Estimating vaccine efficacy from outbreak size household data in the presence of heterogeneous transmission probabilities

Estimating vaccine efficacy under the heterogeneity of vaccine action in a nonrandomly mixing population

Vaccines often have heterogeneous actions because of possible variation in the immune systems of hosts. One must consider such heterogeneity of vaccine action when developing a vaccine efficacy parameter. Addressing this issue the summary model of vaccine action has been proposed in the literature to estimate vaccine efficacy in a randomly mixing population. However, nonrandom mixing is common, particularly in a small-group-mixing population. This article extends the summary model of vaccine action to such a nonrandomly mixing population. The interpretation and estimation of the summary vaccine efficacy were discussed in light of other two models of vaccine action: the leaky and all-or-nothing model. Vaccine efficacy under all models is defined as the relative reduction in transmission probability due to vaccine. Estimation of the transmission probabilities is described based on a deterministic epidemic model of an acute transmitted disease. This article further discusses, based on the above vaccine models, the estimation of vaccination coverage required to control epidemic. Methods are illustrated using data simulated by considering different patterns of mixing and vaccine action. Results confirm that the summary model performs better than other two models when vaccine action is heterogeneous.

Predictive assessment of a non-linear random effects model for multivariate time series of infectious disease counts

Infectious disease counts from surveillance systems are typically observed in several administrative geographical areas. In this paper, a non-linear model for the analysis of such multiple time series of counts is discussed. To account for heterogeneous incidence levels or varying transmission of a pathogen across regions, region-specific and possibly spatially correlated random effects are introduced. Inference is based on penalized likelihood methodology for mixed models. Since the use of classical model choice criteria such as AIC or BIC can be problematic in the presence of random effects, models are compared by means of one-step-ahead predictions and proper scoring rules. In a case study, the model is applied to monthly counts of meningococcal disease cases in 94 departments of France (excluding Corsica) and weekly counts of influenza cases in 140 administrative districts of Southern Germany. The predictive performance improves if existing heterogeneity is accounted for by random effects.