Assessing influence for pharmaceutical data in zero-inflated generalized Poisson mixed models

For clustered count data with excess zeros where the observations are either over-dispersed or under-dispersed, the zero-inflated generalized Poisson mixed (ZIGPM) regression model may be appropriate, in which the baseline discrete distribution is a generalized Poisson distribution, which is a natural extension of standard Poisson distribution. Motivated by one data set drawn from a pharmaceutical study, influence diagnostics for ZIGPM models based on case-deletion and local influence analysis are developed in this work. The one-step approximations of the estimates under case-deletion model and some case-deletion measures are given. Meanwhile, local influence measures are obtained under various perturbations of the observed data or model assumptions. Results from a pharmaceutical study illustrate the usefulness of the diagnostic statistics.