Sample size calculation

In three randomised controlled trials on postoperative delirium in elderly patients undergoing cardiac surgery, delirium incidence varied from 13.7% to 34.0%.^18–20 Based on this literature, we hypothesised a delirium incidence of 25% in the population studied. In two of the three studies, the magnitude of the treatment effect was a 50% decrease of postoperative delirium and subsyndromal delirium.^{18 19} Therefore, a 50% decrease in incidence of delirium was chosen to remain in line with the previous publications. Using a one-sided alpha=0.05% and 90% power, a sample size of 332 is needed. Considering a loss-to-follow-up rate of 5%, we plan to enrol 348 patients.

A one-sided alpha was chosen because no publication reported any worsening of the patient’s outcome compared with placebo. A two-sided alpha estimate is more robust but requires a bigger sample size.