Estimating Serotype-specific Efficacy of Pneumococcal Conjugate Vaccines Using Hierarchical Models

Abstract

Pneumococcal conjugate vaccines target 10 or 13 specific serotypes. To evaluate the overall efficacy of these products, the vaccine-targeted serotypes are typically aggregated into a single group. However, it is often desirable to evaluate variations in effects for different serotypes. These serotype-specific estimates are often based on small counts, resulting in a high degree of uncertainty (i.e., large standard errors and wide confidence intervals). An alternative is to use a hierarchical Bayesian statistical model, which estimates overall effectiveness while simultaneously providing estimates of serotype-specific vaccine effects. These shrunken serotype-specific estimators often have smaller mean squared errors (MSEs) than unbiased versions due to a large decrease in posterior uncertainty. We reanalyzed published data from a randomized controlled trial on the efficacy of 13-valent pneumococcal conjugate vaccine (PCV13) against community-acquired pneumonia caused by vaccine-targeted serotype using a hierarchical model. This model provides a potential framework for obtaining estimates of serotype-specific vaccine effects with reduced MSEs.

Figure 1.

Estimates of serotype-specific vaccine efficacy (VE) from a non-hierarchical model. The plot shows the posterior median and 95% highest posterior density credible intervals (CrIs).

Figure 2.

Estimates of serotype-specific vaccine efficacy (VE) from a hierarchical model. The plot shows the posterior median and 95% highest posterior density credible intervals (CrIs).

Figure 3.

Comparison of the point estimates (posterior medians) of vaccine efficacy for each serotype from the non-hierarchical model and the hierarchical model. The area of the bubble is proportional to the number of cases of pneumonia due to that serotype in both study arms.