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Computerized adaptive testing (CAT) enhances assessment precision and efficiency by tailoring item difficulty to individual ability levels. However, traditional CAT algorithms, such as those based on the unidimensional 2PL IRT model, often overlook test-taking behaviors like omissions, potentially biasing ability estimates and compromising validity. This study introduces an innovative CAT algorithm using the Item Response Tree (IRTree) model to jointly estimate ability and omission propensity traits. A pilot simulation with 1,000 test-takers demonstrated that the IRTree-based CAT maintains comparable precision while modeling omissions, enhancing fairness and interpretability. Findings highlight the potential of IRTree models for advancing equitable high-stakes assessments.