Between-case Incidence Rate Ratio: A Design Comparable Effect Size for Count Outcomes in Single Case Experimental Designs

Single-case experimental designs (SCEDs) are essential for evaluating interventions inpsychological, educational, and behavioral research. While the field has made significantprogress in developing effect size measures for SCEDs, existing metrics, such as the between-case standardized mean difference (BC-SMD), have limitations when applied to count outcomes.Count data often violate assumptions of normality and homoscedasticity, presenting challengesfor accurate effect size estimation. This study addresses the need for an alternative effect sizemeasure tailored to count outcomes in SCEDs that is directly comparable to the incidence rateratio (IRR) used in between-subjects designs. We define the between-case incidence rate ratio(BC-IRR) within a counterfactual framework and demonstrate its equivalence to the IRR inrandomized controlled trials under specific conditions. Using real-world SCED data, weillustrate the estimation of BC-IRR via generalized linear mixed models (GLMMs). The studyalso discusses the assumptions underlying BC-IRR, its potential misuse, and its limitations whileproviding directions for future research.