Sample size estimates for superiority, non-inferiority and equivalence trials of second-generation malaria vaccines, according to different incidence risk of malaria in the first-generation vaccine group. The figures show the estimated sample size required to detect a range of differences in the efficacy (margin %) between a second and first-generation malaria vaccine. The margin represents the absolute difference in the efficacy between the two vaccines for active-controlled trials; the relative difference for each value of absolute risk difference will therefore be greater for areas with a lower transmission (for example, absolute risk difference of 10% units equates to a relative risk of 0.67 and 0.80 when the baseline risk is 30% and 50%, respectively). The different incidence risks of malaria (proportion of individuals with malaria outcome during follow-up) in the first-generation vaccine groups corresponds to the approximate baseline risk observed in RTS,S phase II and III trials (that is, 30% and 50%) [4, 5]. Sample sizes are calculated with 90% power at the 5% significance level by the authors using STATA (StataCorp; College Station, TX, USA). Note, as the incidence risk approaches 0.5, the standard error gets marginally larger; this explains why the sample size for the same absolute risk difference is bigger for a baseline risk of 50% compared with 30% (for example, total sample size required for a superiority trial with risk difference of 10% units is 778 and 1,030 for a baseline risk of 30% and 50%, respectively).