Long Covid Informal Study Results

Introduction

Yesterday* I talked about a potential treatment for Long Covid, and referenced an informal study I’d analyzed that tried to test it, which had seemed promising but was ultimately a let down. That analysis was too long for its own post, so it’s going here instead. 

Gez Medinger ran an excellent-for-its-type study of interventions for long covid, with a focus on niacin, the center of the stack I took. I want to emphasize both how very good for its type this study was, and how limited the type is. Surveys of people in support groups who chose their own interventions is not a great way to determine anything. But really rigorous information will take a long time and some of us have to make decisions now, so I thought this was worth looking into.

Medinger does a great analysis in this youtube video. He very proactively owns all the limitations of the study (all of which should be predictable to regular readers of mine) and does what he can to make up for them in the analysis, while owning where that’s not possible. But he delivers the analysis in a video rather than a text post ugh why would you do that (answer: he was a professional filmmaker before he got long covid). I found this deeply hard to follow, so I wanted to play with the data directly. Medinger generously shared the data, at which point this snowballed into a full-blown analysis.

I think Medinger attributes his statistics to a medical doctor, but I couldn’t find it on relisten and I’m not watching that damn video again. My statistical analysis was done by my dad/Ph.D. statistician R. Craig Van Nostrand. His primary work is in industrial statistics but the math all transfers, and the biology-related judgment calls were made by me (for those of you just tuning in, I have a BA in biology and no other relevant credentials or accreditations).

The Study

As best I can determine, Medinger sent a survey to a variety of long covid support groups, asking what interventions people had tried in the last month, when they’d tried them, and how they felt relative to a month ago. Obviously this has a lot of limitations – it will exclude people who got better or worse enough they didn’t engage with support groups, it was in no way blinded, people chose their own interventions, it relied entirely on self-assement, etc. 

Differences in Analysis

You can see Medinger’s analysis here. He compared the rate of improvement and decline among groups based on treatments. I instead transformed the improvement bucket to a number and did a multivariate analysis. 

Much better (near or at pre-covid)1
Significantly better0.5
A little better0.1
No change0
A little worse-0.2
Significantly worseCuriously unused
Much worse-1.2

You may notice that the numerical values of the statements are not symmetric- being “a little worse” is twice as bad as “a little better” is good. This was deliberate, based on my belief that people with chronic illness on average overestimate their improvement over short periods of time. We initially planned on doing a sensitivity analysis to see how this changed the results; in practice the treatment groups had very few people who got worse so this would only affect the no-treatment control, and it was obvious that fiddling with the numbers would not change the overall conclusion.

Also, no one checked “significantly worse”, and when asked Medinger couldn’t remember if it was an option at all. This suggests to me that “Much worse” should have a less bad value and “a little worse” a more bad value. However, we judged this wouldn’t affect the outcome enough to be worth the effort, and ignored it. 

We tossed all the data where people had made less than two weeks ago (this was slightly more than half of it), except for the no-change control group (140 people). Most things take time to have an effect and even more things take time to have an effect you can be sure isn’t random fluctuation. The original analysis attempted to fix this by looking at who had a sudden improvement or worsening, but I don’t necessarily expect a sudden improvement with these treatments.

We combined prescription and non-prescription antihistamines because the study was focused on the UK which classifies several antihistamines differently than the US. 

On row 410, a user used slightly nonstandard answers, which we corrected to being equivalent to “much improved’, since they said they were basically back to normal.

Medinger uses both “no change” and “new supplements but not niacin” as control groups, in order to compensate for selection and placebo effects from trying new things. I think that was extremely reasonable but felt I’d covered it by limiting myself to subjects with >2 weeks on a treatment and devaluing mild improvement. 

Results

I put my poor statistician through many rounds on this before settling on exactly which interventions we should focus on. In the end we picked five: niacin, anti-histamines, and low-histamine diet, which the original analysis evaluated, and vitamin D (because it’s generally popular), and selenium (because it had the strongest evidence of the substances prescribed the larger protocol, which we’ll discuss soon). 

Unfortunately, people chose their vitamins themselves, and there was a lot of correlation between the treatments. Below is the average result for people with no focal treatments, everyone with a given focal treatment, and everyone who did that and none of the other focal treatments for two weeks (but may have done other interventions). I also threw in a few other analyses we did along the way. These sample sizes get really pitifully small, and so should be taken as preliminary at best. 

