Use of an individual-based model of pneumococcal carriage for planning a randomized trial of a whole-cell vaccine

Abstract

For encapsulated bacteria such as Streptococcus pneumoniae, asymptomatic carriage is more common and longer in duration than disease, and hence is often a more convenient endpoint for clinical trials of vaccines against these bacteria. However, using a carriage endpoint entails specific challenges. Carriage is almost always measured as prevalence, whereas the vaccine may act by reducing incidence or duration. Thus, to determine sample size requirements, its impact on prevalence must first be estimated. The relationship between incidence and prevalence (or duration and prevalence) is convex, saturating at 100% prevalence. For this reason, the proportional effect of a vaccine on prevalence is typically less than its proportional effect on incidence or duration. This relationship is further complicated in the presence of multiple pathogen strains. In addition, host immunity to carriage accumulates rapidly with frequent exposures in early years of life, creating potentially complex interactions with the vaccine's effect. We conducted a simulation study to predict the impact of an inactivated whole cell pneumococcal vaccine-believed to reduce carriage duration-on carriage prevalence in different age groups and trial settings. We used an individual-based model of pneumococcal carriage that incorporates relevant immunological processes, both vaccine-induced and naturally acquired. Our simulations showed that for a wide range of vaccine efficacies, sampling time and age at vaccination are important determinants of sample size. There is a window of favorable sampling times during which the required sample size is relatively low, and this window is prolonged with a younger age at vaccination, and in a trial setting with lower transmission intensity. These results illustrate the ability of simulation studies to inform the planning of vaccine trials with carriage endpoints, and the methods we present here can be applied to trials evaluating other pneumococcal vaccine candidates or comparing alternative dosing schedules for the existing conjugate vaccines.

Fig 1. Age-specific carriage prevalences from representative simulation runs.

(A) Carriage prevalences, sampled every month starting from birth, is shown for three arms–control (black), those vaccinated as infants (blue), and those vaccinated as toddlers (purple)–in a simulated trial in the higher transmission setting. Only the 10 colonization equivalent (c.e.) wSP vaccine efficacy is presented here. On the x-axis, two arrows indicate the age at which the vaccine was administered for the vaccinated arms. (B) Similar to (A), but for a simulated trial in the lower transmission setting.

Fig 2. Prevalence and sample size over the follow-up period in the higher transmission setting.

Panels are organized column-wise by vaccine efficacy: 3 colonization equivalents (c.e.), or 26% reduction in carriage duration (A, D); 5 c.e., or 39% (B, E); and 10 c.e., or 63% (C, F). Within each panel, results are presented separately for infants (blue) and toddlers (purple). (A-C) The joint kernel density estimate (see Methods) of the control and vaccine arm prevalences at each sampling time (every 3 months until 24 months post-vaccination) is shown as a contour map truncated by the convex hull of the simulated points, with the median values marked by a cross. These crosses are connected chronologically, and those corresponding to 0, 12, and 24 months post-vaccination are labeled. The dashed line indicates equal prevalences in the two arms. (D-F) The kernel density estimate of the total sample size (combined size of both samples) needed to detect a difference between control and vaccine arm prevalences at each sampling time (assuming 80% power, 5% type I error rate, balanced arms). The horizontal bars in each violin plot indicate the minimum, median, and maximum values across all simulations. In (D), the maximum sample sizes for infants and for toddlers at 3 months post-vaccination are greater than one million (236 million and 4 million, respectively) and outside the limits of the y-axis.

Fig 3. Prevalence and sample size over the follow-up period in the lower transmission setting.

Panels are organized column-wise by wSP vaccine efficacy: 3 colonization equivalents (c.e.), or 26% reduction in carriage duration (A, D); 5 c.e., or 39% (B, E); and 10 c.e., or 63% (C, F). Within each panel, results are presented separately for infants (blue) and toddlers (purple). (A-C) The joint kernel density estimate (see Methods) of the control and vaccine arm prevalences at each sampling time (every 3 months until 24 months post-vaccination) is shown as a contour map truncated by the convex hull of the simulated points, with the median values marked by a cross. These crosses are connected chronologically, and those corresponding to 0, 12, and 24 months post-vaccination are labeled. The dashed line indicates equal prevalences in the two arms. (D-F) The kernel density estimate of the total sample size (combined size of both samples) needed to detect a difference between control and vaccine arm prevalences at each sampling time (assuming 80% power, 5% type I error rate, balanced arms). The horizontal bars in each violin plot indicate the minimum, median, and maximum values across all simulations. In (D), the maximum sample sizes for infants and for toddlers at 3 months post-vaccination are greater than one million (510 million and 18 million, respectively) and outside the limits of the y-axis.