Ethical Dilemmas in Valuing Human Lives

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Can we help individual people cost-effectively? Our trial with three sick kids, published by NickLaing on February 20, 2024 on The Effective Altruism Forum.
TLDR: My wife and I tried to help three children with severe illness cost-effectively. We paid for their medical care, followed up on what happened and reflected on the process.
"Hearing about her death hurt badly - as it should. But not only had I done what I could, it made sense. Those 300 dollars gave her a chance of not only surviving, but living a long and happy life."
My wife and I live in Gulu, Northern Uganda, where I operate OneDay Health, a social enterprise which provides cost-effective health care in remote rural areas - but this post isn't about that.
We naturally encounter many situations where we feel compelled to help those around us, We sometimes help with school fees, medical bills and sometimes just cash bailouts. Many of these might not be very cost effective and fall into the "fuzzy giving" category, but by virtue of living in Uganda I suspect these contributions may often hit the unusual jackpot of both feeling good and being cost-effective, earning both "fuzzys" and "utilons" at the same time (sorry Yudkowsky, we mix them).
Which got me thinking, could we target some of our support in a more cost-effective way? As a medical guy in Uganda, I figured we might be in a decent position to try, so we embarked on a mini-experiment to see if we could find a few medical cases which could be super cost-effective to treat, on par with top GiveWell charities.
Our Cost-Effectiveness Bar
We kept it simple here, and deferred to GiveWell's top-charity bar of $5500 per life saved. [1] I estimated cost effectiveness by dividing the money we would spend on medical care by a series of discount multipliers based on loosely estimated counterfactuals (see calculations below). My approach is deeply flawed as it fails to account for many variables, but allowed me to make a reasonable estimate in about 15 minutes.
Feel free to criticize and discuss the method, I'm sure there more accurate and easier ways (@NunoSempere @Vasco Grilo). I didn't attempt a cost-effectiveness range as it would take longer.
But where to find these sick people who might be cost-effectively helped? We planned to identify poor rural farmers who had life-threatening treatable illnesses, who were unlikely to be treated unless we paid for it. So I asked a couple of our OneDay Health managers to be on the lookout for sick people who presented to our Health Centers, while I also kept an eye out in the health center where I work as a doctor - people who could die without treatment that they couldn't afford.
Finding people to "cost-effectively" help turned out to be harder than expected. Over a 2 month period we identified three young girls to help, while we decided not to help in another 5 or so cases. These are the stories people we tried to help- feel free to skip the BOTECS if you aren't into that!
Lamunu - age 9
Even for a hardened doctor, Lamunu's photo was tough to look at. She showed up in our Health center with about 30% of her body burned after falling into a fire. She had spent 10 days in an ill-equipped government hospital and she continued deteriorate. Her father ran out of money and took her home, before arriving one of our health centers (which can't treat burns) as perhaps desperate last-ditch effort.
Her burns were infected, she was malnourished and everybody involved knew that she probably wasn't long for this world.
I happen to live 500 meters away from the best burns unit in Northern Uganda at St. Mary's hospital Lacor so I thought we might be able to help. We paid for her father to take a 5 hour bus ride to Lacor hospital, and supported the family with hospital fees and some food.
Cost effectiveness BOTEC?
Chance of death withou...