TreatmentNiacin, > 2 weeksSelenium, > 2 weekVitamin D, > 2 weekAntihistamines, > 2 weeksLow-histamine diet, > 2 weeksChange (1 = complete recovery)95% Confidence Interval n
No change000000.04± 0.07140
Niacin, > 2 weeks10.23± 0.0791
Selenium, > 2 weeks10.24±0.0788
Vitamin D, > 2 week10.15±0.05261
Antihistamines, >2 weeks10.18± 0.06164
Low histamine diet10.18±0.06195
Niacin, > 2 weeks, no other focal treatments100000.15±0.211
Selenium, > 2 weeks, no other focal treatments010000.05±0.064
Vitamin D, > 2 week, no other focal treatments001000.07±0.08106
Antihistamines, >2 weeks, no other focal treatments000100.08±0.1326
Low histamine diet, > 2 weeks, no other focal treatments000010.13±0.1444
All focal treatments111110
Niacin + Antihistamines, >2 weeks1100.33± 0.0738
Niacin + Low Histamine Diet, > 2 weeks100010.29±0.1036
Selenium + Niacin, no histamine interventions11000.05±0.1917
Niacin, > 2 weeks, no other focal treatments, ignore D10000.13±0.1219
Selenium, > 2 weeks, no other focal treatments, ignore D01000.16±0.1218

1 = treatment used

0 = treatment definitely not used

– = treatment not excluded

Confidence interval calculation assumes a normal distribution, which is a stretch for data this lump and sparse but there’s nothing better available.

[I wanted to share the raw data with you but Medinger asked me not to. He was very fast to share with me though, so maybe if you ask nicely he’ll share with you too]

You may also be wondering how the improvements were distributed. The raw count isn’t high enough for really clean curves, but the results were clumped rather than bifurcated, suggesting it helps many people some rather than a few people lots. Here’s a sample graph from Niacin (>2 weeks, no exclusions)

Reasons this analysis could be wrong

  • All the normal reasons this kind of study or analysis can be wrong.
  • Any of the choices I made that I outlined in “Differences…”
  • There were a lot of potential treatments with moderate correlations with each other, which makes it impossible to truly track the cause of improvements.
  • Niacin comes in several forms, and the protocol I analyze later requires a specific form of niacin (I still don’t understand why). The study didn’t ask people what form of niacin they took. I had to actively work to get the correct form in the US (where 15% of respondents live); it’s more popular but not overwhelmingly so in the UK (75% of respondents), and who knows what other people took. If the theory is correct and if a significant number of people took the wrong form of niacin, it could severely underestimate the improvement.
  • This study only looked at people who’d changed things in the last month. People could get better or worse after that.
  • There was no attempt to look at dosage.

Conclusion

For a small sample of self-chosen interventions and opt-in participation, this study shows modest improvements from niacin and low histamine diets, which include overlap with the confidence interval of the no-treatment group if you exclude people using other focal interventions. The overall results suggest that either something in the stack is helping, or that trying lots of things is downstream of feeling better, which I would easily believe.

Thank you to Gez Medinger for running the study and sharing his data with me, R. Craig Van Nostrand for statistical analysis, and Miranda Dixon-Luinenburg⁩ for copyediting.

* I swear I scheduled this to publish the day after the big post but here we are three days later without it unpublished, so…

Niacin as a treatment for covid? (Probably no, but I’m glad we’re checking)

Introduction

This article contains an interview with a doctor who believes NAD+ is the secret to covid’s heavy morbidity and mortality toll. The description was unusually well done for internet crackpottery. This is hard to convey rigorously, but it had a mechanistic-ness and the right level of complexity about it, and it made the right level of promises for a treatment. None of this is to say it’s definitely correct, but it had a bunch better chance of being correct than your average alt-covid-cure scribbled out in crayon. So I did some checks on it.

[Didn’t you say the risk of long covid was small? NO I SAID IT WAS TOO SMALL TO MEASURE AGAINST THE DELUGE OF CRAP THAT HAPPENS TO US EVERYDAY THAT IS NOT THE SAME]

*ahem*

This post is organized as follows:

  • Description of theory. 
  • Long section defining terms. These are all useful for understanding the claims I check later on, but depending on who you are they may not be helpful, and you may find the contextless infodump kind of a drag. Feel free to skip if it’s not useful to you personally, and know that it’s there if you need it.
  • Deep dive onto particular claims the article makes.
  • Does it work?
  • Is it safe?
  • My personal experience with the protocol 
  • Some meta

This is your reminder that my only credential is a BA in biology and I didn’t specialize in anything relevant. It is a sign of civilizational inadequacy that this post exists at all, and you should think really hard and do your own research before putting too much weight on it.

