Sketch of a design for an experimental study on the effects of Lithium in drinking water

Since I wrote my last essay, this essay by Gwern on Lithium in groundwater was brought to my attention. I wanted to write out my naive and ill-informed ideas, merely by way of proposal, since I am far from certain any of this is right, but it seems worth talking about.

I agree with the thrust of Gwern’s article. There is suggestive evidence that Lithium in tap water may do an enormous amount of good. We should hurry up and test it then. As Gwern puts it:

The potential benefits seem so overwhelming that I am puzzled that, in the 42+ years since the correlation was first noted, no one has done a simple experiment of randomizing some counties and increasing their trace lithium concentrations within the normal range of natural variations in trace lithium concentrations. A quick estimate for what I mean. In Dawson et al 1972, the counties in the highest lithium category had 30% of the mental hospital admissions that the lowest lithium counties did; the USA spends something like$60b annually on mental health issues (the NYT quotes $150b government expenditure & $500b society-wide costs). If the reduction in admissions was equivalent to a reduction in the underlying disorders and expenditures scale exactly with number of disorders, then lithizing the USA would reap gains of something like $35b annually (NPV at 5%: ~$615b); however, this is only the direct expenditures, arguably the field is underfunded (reportedly, less than half the sufferers of mental illness may be treated), and of course the losses to society is far larger than that as peoples’ lives are destroyed, crime increases (with its massive negative externalities), careers abandoned, etc. At 1% prior odds and $615b total payoff, the expected value is ~$600m; a conclusive experiment ought to be trivially cheap to run (a few millions?), since it requires only supplementation of lithium at centralized water facilities, presents minimal ethical concerns due to remaining strictly within natural variation & regulatory limits (and vastly less than people voluntarily consume in bottled mineral waters), and can be analyzed using only statistics already being collected by police or health departments.

I’d add that, in my view, this somewhat understates the moonshot of the best possible outcomes of adding lithium to tap water. All the lives of ‘quiet desperation’ that might be helped, all the crime that might be stopped, as Gwern alludes but does not spell out… I am sure I could make a model in which the net present value of getting lithium levels right might be in the trillions. And once we factor in countries outside the US, it gets even bigger. But past a certain point, it doesn’t matter how many zeroes you add on, it’s clearly worth checking.

{Also net present value figures understate total value, because standard methodologies factor in prejudice against the future and therefore use too high a discount rate, but this is a story for another day}

Gwern notes that:

the psychiatric-useful doses are something like 100x the higher groundwater doses;

Gwern concludes:

It is unlikely that further such correlational research will resolve the debate, despite the mounting opportunity cost. I suggest that formal experimentation is required, and concerns about harms from lithium supplementation making experiments ‘unethical’ can be circumvented by instead removing lithium or looking for natural experiments with cause changes (such as changes or upgrades to water treatment plants or plumbing modify lithium concentration).

I agree with Gwern’s negative claim but note difficulties with the positive alternatives he suggests. Natural experiments have methodological difficulties and are hard to find. Removing Lithium has its own ethical difficulties that I’m surprised Gwern didn’t anticipate (try telling an ethics board “We think Lithium in groundwater stops people killing themselves and we want to remove it to test this”).

I propose instead the following alternative. Go to an area with low Lithium in the tap water. Recruit a large population of volunteers and give them lithium tablets at a dose designed to get them up to the ‘dose’ people in an area with higher tapwater lithium would get daily. Lithium is extremely bioavailable, there should be no difference in taking a tablet or drinking water with extra Lithium in it. As Gwern notes, this dose would probably be in the order of 100th of the clinical dose.

Who to target? Two options:

1. People with mild to moderate depression and anxiety, since there are plausibly clinical benefits for this population.

2. The general population.

The main problem is that an experiment of this sort is going to be underpowered to test for suicide and violent crime, they’re just too rare- unless you choose an ultra-at-risk population, which has its own ethical difficulties. However, if you set as your primary dependent variables:

1. Self-assessed mood

2. Self-assessed mood variability

3. Family assessed mood

4. Family assessed mood variability

5. Self-assessed anger

6. Self-assessed anger variability

7. Family assessed anger

8. Family assessed anger variability

It is very likely that if there is an effect on aggression and suicide, it will be picked up through changes in these lower-level proxies.

In addition, the following secondary dependent variables would be good inclusions:

1. Depression

2. Anxiety

3. Creativity- Gwern worries that Lithium might reduce creativity, this is worth investigating as a risk.

4. Intelligence- See above.

5. Energy- Also a potential risk that it will deplete energy

6. Sleep

7. Weight- it will be important to rule out weight gain as an effect, given this is a major side effect of Lithium

8. Altruism- This is my special interest, so I want to see it included. Prisoners dilemma plus impunity game would be good measures.

In terms of power, because the posited effects are modest, the experiment would have to be large. Assuming an effect size of Cohen’s d=0.1, a significance level of 0.01, and a power of 90%, one gets 5952 as the recommended enrollment size (split equally between both groups). If we instead aim for a power of 80% we get 4672. Cohen’s d=0.1 might sound very low, but on a population level, it would be massive. This is the first big problem with the plan- how to recruit enough people? This experiment would cost a fair bit of dough. How to get the resources?

Now the second big problem with the experiment. There is a story about some holy men who tried to stop idol worship by blinding the angel of desire in one eye. They succeeded, but prophecy left the world. We really don’t want to do the equivalent of that- take the lightning out of people to make things a bit more orderly. It’s vital to check Lithium doesn’t affect, for example, energy, creativity, or intelligence. There are too many problems that need lightning. As Gwern notes, there is a huge difference between the clinical dose and the groundwater dose. It is unlikely that the groundwater dose is enough to douse or lower the fire in bellies, but you want to be quadruply sure with this sort of thing. Just because lithium would be kept within the range of natural variation does not guarantee against a significant negative effect.

Overcoming the second problem is a matter of checking. Overcoming the first problem is a matter of getting support for such a large experiment. I propose that as a build-up, we start with an observational large study correlating blood lithium with mood- a much more direct test than correlating tapwater levels. This experiment would track the variables previously outlined. There are only small experiments that have correlated blood lithium in patients who hadn’t taken lithium as a medicine thus far in their lives. Although early results are promising. The two studies I linked focused on suicide and suicide attempts, checking the correlation with mood, and various depression inventories would make it much easier to recruit participants than checking the correlation with suicide and suicidality.

{There’s a more general point here: medical science, in not always recognizing the continuous, dimensional qualities of mental disorders, has often neglected variation of mood within the ‘normal’ range as a source of evidence. Relatedly it can be difficult to find large publicly available datasets including both psychological variables and an extensive range of medical variables- such as important blood levels e.g. lead, lithium, medical history, etc. This is so inefficient. More omnibus correlational studies would make individual data gathering for many studies obsolete.}

There is some evidence that men and women may respond differently to lithium, with little to no effect on women. A good serum study would help sort this out before the experimental study.

If this experiment worked, really worked at the high end of how well it might, it would suggest an inexpensive public health intervention that would save thousands of lives. Over time and over the globe it might save millions of QALYS through reduced mental illness, reduced crime, reduced suicide, increased happiness ratings, possible neuroprotective effects- the whole shebang.

Finally, Suppose you want to keep up the correlational research. There’s some really big datasets that haven’t been tapped into yet. There is a lot of lithium data across the US, and there is a lot of suicide and homicide data. I’m surprised no one has done a whole of the US study yet. Also note that sodium closely tracks lithium, so this is another option:

Bear comforts the angel of desire who has been blinded in one eye