Open Philanthropy's recent blog post announcing new hires in South Asian Air Quality and Global Aid Advocacy states that the U.S. President's Emergency Plan for AIDS Relief (PEPFAR) "has plausibly saved tens of millions of life-years since it was created in 2003." The post provides a link to a PEPFAR page that credits the program with "saving over 20 million lives", but unfortunately that page doesn't give a source for the estimate. The same estimate is mentioned in the PEPFAR Wikipedia page, but the other listed sources either merely repeat that figure or do not even give an estimate (Fauci & Ensinger 2018 is entitled 'PEPFAR — 15 Years and Counting the Lives Saved' but the paper does not actually count the lives saved by the program; it rather lists various intermediate outputs such as the number of people given retroviral therapy or the number of voluntary male circumcisions supported).

So, does anyone happen to know the source of the 20 million lives estimate, or is aware of other attempts to estimate the program's impact, measured in lives or life-years saved? Background: I'm interested in this mostly because I would like to expand the list of examples of successful aid programs in the Wiki entry on foreign aid skepticism.

(This question was adapted from a draft email I wrote to the Open Phil post author. After finishing the draft, I realized I didn't have his email address and couldn't find it online.)

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This Vox article by Dylan Matthews cites these two studies, which try to get at this question:

EDIT to add: here's a more recent analysis, looking at mortality impact up to 2018 — Kates et al. (2021)

Thanks! Coincidentally, I also found Dylan's article (as well as another study from 2015) and added an answer based on it, before seeing yours.

EDIT: Oh, I now see that you were linking to an earlier piece by Dylan from mid-2015, also published in Vox. The article in my answer is from late 2018.

Since writing the question, I found this study estimating the impact of PEPFAR during its first decade. It concludes that the program resulted in 11,560,114 life-years gained (p. 3). Rough linear extrapolation from the chart on p. 5 (though note that growth was superlinear in the reference period) would suggest an additional 25 million or so life-years were gained between 2014 and 2021, vindicating the "tens of millions of life-years" Open Phil estimate.

Dylan Matthews points to another study finding 1.2 million deaths averted by PEPFAR by 2007. Matthews points out that naive extrapolation from this finding would suggest 6 million deaths saved by the end of 2018 (when the Vox article was written), also noting that the true figure is probably higher because of the study's focus on a limited number of partner countries and because of significant growth in PEPFAR's funding over time. In drawing this inference, Matthews links to a webpage on the PEPFAR's website. The link now redirects to PEPFAR's homepage, but a Wayback Machine search reveals the contents of the original URL: a press release announcing that "Latest Results Show PEPFAR Has Saved Over 17 Million Lives". However, again no source is cited for the estimate. The press release does mention a report, but the archived report I found had no explanation for its estimates of lives saved.