ABSTRACT: Current methods for screening and detecting delirium are not practical in clinical settings. We previously showed that a simplified EEG with bispectral electroencephalography (BSEEG) algorithm can detect delirium in elderly inpatients. In this study, we performed a post-hoc BSEEG data analysis using larger sample size and performed topological data analysis to improve the BSEEG method. Data from 274 subjects included in the previous study were analyzed as a 1st cohort. Subjects were enrolled at the University of Iowa Hospitals and Clinics (UIHC) between January 30, 2016, and October 30, 2017. A second cohort with 265 subjects was recruited between January 16, 2019, and August 19, 2019. The BSEEG score was calculated as a power ratio between low frequency to high frequency using our newly developed algorithm. Additionally, Topological data analysis (TDA) score was calculated by applying TDA to our EEG data. The BSEEG score and TDA score were compared between those patients with delirium and without delirium. Among the 274 subjects from the first cohort, 102 were categorized as delirious. Among the 206 subjects from the second cohort, 42 were categorized as delirious. The areas under the curve (AUCs) based on BSEEG score were 0.72 (1st cohort, Fp1-A1), 0.76 (1st cohort, Fp2-A2), and 0.67 (2nd cohort). AUCs from TDA were much higher at 0.82 (1st cohort, Fp1-A1), 0.84 (1st cohort, Fp2-A2), and 0.78 (2nd cohort). When sensitivity was set to be 0.80, the TDA drastically improved specificity to 0.66 (1st cohort, Fp1-A1), 0.72 (1st cohort, Fp2-A2), and 0.62 (2nd cohort), compared to 0.48 (1st cohort, Fp1-A1), 0.54 (1st cohort, Fp2-A2), and 0.46 (2nd cohort) with BSEEG. BSEEG has the potential to detect delirium, and TDA is helpful to improve the performance.