Statistics

Determination of sample size
Since there are no double-blind studies comparing treatment with methylphenidate and placebo in manic patients the following considerations have been taken into account:
1. The vigilance regulation capacity varies among manic patients: 35% of patients are expected to have a markedly instable vigilance regulation and therefore are expected to strongly respond [38]. In these cases a remission of manic symptoms after 2.5 days of treatment with methylphenidate will be operationalized as 14 points decrease in the YMRS. 35% of patients are expected to have a partially instable vigilance regulation and the expected treatment response is 7 points YMRS decrease; 30% of patients are expected to have a stable vigilance regulation and in these patients the response to treatment is expected to be 3 points YMRS decrease (placebo level);
2. Expected placebo effect after 2.5 days of treatment: 3 ± 2 points on the YMRS;
3. Expected drop out rate: 5% at maximum considering the study design (short duration, inpatients).
For the statistical testing of the primary study objective a statistical power of 1- β = 0.8, and a significance level of α = 0.05 are envisaged. Using these assumptions, the number of patients per treatment group was calculated as follows: ([z1 + z22 x [σ12 + σ22)/(μ1 – μ2)2; z1: 0,96 (type I error of 5%); z2: 0,842 (power of 80%), μ1: mean verum group: 7.9, μ2: mean placebo group: 3, σ1: SD verum group 4.7, σ2: mean placebo group 2). According to this calculation, 42 patients per treatment group will be required + 5% (= 2 patients) for dropouts. Thus, 44 patients per group will be required. It is therefore planned to recruit a total of 88 patients into the study. Since the empirical basis for this power analysis is small, an adaptive interim analysis will be performed after inclusion of 20 patients per study arm with the following rules [47]: 
• Early stopping due to futility, i.e. it is unlikely that the null hypothesis (Ho) can be rejected with a larger sample size (p1 ≥ 0.30 (α0));
• Early stopping with rejection of the null hypothesis (Ho) (p1 ≤ 0.03 (α1));
• Re-estimation of the sample size in case of continuation (if p1 ∈ (α1,α0)).