On the Use of Zero-Inflated and Hurdle Models for Modeling Vaccine Adverse Event Count Data

Abstract

We compared several modeling strategies for vaccine adverse event count data in which the data are characterized by excess zeroes and heteroskedasticity. Count data are routinely modeled using Poisson and Negative Binomial (NB) regression but zero-inflated and hurdle models may be advantageous in this setting. Here we compared the fit of the Poisson, Negative Binomial (NB), zero-inflated Poisson (ZIP), zero-inflated Negative Binomial (ZINB), Poisson Hurdle (PH), and Negative Binomial Hurdle (NBH) models. In general, for public health studies, we may conceptualize zero-inflated models as allowing zeroes to arise from at-risk and not-at-risk populations. In contrast, hurdle models may be conceptualized as having zeroes only from an at-risk population. Our results illustrate, for our data, that the ZINB and NBH models are preferred but these models are indistinguishable with respect to fit. Choosing between the zero-inflated and hurdle modeling framework, assuming Poisson and NB models are inadequate because of excess zeroes, should generally be based on the study design and purpose. If the study's purpose is inference then modeling framework should be considered. For example, if the study design leads to count endpoints with both structural and sample zeroes then generally the zero-inflated modeling framework is more appropriate, while in contrast, if the endpoint of interest, by design, only exhibits sample zeroes (e.g., at-risk participants) then the hurdle model framework is generally preferred. Conversely, if the study's primary purpose it is to develop a prediction model then both the zero-inflated and hurdle modeling frameworks should be adequate.

Key Words:

• Excess zeroes
• Hurdle model
• Negative binomial
• Poisson
• Vaccine adverse events
• Zero-inflated model

ACKNOWLEDGMENTS

The authors would like to express our gratitude to the AVA Human Clinical Trial Principal Investigator, Dr. Nina Marano. Without her encouragement and guidance our work would not have come to fruition. We would like to thank Drs. Drew Baughman and Mike McNeil along with two anonymous reviewers for their review of the manuscript.

Notes

Note: Count = number of unique systemic adverse events experienced after an AVA injection. ZIP = zero-inflated Poisson, PH = Poisson hurdle, NB = Negative Binomial, ZINB = zero-inflated Negative Binomial, and NBH = Negative Binomial hurdle models. All models include treatment, gender, race, location, and time covariates.

Notes: Estimate is the contrast estimate, SE is the robust standard error, OR = odds ratio, RR = risk ratio, LCL and UCL are lower and upper 95% confidence limits.