Table 3.

Statistical power for treatment factors in a monotherapy design versus a combination treatment 2 × 2 factorial design

Total sample size (n)	Single treatment design (effect sizea/power), treatment A	Combination treatment factorial design (effect sizeb/power)
		Treatment A	Treatment B	Treatments A and B
Suppose treatments A and B have equal and fully additive effects…
128	−0.5σ/80%	−0.5σ/80%	−0.5σ/80%	−1.0σ/—
144	−0.5σ/85%	−0.5σ/85%	−0.5σ/85%	−1.0σ/—
176	−0.5σ/91%	−0.5σ/91%	−0.5σ/91%	−1.0σ/—
Suppose treatments A and B have equal and 50% synergistic effects…
128	−0.5σ/80%	−0.5σ/98.8%	−0.5σ/98.8%	−1.5σ/29%
144	−0.5σ/85%	−0.5σ/99.4%	−0.5σ/99.4%	−1.5σ/32%
176	−0.5σ/91%	−0.5σ/99.8%	−0.5σ/99.8%	−1.5σ/38%
Suppose treatments A and B have equal and 75% synergistic effects…
128	−0.5σ/80%	−0.5σ/99.8%	−0.5σ/99.8%	−1.75σ/56%
144	−0.5σ/85%	−0.5σ/99.9%	−0.5σ/99.9%	−1.75σ/61%
176	−0.5σ/91%	−0.5σ/99.9%	−0.5σ/99.9%	−1.75σ/70%

σ represents the SD for error in the statistical model of the primary end point, and the trial is powered to detect a treatment effect as small as 0.5 SD. While power for main effect tests is shown in the synergy scenarios, the main effect tests are somewhat moot in the presence of synergy, since that interaction means that the effect of one constituent level depends on the level of the other constituent. Using a phase 2/3 design, with the phase 2 portion configured as a factorial design, the evidence of synergy could trigger initiation of the phase 3 portion of the design, with further patient accrual as a two-group comparison of the combination versus placebo/SOC.

^aEffect size expressed as a function of the end point error variance (σ) in a one-way ANOVA model with treatment A as its only factor.

^bEffect sizes expressed as a function of the end point error variance in a 2 × 2 factorial ANOVA model with treatment A, treatment B, and A and B interaction as factors.

Analogous findings would hold for an ANCOVA model with a continuous baseline covariate like HbA_1c.