1. Sample size calculation (a) Suppose that the interest is in whether there is a difference in the efficacy of mirtazapine (new drug) and sertraline (standard drug) for the treatment of resistant depression in 6-week treatment duration. The parameters are: P = 0.40, Pd = 0.55, a = 0.05, 3= 0.20, the margin A* = 0.10. Compute the required sample size for non-inferiority, equivalence, statistical superiority, and clinical superiority trials. (b) The research question is whether there is a difference in the efficacy of ACE II antagonist (new drug) and ACE inhibitor (standard drug) for the treatment of primary hypertension. Change of sitting diastolic blood pressure (SDBP, mmHg) is the primary measurement, compared to the baseline measurement. Calculate the required sample sizes for non-inferiority, equivalence, statistical superiority, and clinical superiority trials with the parameters, mean change of SDBP in new drug treatment group 18 mm Hg: mean change of SDBP in standard treatment group 14 mm Hg; a = 0.05; 3= 0.20; the margin A* = 3 mm Hg; s = 10 mm Hg.