Mirrored histogram showing “weird” parts of the population: treated people who were unlikely to be treated, and untreated people who were likely to be treated
Mirrored histogram showing pseudo-populations of treated and untreated people that have been reweighted to be more comparable and unconfounded
Table showing potential and realized outcomes for 9 simulated people
Before we calculate these different treatment effects with the realized outcomes instead of the hypothetical potential outcomes, let's look really quick at the practical difference between the true ATE, AT 1, and ATU. All three estimands are useful for policymaking!
The ATE is -15, implying that mosquito nets cause a 15 point reduction in malaria risk for every person in the country. This includes people who live at high elevations where mosquitoes don't live, people who live near mosquito-infested swamps, people who are rich enough to buy Bill Gates's mosquito laser, and people who can't afford a net but would really like to use one. If we worked in the Ministry of Health and wanted to know if we should make a new national program that gave everyone a free bed net, the overall reduction in risk is -15, which is probably pretty good!
The ATT is -16.29, which is bigger than the ATE. The effect of net usage is bigger for people who are already using the nets. This is because of underlying systematic reasons, or selection bias. Those using nets want to use them because they need them more or can access them more easily-they might live in areas more prone to mosquitoes, or they can afford to buy their own nets, or something else. They know themselves and understand some notion of their personal individual causal effect and seek out nets. If we removed access to their nets, it would have a strong effect.
The ATU is -13.63, which is smaller than the ATE. The effect of net usage is smaller for people who aren't using the nets. Again, this is because of selection bias. Those not using nets are likely not using them for systematic reasons-they live far away from mosquitoes, they've received a future malaria vaccine, they have some other form of mosquito abatement, or something else. Because they can read their own minds, they know that mosquito net use won't do much for them personally, so they don't seek out nets. If we expanded access to nets to them, they wouldn't benefit
From the archives: Have you (like me!) wondered what the ATT means and how it's different from average treatment effects? I use #rstats to explore why we care about (and how to calculate) the ATE, ATT, and ATU #polisky #episky #econsky www.andrewheiss.com/blog/2024/03...
