Our work on benchmarking efficiency is now out: http://bmcmedicine.biomedcentral.com/articles/10.1186/s12916-016-0653-z
It uses some very cool econ and OR methods, and it even has a press release: http://www.healthdata.org/news-release/improving-health-facility-efficiency-could-markedly-expand-hiv-treatment :
“Improving efficiency can support major gains in expanding ART to people who need treatment, especially when funding is limited,” says IHME Assistant Professor Abraham Flaxman, senior author of the study. “Now we, as a global health community, need to figure out how.”
Healthy Algorithms 