If we were to hypothesise that some environmental factor is causing a significant fraction of the obesity problem then how would we test it?
The statistical silver bullet you're looking for, assuming you can't run multi-decade RCTs or convince entire countries to dramatically change their water policies (sounds a bit tricky?), is variance components analysis.
You want a variance component analysis equivalent to heritability, but for water/obesity. This is a perfect match: you have a very high-dimensional measurement (GC-MS of drinking water & foodstuffs), whose components you can't observe because you don't even know how many there are much less which ones (like the unknown chemicals that the original contaminants may react into along the way**), where direct prediction/regression would fail because it requires absurd amounts of data (especially given the statistical issues they outline), and where your original research question is not "where is the needle in the haystack" but "does this haystack have any needles at all".
In behavioral genetics, if you plot pairs of people by their genetic similarity and their phenotypic similarity, you will find that people similar on both tend to cluster; and the more heritable the trait is, the more they cluster. You can do this for kinds of similarity which aren't 'genetic'. The idea of variance components is to switch from directly correlating/regressing the specific chemical levels in water, trying to measure the exact direct effect of each chemical on obesity, to instead asking, "how similar, in terms of overall water chemical composition, are similarly far or thin people? Do the chemical spectrums of fat people tend to look similar, and the spectrums of thin people look similar? Do they co-vary, and cluster?"
Think of the water GC-MS as a sort of fingerprint or high-dimensional summary. It doesn't need to contain the actual critical datapoint, just a lot of correlates/proxies thereof (eg you can just shine some light on leaves and it'll work!). The point is not to directly measure the culprit, but to indirectly measure how distant the datapoints are; perhaps chemical A shows up and chemical B does not show up clearly, and B is the real cause, but as long as chemical A correlates with chemical B (maybe it's a different reaction product, or just gets manufactured or used in close correlation with B), then you will see that fatties tend to have close-together water spectra (because of A) and you will have strong evidence that "there is something in the water" because where the bad water clusters the fatties cluster.
So, you'd do something like record the BMI of 10,000 people, take a sample of their drinking water, GC-MS it (ideally, but many other analytical techniques could be used and maybe some would be better here, I'll defer to any actual analytical chemists on that topic), and then plug into a mixed linear-model. You can plug in covariates as necessary (families/pedigrees to jointly model genetic heritability, ZIP codes, age, sex, local mining/factories, already known harmful contaminants the GC-MS detected, that sort of thing). This can be done at multiple levels: individuals nested in households, within regions, within countries, etc. The amount of covariance between the water spectrum and BMI measures the amount of variance the contents of the water en masse can explain, and depending on measurement error and whatnot, given the genetic heritability bounding how much water-heritability can explain, you should get somewhere <30%. Under most theories of obesity, it's difficult to see why one would predict a water-heritability different from 0%*, especially if one has already included altitude/SES/household/region as covariates (which should cover all the obvious confounders like "maybe contaminated water is just a proxy for living in a poor region / having mining nearby / being poor"), so anything >0% is highly suspicious.
This doesn't require any RCTs (or interventions of any kind), longitudinal datasets, n in the millions, or any of the barriers to most of the proposed tests. You only need a cross-section of obesity/water-samples. Individual level is ideal, but doing it with geographic units can be useful too if that is what is available across enough units (individual n are much nosier than k, but also much easier to get high statistical power with). This may even already exist! Drinking water is often tested for many reasons, and obesity health data is standard medical data collected in almost any relevant research; so there ought to be a lot of possible cross-references.
* you could do this with food as well but I focus on water because water is a lot more consistent day to day, and food results would be ambiguous. A single day's food is still not very representative of individual consumption (maybe your wife cooks healthy at home but then you eat processed garbage at the office, and the sample comes from the weekend), so it provides a very poor measurement of the overall diet's chemical signature. And if you demonstrated a large food-heritability of obesity, this would just be taken as proving that "see? sugar / fat / calories / highly-palatable processing causes everything, just like we said all along!", and be weak evidence for contamination at best.
** They also raise the problem of interactions & nonlinear responses. These are issues in behavioral genetics too, of course, with dominance/epistasis particularly, and can be dealt with similarly in the water context: "narrowsense" vs "broadsense" heritability covers simple additive vs interactions, and you can do things like DeFries-Fulker, I think, for nonlinear responses. My guess is that contamination would be 'additive' mostly, for similar underlying reasons as genetics tends to be 'additive': many interactions are just constants because they are done on a fixed background of chemistry, and promiscuous interactions average out to additive effects. But this is the sort of thing to worry about only after having done the straightforward work.
Yes, that is what I meant by geographic units. It has both advantages and disadvantages: data may already be available, and may be much more statistically-powerful; on the other hand, variance-components like BLUP usually are done with individuals available, and I'm not sure about the interpretation/correctness of doing it otherwise.
This is a summary of a paper that I found open in a browser tab; I don't recall where I came across it. I think it's a nice paper, but it's also 63 pages long and seemed worth a synopsis for those who wouldn't otherwise tackle it.
Scott concluded in For, then Against, High-saturated-fat diets that the obesity crisis seemed to imply one of three answers:
This paper argues for the second answer, and against the other two.
At the outset, there are reasons to be wary of this paper: neither author (who share a family name) appear to have expertise in applicable fields, and it appears to be set in Computer Modern Roman, hardly the style of a journal submission. So it's coming from outside of traditional expertise. (I don't have any expertise here either.)
