On the robustness of truncated negative binomial regression model: application to field epidemiology

Truncated count data are often obtained from field investigations conducted for individuals with some health-related symptoms to discover the possible causes of food-borne outbreaks quickly and accurately. This study shows two robust properties of the truncated negative binomial (TNB) model. First, by characterizing the whole set of models leading to the same likelihood function as the TNB model, we find a practical meaning that the TNB model gives reliable inference for the regression coefficients even zero inflation is allowed, but a careful interpretation of the regression coefficients is needed. Second, the TNB model can be derived from the Poisson distribution with the random intercept following a gamma distribution, however, it is difficult to justify the distribution assumption for the random intercept. We find that the TNB model presents robust inference for the slope parameters against a misspecified random effect distribution. With some analytic justifications, our numerical study shows that the empirical coverage based on the TNB model is close to its nominal level, even when the random effect distribution is misspecified. The TNB model is applied to analyze truncated count data from the food-borne outbreak that occurred in South Korea.