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.
I wonder if the GC-MS exists for municipal water supplies already, and can just be aggregated and compared against population obesity rates? Less precise than doing it house-by-house, but much cheaper if someone has already done it for you and also it might not vary much house-by-house.
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.
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.
I wonder if the GC-MS exists for municipal water supplies already, and can just be aggregated and compared against population obesity rates? Less precise than doing it house-by-house, but much cheaper if someone has already done it for you and also it might not vary much house-by-house.
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.