Association between anti-CSP antibody titre and protection. (a,b,c) Estimated dose–response curves from equation (2) for the association between anti-CSP antibody titre CSP and vaccine efficacy against infection V (the probability that an infection is prevented by RTS,S induced responses) for infants (<3 months), children (>3 months and <5 years), and adults (>18 years). The yellow shaded region denotes the 95% credible interval. The grey histograms denote the observed distribution of each trial participant’s average anti-CSP titre during the first year of follow-up. (d) Comparison of observed (solid lines) and simulated (dashed lines) efficacy against infection from phase 2 trials. (e) Comparison of observed (solid lines) and simulated (dashed lines) efficacy against clinical malaria. The range of the solid lines represents the 95% confidence intervals of vaccine efficacy observed in phase 2 trials. The dashed lines represent the 95% range due to stochastic variation in simulated vaccine efficacy in cohorts of equal size to the original trial using the model with posterior median parameter estimates. CSP, circumsporozoite protein.