Estimated sample size and power

Both interventions are considered for determining the sample size for this factorial trial.³⁴ We expect the two primary hypotheses to be independent of each other and do not expect an interaction between both interventions. Therefore, we powered each hypothesis individually, but accounted for multiple testing by adjusting the type-I error rate by setting the alpha level to 0.025 in each test to keep the overall type-I error rate at 0.05. Thus, we aimed to include 120 patients to account for a drop-out of 10% which will allow to proof non-inferiority of the metamizole treatment at a one-sided alpha-level of 2.5% with a power of 90%.

The sample size calculation for the comparison of metamizole versus ibuprofen was based on a difference in the change of pain score in the Numeric Rating Scale (NRS; range 0–10, higher score indicates more pain). We considered a change of ≥2 points between the two groups as clinically relevant and a change of ≤1 point as negligible.^{35 36} Therefore, we set the non-inferiority margin to −1 score point. Based on a two-sample means test and an SD of 1.6,³⁵ we will need 108 patients (54 per group) to proof non-inferiority of the metamizole treatment at a one-sided alpha-level of 2.5% with a power of 90%.

The sample size for the primary outcome comparison short intervention versus usual care (superiority) is based on a change in Core Outcome Measures Index (COMI; range 0–10, higher score indicates higher level of complaint, see primary outcomes) from baseline to week 6. We hypothesise that there is a difference between the two intervention groups regarding COMI. Mannion et al³⁷ reported a minimal clinically important difference (MCID) for improvement in the COMI of 2.2 points and SD for changes in COMI ranging from 1.7 to 2.5 points. We see a difference of 2.2 points between the two groups as clinically relevant and assume a SD of 2.2 points. Based on a two-sample means test, we will need 54 patients (27 per group) to detect a difference in the change of the COMI at a two-sided alpha-level of 2.5% with a power of 90%.