Inclusion of historical control data in the analysis of a current trial for zero-inflated count models

Historical control information can be used to improve the efficiency and precision of treatment-effect estimation in a current trial. However, this benefit depends on the similarity between historical and current controls as well as the methods used to borrow information from the historical data. This study extends the meta-analytic-predictive (MAP) framework to zero-inflated count models. The MAP approach is a Bayesian method for borrowing information from multiple historical controls under exchangeability assumptions for model parameters. We assess the benefits of allowing exchangeability across multiple model parameters, including the mean, dispersion, and zero-inflation rate. Clinical trials evaluating an active treatment versus a control treatment in patients with overactive bladder are considered. The endpoint of interest is the number of incontinence episodes recorded during the three days preceding week 12 after treatment initiation. This outcome is a count variable with a high proportion of zero observations. Simulation studies were conducted to evaluate the performance of the MAP approach compared with the power prior approach under various levels of heterogeneity among the historical and current control arms. When historical and current data are similar, all borrowing approaches improve statistical power compared with No-borrowing. However, the Pooling approach leads to substantial inflation of type I error rates in the presence of heterogeneity. When variation is driven by the mean, the power prior approach results in inflated type I error rates. If exchangeability in the MAP approach is assumed only for the mean, type I error inflation also occurs when heterogeneity arises in the dispersion or zero-inflation parameters. In contrast, the MAP approach that assumes exchangeability for multiple parameters maintains the nominal type I error rate of 5% in all scenarios, with unbiased estimates in most scenarios. In conclusion, careful consideration of modeling assumptions is essential when borrowing historical information to avoid biased inference and type I error inflation. The proposed approach provides a practical framework for incorporating relevant historical control information into current clinical trials while maintaining valid statistical inference.