With that in mind, the paper starts by posing a series of challenging facts about obesity. (References in the original:)
The next section answers some of the competing explanations for obesity:
“It's from overeating!”, they cry. But controlled overfeeding studies (from the 1970's—pre-explosion) struggle to make people gain weight and they loose it quickly once the overfeeding stops. (Which is evidence against a hysteresis theory.)
“It's lack of exercise”, they yell. But making people exercise doesn't seem to produce significant weight loss, and obesity is still spreading despite lots of money and effort being put into exercise.
“It's from eating too much fat”, rings out. But Americans reduced their fat intake in response to messaging about the evils of fat some decades ago and it didn't help. Nor are low-fat diets very effective.
“It's too much sugar / carbs”, you hear. But Americans reduced their sugar and (more generally) carb intakes over recent years and that didn't help either. Gary Taubes's study was a bit of a damp squib.
In this section there's a hunter-gatherer tribe for everything. I'm a little suspicious of this line of evidence because these small human populations could plausibly have evolved to tolerate their specific environment but, if you want a group of humans with zero-percent obesity who eat 60%+ carbs, or 60%+ fat, this paper has one for you. They have plenty of food, they just live happily and remain thin.
Next the paper establishes that there is clearly some degree of homeostatic regulation of weight by the brain. You can damage a specific part of the brain and cause obesity. Or you can have a genetic flaw that results in fat cells not producing leptin, which results in an insatiable appetite. (But adding leptin to overweight people doesn't work.)
Now the paper presents its thesis: it's all caused by a subtle poison! Manufacture of which really took off slightly before 1980, and is increasing or is bio-accumulative. Diets don't work because it's not a diet problem. Supermarket food fattens rats much more than any macro-nutrient chow because supermarket food contains more of the contamination. Wild animals are getting fatter because they're consuming it too. Living at sea-level means that your water supply has traveled much further and picked up more of it, which is why altitude is anti-correlated with obesity.
There are many drugs that cause weight gain and that appear to do so by acting on the brain, so these things can exist. This is hardly the first paper to suggest that certain chemicals contribute to the problem, but this paper is distinguishing itself by saying that it's the dominant factor.
Three specific families of chemicals are detailed for consideration: antibiotics; per-, and poly-fluoroalkyls (PFAS); and lithium. All have ambiguous evidence.
Antibiotics certainly make animals fatter, but do they do the same to humans in the amounts consumed? If so, why aren't places that use a lot in livestock fatter than those which use less? Why aren't vegan diets magic for weight loss?
PFAS is a family of thousands of under-studied chemicals, but they doesn't clearly cause weight gain in humans at plausible levels. But they are certainly getting everywhere.
Lithium clearly does cause weight gain in humans, but are the amounts that people are exposed to increasing, and they are large enough to cause weight gain?
The paper also notes that things are even worse to think about because chemicals do complex things in the environment, and in animals. You don't just have to think about the chemicals that are made, you have to worry about everything they can become. The paper includes the example of a factory in Colorado that made “war materials” and released some chemicals into the ground around the factory. It took several years for the chemicals to travel through the ground water to farms several miles away. During that time they had reacted to form 2,4-D, a herbicide, which killed crops on those farms. (The unreacted chemicals were also pretty nasty.)
Switching to speculation that should be blamed entirely on me, not the paper: it seems that there might be a tendency for any chemical that affects the regulation of adiposity to do so in the direction of obesity. There are several drugs that target the brain and cause weight gain, but fewer safe drugs that cause significant down regulation of weight. (If there were several such drugs, lots of people would be taking them.) Rather, drugs that cause weight loss often cause energy to be wasted from the body rather than changing the regulation of weight: DNP causing heat-loss, or SGLT2 inhibitors causing glucose excretion. Thus we might be facing a situation where multiple minor factors affect adipose regulation, but the overall effect is towards obesity because any effect tends to be in that direction.
The obvious example of something that causes down-regulation of weight is smoking. (We wouldn't call it “safe” though.) I wonder whether the paper is overly focused on something that had a step change in prevalence shortly before 1980. It might have been building steadily in the prior decades but the 40%ish of American adults who smoked in the 60s/70s hid it for a while.
If we were to hypothesise that some environmental factor is causing a significant fraction of the obesity problem then how would we test it? It could well be the sum of multiple factors, some of which may be carried in water given the correlation with elevation. It seems that one would need groups of overweight people willing to consume exclusively provided water (from distillation) and a source of food that is somehow pristine. The half-life of PFAS, at least, is measured in years in humans, so the subjects would have to remain compliant with this proscribed diet for extended periods of time. In order to have control groups we would have to (double-blind) contaminate the pristine food with environmentally-plausible levels of candidate chemicals, I guess? Would that get past any IRB? The paper contains easier experiments, like having Kuwait change its desalination process or, more reasonably, have a car-mechanic company change grease, but these would only produce partial answers unless we got lucky and one factor dominates.
The environmental hypothesis is primarily one of exclusion, and this paper makes a good case. (Although one should have significant epistemological humility about any complex technical argument outside of one's expertise.) And I haven't even covered it all! The paper continues with arguments about paradoxical reactions and the occurrence of anorexia! There is much more within if this summary piqued an interest.