The power prior for zero-inflated count models: Analysis based on episodes of urinary incontinence

We have extended the power prior approach for the zero-inflated count models. This helps to incorporate historical information into the analysis of a current study for the zero-inflated Poisson and negative binomial models. Our motivation is based on clinical trials conducted to evaluate an active treatment versus the control treatment for patients with an overactive bladder. The endpoint of interest is the number of incontinence episodes observed three days prior to week 12 after starting treatment. This is a count outcome that contains an excess of zeros. We used the principle of path sampling to compute the scaling constant of the modified power prior (MPP). Our algorithm efficiently works for two historical data sets. A simulation study was conducted to assess operating characteristics under both homogeneous and heterogeneous settings. When heterogeneity among studies arises from differences in dispersion and/or probabilities of zeros, the MPP approach maintains type I error rates close to the nominal 5%, whereas pooling and meta-analytic-predictive (MAP) approaches lead to inflated type I error rates. In contrast, when heterogeneity is due to the mean parameters, the MAP approach maintains the nominal type I error rate, while the MPP method leads to an inflated type I error rate. Across scenarios in which type I error is adequately controlled, the dependent MPP, i.e. the MPP which assumes similar power parameters, consistently achieves the highest statistical power among the borrowing methods.