Key points are not available for this paper at this time.
Overall, the basic heuristic of variable reduction in high-dimensional propensity score adjustment performed, as well as alternative approaches in diverse settings. Minor improvements in variable selection may be possible using Bayesian outcome regression to prioritize variables for propensity score estimation when outcomes are rare. See video abstract at, http://links.lww.com/EDE/B162.
Schneeweiß et al. (Tue,) studied this question.