# How does the WHO calculate the interaction of mortality effects from indoor and outdoor air pollution?

The WHO's landing page on air pollution includes three different estimates of deaths due to air pollution:

• 7 million total
• 4.2 million due to outdoor (ambient) air pollution
• 3.8 due to household (indoor) air pollution

Obviously, 7 < 4.2 + 3.8, so there must be some way in which they decide some of those deaths were caused by a combination of indoor and outdoor air pollution. But what is this methodology?

It's unclear where that 7 million figure originates from, so there's a chance it's a case of citogenesis, and someone just did the math wrong. It appears in WHO's 2021 global air quality guidelines (section 1.3.3), which cites Burden of disease from ambient air pollution for 2016, where the 7 million figure does not appear.

WHO page Indicator 3.9.1: Mortality rate attributed to household and ambient air pollution (per 100 000 population) has this information in the "metadata" tab:

Method of estimation:

[...] To estimate the combined effects of risk factors, a joint population attributable fraction is calculated, as described in Ezzati et al (2003).

Ezzati et al (2003) defined the joint population attributable fraction ($$PAF$$) for $$n$$ biologically independent and uncorrelated risk factors, as (their equation 2):

$$PAF = 1 - \prod_{i=1}^n(1-PAF_i)$$

where $$PAF_i$$ is the population attributable fraction of individual risk factors.

• +1. Nice find. Is there enough information to show the calculation? i.e. how to get to 7 million total from the 4.2 and 3.8 million figures? The Ezzati paper is behind a paywall, and WHO's explanation only includes the formula, not the calculation. Mar 24, 2022 at 15:00
• I've had a look but the data seems to be only by country, I couldn't find global data. So I guess to try to reproduce the calculation, you'd have to calculate each country's contribution to the total by multiplying its mortality rate by its population... Mar 25, 2022 at 10:07