Local sensitivity to nonignorable missingness in the overdispersed count outcome using negative binomial model

Count outcomes with missing observations are a common occurrence in clinical, medical, and psychological research. Typically, such data is analyzed using statistical methods predicated on the missing at random assumption (MAR). However, verifying MAR from the data at hand can often be challenging, and an incorrect assumption could lead to biased results. The Index of Local Sensitivity to Nonignorability (ISNI) method provides a straightforward and user-friendly solution for sensitivity analysis. The corresponding R package, "isni", incorporates the Poisson model for count data. Yet, when the data exhibit overdispersion, using the Poisson model may not be suitable. To address this, we have developed an ISNI index for the Negative Binomial model, often employed for count outcomes in instances of overdispersion. We conducted simulation studies to explore the effects of the degree of overdispersion on the sensitivity to nonignorability, as well as the association between different levels of missing proportions and sensitivity to nonignorability. Our newly developed R function, isniglm.nb(), enables the implementation of the method for the negative binomial model. We demonstrate the application of this negative binomial ISNI method using a real-world dataset drawn from clinical research.