Zero-inflated models for adjusting varying exposures: a cautionary note on the pitfalls of using offset

Abstract

Zero-inflated count data are frequently encountered in public health and epidemiology research. Two-parts model is often used to model the excessive zeros, which are a mixture of two components: a point mass at zero and a count distribution, such as a Poisson distribution. When the rate of events per unit exposure is of interest, offset is commonly used to account for the varying extent of exposure, which is essentially a predictor whose regression coefficient is fixed at one. Such an assumption of exposure effect is, however, quite restrictive for many practical problems. Further, for zero-inflated models, offset is often only included in the count component of the model. However, the probability of excessive zero component could also be affected by the amount of ‘exposure’. We, therefore, proposed incorporating the varying exposure as a covariate rather than an offset term in both the probability of excessive zeros and conditional counts components of the zero-inflated model. A real example is used to illustrate the usage of the proposed methods, and simulation studies are conducted to assess the performance of the proposed methods for a broad variety of situations.

Keywords:

• Count data
• zero-inflated models
• exposure
• offset

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62-07

Acknowledgments

This research was supported by the discovery grant from the Natural Sciences and Engineering Research Council of Canada. The author is also grateful to the Editor, Associate Editor, and two anonymous referees for their very valuable and constructive comments, which greatly helped to improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the discovery grant from the Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada [RGPIN 07212-2019].