... All of these have led to a third wave of methodological developments and novel applications in using power priors. Recently published vast literature on this topic includes the theoretical and computational development of the normalized power prior or the partial-borrowing normalized power prior (Banbeta et al., 2019;Carvalho and Ibrahim, 2021;Ye et al., 2022;Han et al., 2023a,b;Pawel et al., 2023a); adaptive or dynamic borrowing power priors (Gravestock and Held, 2017;Pan et al., 2017;Liu, 2018;Nikolakopoulos et al., 2018;Gravestock and Held, 2019;Ollier et al., 2020;Thompson et al., 2021;Sawamoto et al., 2022;Han et al., 2023a;Hickey et al., 2023;Baumann et al., 2024); propensity score based power priors (US Government Publishing Office, 2016;Lin et al., 2019;Wang et al., 2019;Li et al., 2020;Bennett et al., 2021;Baron et al., 2022;Li et al., 2022a;Lu et al., 2022;Wang et al., 2022;Baron et al., 2024); and Bayesian design of clinical trials and sample size re-estimation using power priors (Hees and Kieser, 2017;Brakenhoff et al., 2019;Feißt et al., 2020;Kopp-Schneider et al., 2020;Nagase et al., 2020;Wiesenfarth and Calderazzo, 2020;Duan et al., 2021;Huang et al., 2022;Kopp-Schneider et al., 2023). Power priors and their extensions have also recently used or applied in behavioral and cognitive neuroscience (Egbon et al., 2023;Mezzetti et al., 2023); causal inference (Li et al., 2022b); clinical trials (Warasi et al., 2016;van Rosmalen et al., 2018;Li and Yuan, 2020;Pateras et al., 2021;Chao et al., 2022;Yu et al., 2022); diagnostic accuracy studies and tests (Bai et al., 2021;Wilson et al., 2022); energy engineering (Lorencin and Pantos, 2017); judicial studies (Pandya et al., 2023); and meta-analysis and replication studies (Zhang et al., 2019;Pawel et al., 2023b). ...