7–2140), at which point 97.9% (95% confidence interval (CI): 92.8–99.7) of subjects were seroprotected. By month 6, median titres had declined to 149 (5th to 95th percentile range: 19–1270), and 96.8% (95% CI: 90.9–99.3) were seroprotected. Titres continued to decline until year 5, when the median titre was 70.0

(5th to 95th percentile range: <10–304) and the seroprotection rate was 93.3% (95% CI: 82.1–98.6%). Statistical models were constructed to estimate the evolution of antibody titres over time and to predict, at the individual level, how long antibody titres will remain above the protective SNS-032 cost threshold. The raw data summarized above revealed three distinct periods of evolution of antibody titres: a rapid rise from day 0 to 28, rapid decay from day 28 to month 6 and slow decay from month 6. Since the focus here is on long-term persistence MK 1775 rather that antibody rise induced by vaccination, we analyzed

data from day 28 when observed titres were highest and developed models focused on antibody decay from that point in time. Given the highly nonlinear nature of antibody decay, and the importance of individual variations in vaccine-induced antibody responses, we constructed three alternative mixed-effects models. The first model estimated linear antibody decay and contained fixed and random effects for both slope and intercept parameters: Yij=(a+ai)+(b+bi)⋅tj+εijYij=(a+ai)+(b+bi)⋅tj+εijwhere Yij is the log of the neutralizing antibody titre for subject i observed much at time tj, a and ai are the population-level (fixed effect) and individual-level (random effect) intercepts and b and bi are the population-level and individual-level slope corresponding to the rate of linear antibody decay. ɛij is the residual error between model prediction and the observed value. The second model was an exponential-type

model constructed from day 28 data with fixed and random effects for slope (a, ai), intercept (b, bi) and exponent (c, ci) parameters: Yij=(a+ai)+(b+bi)⋅tjc+cj+εij The third model was a 2-period piecewise linear model with fixed and random effects for the intercept (a, ai), 2 slope parameters (b, bi, b2, b2i) and a change point Si, representing the point in time when the change in the rate of antibody decay occurs. Yij=(a+ai)+(b+bi)⋅tj+εij, for   t=SiYij=(a+ai)+(b+bi)⋅tj+εij, for   t=Si Yij=(a+ai)+(b+bi)⋅Si+(b2+b2i)⋅(tj−Si)+εij, for   t>SiYij=(a+ai)+(b+bi)⋅Si+(b2+b2i)⋅(tj−Si)+εij, for   t>Si All models were constructed using a Bayesian Monte-Carlo Markov chain approach [13] and were implemented with OpenBugs V3.12.1. Posterior summary Libraries statistics were based on 3 Markov chains of 40,000 lengths after a burn-in period of 60,000 iterations. Convergence of the model estimates was assessed using Gelman–Rubin statistics [14] as well as inspection of the parameters’ iteration history and posterior densities.