1. In most psychiatric trials the efficacy of a treatment is measured as a score reduction (e.g. HAMD score) from baseline.
For example, a standardized treatment mean of a new treatment can be 2 and placebo mean 1.6, yielding the standardized treatment effect (difference) of 0.4.
The software below implements a onesided test with negative value of the treatment effect as an input.
2. We assume that the marginal placebo mean in stage 2, μ_{X}, that is, the mean in the whole population, is equal to the marginal placebo mean in stage 1.
Similarly for the marginal drug mean μ_{Y}. We also assume that the correlation between placebo responses in stages 1 and 2 is nonnegative.
Calculating required sample size for a given power Type I error rate, α (onesided):   * * *  Power:   * * *  Allocation ratio, a:   * *  Marginal treatment effect μ_{Y} – μ_{X} in stages 1 and 2, θ_{1}:   * *  Conditional treatment effect in stage 2, θ_{2}:   * *  Marginal standard deviation in placebo group in both stages, σ_{X}:   * * *  Conditional standard deviation in the placebo group in stage 2, τ_{x}:   * *  Marginal standard deviation in drug group in both stages, σ_{Y}:   * *  Proportion of placebo nonresponders in stage 1, r:   * *  Retention rate, s:   * *  Firststage weight in the linear combination of treatment effects, w:   * *  
 Calculating power for a given total sample size Type I error rate, α (onesided):   * *  Total sample size:   * *  Allocation ratio, a:   * *  Marginal treatment effect μ_{Y}  μ_{X} in stages 1 and 2, θ_{1}:   * *  Conditional treatment effect in stage 2, θ_{2}:   * *  Marginal standard deviation in placebo group in both stages, σ_{X}:   * * *  Conditional standard deviation in the placebo group in stage 2, τ_{x}:   * *  Marginal standard deviation in drug group in both stages, σ_{Y}:   * *  Proportion of placebo nonresponders in stage 1, r:   * *  Retention rate, s:   * *  Firststage weight in the linear combination of treatment effects, w:   * *  
