Estimating overall exposure effects for zero-inflated regression models with application to dental caries

Zero-inflated (ZI) models, which may be derived as a mixture involving a degenerate distribution at value zero and a distribution such as negative binomial (ZINB), have proved useful in dental and other areas of research by accommodating 'extra' zeroes in the data. Used in conjunction with generalised linear models, they allow covariate-adjusted inference of an exposure effect on the mixing probability and on the mean for the non-degenerate distribution. However, these models do not directly provide covariate-adjusted inference for the overall exposure effect. Focusing on the ZINB and ZI beta binomial models, we propose an approach that uses model-predicted values for each person under each exposure state. This 'average predicted value' method allows covariate-adjusted estimation of flexible functions of exposure group means such as the difference or ratio. A second approach considers a log link for both components of the ZINB to allow a direct approach to estimation. We apply these new methods to a study of dental caries in very low birth weight adolescents. Simulation studies show good bias and robustness properties for both approaches under various scenarios. Robustness diminishes when there is exposure group imbalance for a covariate with a large effect.