Modeling excess zeroes in an integrated analysis of vaccine safety

Abstract

In prophylactic vaccine studies in healthy populations, many subjects do not experience a single adverse event (AE). Thus, the number of AEs observed in such clinical trials may be difficult to model because of an excess of zeroes relative to the parametric distributions assumed. To determine which type of modeling provides a better fit for observed AE data, a variety of models were applied to data from an integrated safety database from clinical trials of the meningococcal vaccine MenB-FHbp (Trumenba®, bivalent rLP2086; Pfizer Inc, Philadelphia, PA). MenB-FHbp was the first vaccine approved in the United States to prevent meningococcal serogroup B disease in individuals aged 10 to 25 years. Specifically, this report presents an integrated analysis of AEs from 8 randomized controlled trials that compared MenB-FHbp to placebo or active controls. The number of AEs occurring from dose one to 30 days after the last dose was analyzed. Six models were compared: standard Poisson and negative binomial models and their corresponding zero-inflation and hurdle models. Models were evaluated for their ability to predict the number of AEs and by goodness-of-fit statistics. Models based on the Poisson distribution were a poor fit. The zero-inflated negative binomial model and negative binomial hurdle model provided the closest fit. These results suggest that zero-inflated or hurdle models may provide a better fit to AE data from healthy populations compared with conventional parametric models.

Keywords: Poisson; excess zeroes; hurdle models; negative binomial; vaccine adverse events; zero-inflated models.

Figures

Figure 1.

Observed vs predicted number of subjects with each number of AEs for the Poisson-related models. AE = adverse event; PH = Poisson hurdle; ZIP = zero-inflated Poisson.

Figure 2.

Observed vs predicted number of subjects with each number of AEs for the NB models. AE = adverse event; NB = negative binomial; NBH = negative binomial hurdle; ZINB = negative binomial model with zero-inflation.