Bayesian Marginalized Zero-inflated Poisson Model with Random Effects for Single-case Experimental Designs: A Simulation Study

Analyzing zero-inflated count data in single-case experimental designs (SCEDs) presents a significant analytical challenge. While traditional zero-inflated generalized linear mixed-models are available, they estimate a conditional treatment effect given an individual coming from the count process, which often mismatches the applied researcher's interest in the overall effect of an intervention for each subject. These conditional models also face interpretational and estimation challenges within the small-sample context of SCEDs. This study introduces and evaluates a Bayesian marginalized zero-inflated Poisson (mZIP) model with random effects. This framework re-parameterizes the model to estimate the marginal intervention effect, aligning the statistical estimand with the typical research question. A Monte Carlo simulation study was conducted to evaluate the mZIP model's performance. We compared its performance to other methods that also target the marginal treatment effect: the Log Response Ratio (LRR), a Poisson GLMM, and a Negative Binomial GLMM. Simulation results indicate that the Bayesian mZIP model consistently recovers unbiased estimates of the marginal treatment effect and provides reliable statistical inference. The LRR, Poisson GLMSS, and NB GLMM produced biased estimates for the marginal effect under conditions with smallest sample size and highest zero-inflation rate. They also suffered from low coverage rate, making their inferential statistics invalid. The LRR indicated lower statistical power than the mZIP model. We apply the mZIP model to an empirical dataset to illustrate its application and interpretation. Finally, we discuss the distinction between conditional and marginal estimands as well as the limitations and future directions.