responder proportions of 56.5% and 33.5% for the $+1$ and $-1$ levels of $A_1$. Because of a small remaining indirect effect of $Y_0$ and $Y_1$ via $R$ (i.e., correlations between pretest, response variable and posttest), the lowest level of correlation considered here is still not exactly zero (about 0.06), despite specifying a zero parameter for the conditional effect of $Y_0$ and $Y_1$.