Population Attributable Fraction…. Isn’t.

I thought I could stay out of it, I really did. I thought I could be like the green reed, and let all the hot air of the “gas stove” crisis bend me, but not break me, and move on to issues that are far more important.

But then, my editor Adam reached out to me to ask a simple question about the concept of population attributable fraction – a statistical idea that plays into one of my biggest pet peeves of all time – the false implication of causality.

And so now, because I had to face the demon once again, I will bring you with me, into the depths of epidemiology, to understand how a simple word can change the tenor of a national conversation. There will be some math.

By now, you’ve probably seen the news stories. In October of 2022, minutes of the United States Consumer Product Safety commission announced that in 2023, the commission would begin “rulemaking” with regard to gas stoves.

“All options are on the table”, commissioner Trumka is reported to have said, leading to breathless denunciations of the impending gas stove ban, or worse, forceful government seizure of said cooking implements.

I’m sort of over the big government boogeyman at this point – honestly, if the government instituted a successful nationwide stove seizure, aside from being a terribly stupid idea, I would be impressed that they got their logistics straight.

And I don’t want to talk about rights and liberty because, let’s be honest, we all know no one is coming for your stove. It’s a straw man argument. 

No. I want to talk about the data. What is the problem with these gas stoves? Well, like all things, it’s not necessarily one thing. There’s the issue of carbon monoxide poisoning, greenhouse gas emissions, etc. But what has been discussed mostly is this statistic – 12.7% of childhood asthma in the United States is due to gas stoves.

That statistic comes from this paper, published in the International Journal of Environmental Research and Public Health.

The population attributable fraction. There it is. A statistical concept with a horrible name.

This paper getting all the press is an updated analysis of a prior paper, published in 2013, which was itself a meta-analysis of 27 studies looking at the relationship between gas stoves and asthma, wheezing, and other respiratory issues.

Interestingly, the authors of the new paper searched for new data from 2013 to now to add to the original study, and despite chasing down 27 articles that seemed to address the issue, none provided effect estimates. In other words, the current paper has the exact same data as the paper from 2013.

That’s right. There’s no new information here. So fine – that’s the playing field.  What are the results?

Well, the authors find, after combining all this data, that the odds of developing asthma among children exposed to gas stoves is 34% higher than the odds of developing asthma among kids not so exposed.

This finding is statistically significant. There is an association between gas stove use and asthma in kids.

And if the study were to stop there, reporting an odds ratio of 1.34, we might not be in the pickle we’re in. We’re all used to reading studies that link some exposure to some outcome in this way.  And we’re all careful no to conflate correlation with causation. People who eat foie gras live longer than people who don’t, but I promise it’s not the foie gras that helps.  (It’s the money).

That brings us to this misunderstood statistical concept called the population attributable fraction.  It works like this.

For any given disease, there are underlying causes. And it would be useful to know how much individual causes contribute to the total burden of a particular disease. Why?  Because then we could know how much we would reduce the disease if we eliminated that particular cause.

So let’s calculate the population attributable fraction for stoves and asthma. Full disclosure here, I had to estimate some numbers to make the math work – but I think they’re pretty close. Let’s say I want to know how much asthma I could eliminate if I eliminated gas stoves.

Let’s say we’ve got 100,000 households.

Roughly 35% of Americans households have gas stoves, so I can fill in the edge like this.

The prevalence of asthma in houses with gas stoves is something like 15%, so I can fill in the upper boxes like this.

And the prevalence in houses without gas stoves is something like 11 or 12%, so I can fill in the bottom boxes like this.

These are the only numbers I’m going to use moving forward. Note that the rate of asthma is higher in houses with gas stoves, but that’s simply a correlation. I’m not proving gas stoves cause asthma, just that people with gas stoves are more likely to have asthma. But let’s push the math harder.

Ok, focusing just on those cases of asthma now.  We’ve got 13000 cases, 5500 of which are among people who live with gas stoves.

You’ll be tempted to say that 42% of asthma cases are due to gas stoves.  But not so fast.

Remember there is a background rate of asthma in the population that, presumably affects people regardless of their gas stove status – that’s that 11 or 12% number. So it turns out that 4000 or so of the cases of asthma in houses with gas stoves would be expected to have asthma anyway – can’t blame the stoves for those cases.

That little adjustment brings us down to a population attributable fraction of 11%, which is close enough to what the study authors found. These were all very rough numbers, but it lets me as an epidemiologist conclude that I could reduce the prevalence of asthma by 11% if I just eliminated all gas stoves.

But here’s the problem. Though the math is nice, the conclusion implies something that I never proved – causality. It assumes that gas stoves cause asthma. But the only numbers I had to do all this math were observational – correlations.

Do you get the problem?

The Population Attributable Fraction calculation takes data which may be purely correlational, and attaches this word to it “attributable” – which implies causation. It plucks causality out of thin air. And I see this all the time with this metric. All of a sudden, a nice observational study where we’d normally conclude there is an “association” between A and B turns into A causes B and it changes the narrative completely. Because if A causes B, then changing A changes B. And changing A requires policy.

To be clear, I’m not saying gas stoves don’t cause asthma – there are biologically plausible reasons why they would. What I don’t agree with are statements that 12.7% of asthma would be eliminated if gas stoves are eliminated. The actual number is almost certainly less than that, because factors associated with gas stove ownership (particularly socioeconomic factors) may themselves be leading to asthma and removing gas stoves won’t change those factors.

I hope you now see the problem, as well as my frustration with this good statistical concept that comes with a very inappropriate name. This whole debate hinges on one bad word – attributable.

A version of this commentary first appeared on Medscape.com.