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

Question

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?

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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.

Answer 1

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.