My question is: did I do the calculation for the non inferiority margin correctly ?

Non-inferiority margin: Based on previous studies that suggest a 30-day mortality of 10% to 13% and relapse rate of 2.2% to 6.3% in patients treated with the appropriate standard antibiotics for CRSAB, which translates to around 81% to 88% successful antibiotic response rate taking into account both outcomes together to produce the composite outcome (5-7). A 10 % non- inferiority margin was chosen based on the above mentioned studies which would be an acceptable minimal clinical difference. Based on the current literature the best response rate is around 80-88% (4, 5). The null hypothesis is that 10 day is worse than 14 day course of antibiotics by a delta of 10%.

Assuming a 10 % inferiority margin, treatment success rate of 88% was chosen because it presents the current practice era to be decreased by 10% to produce a treatment success rate of 79.2%, and statistical power of 90% with a 5% one-sided type I error, the number required is 302 patients in each arm to establish non-inferiority.