Table 4.

Gain in concordance and change in equity for alternative designs when compared to the standard, parallel group design.

	Two-stage	Zelen single consent, treatments concealed	Zelen single consent, treatments revealed	Zelen double consent, treatments concealed	Zelen double consent, treatments revealed
Gain in Concordance rate for patients who prefer treatment A	θ(1 − ρ)	θφ − ρ	θ − ρ	1 − φ(1 − θ) − ρ	1 − ρ
Gain in concordance rate for patients who prefer treatment B	θρ	ρ − θφ	ρ	ρ − θφ	ρ
Gain in overall concordance rate	θ[1 − αρ − β(1 − ρ) − γ] = θ [α (1 − ρ) + βρ]	(α − β)(θφ − ρ)	α(θ − ρ) + βρ	(α − β)(θφ − ρ) + α(1 − φ)	α(1 − ρ) + βρ
Change in equity (A vs. B)	−θ(2ρ − 1)	2(θφ − ρ)	θ − 2ρ	φ(2θ − 1) − (2ρ − 1)	1 − 2ρ

ρ = proportion randomised to treatment A in standard design, and in a random arm of 2-stage design; (α, β) = preference rates for treatment A or B; γ = undecided rate; θ = proportion randomised to choice arm in two-stage design, or to A-consent arms in Zelen designs; φ = proportion of patients who consent to randomised treatment in Zelen concealed designs.