For those of you would like to skip to the take home message: science is very hard, I’m glad they’re running larger studies to follow up on all of these because that’s a reasonable thing for a rich society to do, but I’m not super hopeful about this protocol.

The Theory

As described by Dr. Ade Wentze:

There is an extremely widely used coenzyme in your body, NAD. The more active form of this compound, NAD+, is depleted by covid (converted to NADH). In people with a preexisting deficiency or difficulty rebounding after depletion, covid infection results in a persistent NAD+ deficit. This is bad in and of itself, but causes additional problems when your body tries to make up for it by requisitioning all your tryptophan to make more. Tryptophan is also a precursor for serotonin, so this leads to either low serotonin or activation of mast cells to release their serotonin stores, accompanied by histamines (which cause allergies and other issues). 

Background

There is a lot of vocabulary in that theory and in the supporting claims, which I go over here. If you’re reading for conclusions rather than deep understanding I would skip this.

NAD+

Nicotinamide adenine dinucleotide is a coenzyme that plays an essential role in hundreds of chemical reactions in your cells, including many relating to processing energy and genetic transcription.  This is a mixed blessing as a foundation for crackpot theories go: something involved in hundreds of processes across every kind of tissue in your body can cause almost any symptom, which is great because long covid has a lot of symptoms to cover. On the other hand, it can cause almost any symptom, which means it’s hard to disprove, and you should distrust things in proportion to the difficulty to disprove them. Alas, sometimes core processes are impaired and they do express that impairment in a range of unpredictable ways that vary across people, but it’s also an easy home for crackpots. 

NAD+ has two major components, one made from either tryptophan or aspartic acid (both amino acids), or by altering niacin.

Niacin

Like many vitamins, niacin aka vitamin B3 refers to a few different closely related compounds (most commonly nicotinic acid, nicotinamide, nicotinamide riboside, and inositol nicotinate, but there are others) that are almost but not quite interchangeable.

Chemical structures of niacin compounds: (a) nicotinamide; (b) nicotinic acid; (c) nicotinamide adenine dinucleotide (NAD þ ); (d) nicotinamide adenine dinucleotide phosphate (NADP þ ) (source)

Niacin is commonly prescribed for treating high cholesterol, although a metareview found it did not reduce overall mortality and may contribute to the development of type-2 diabetes. 

Severe niacin deficiency is called pellagra, and can be caused by either insufficient consumption or problems processing the vitamin. Pellagra is mostly defined as niacin deficiency but can also be caused by tryptophan deficiency, which you may remember is another path to manufacturing NAD+. Pellagra can cause diarrhea, dermatitis, dementia, and death, which are not a great match for acute or long covid. Niacin supplementation treats pellagra, often within a few days.

SIRT1

Sirtuin 1, also known as NAD-dependent deacetylase sirtuin-1, is a protein that regulates the expression of some genes in ways that haven’t yet been made clear to me but seem to be associated with aging (more SIRT1 is associated with better outcomes, although we haven’t broken down cause and effect). As indicated by its name, it’s dependent on NAD+ to operate, which means NAD+ is involved in the regulation of expression of some genes via some mechanism, which means niacin is involved in the regulation of expression of some genes via some mechanism.

SIRT1 is downregulated in cells that have high insulin resistance and inducing its expression increases insulin sensitivity, suggesting the molecule is associated with improving insulin sensitivity.

SIRT1 may be upregulated by selenium.

PARP

Another many-purposed enzyme whose activities include DNA repair, killing cells that are beyond repair. PARP requires NAD+ as a coenzyme.

Individual Claims

Groups with low NAD+ suffer more from covid

NAD+ declines with age

NAD+ does definitely decline with age but so does literally everything bad in your body, so I don’t find this very compelling.

Correlation between NAD+ levels and Age in (A) Males (B) Females (source)

Obese people have lower NAD+ levels, leading to worse outcomes

Yes, although obese people tend to do worse on a lot of metrics. However, that paper highlights that SIRT1 seems to be involved in this correlation somehow.

Diabetics have worse NAD+ levels

Yes, although diabetics also have more immune problems generally (definitely Type 2, some pop sites said the same for Type 1 and that’s believable but I didn’t quickly find a paper I liked that backed the claim).

Low selenium is associated with bad outcomes in covid

The post cites Zhang et al, which took advantage of high variations in selenium consumption in China to do a natural experiment. Variations in the population selenium levels do seem insanely correlated with the overall cure rate (defined as not dying). The study took place in February 2020 so neither data collection nor treatment was very good, but damn that is interesting.

Moreover, this study, which came out several months after the blog post was published, took advantage of the same variation and came to the same conclusion, with a much larger sample size and much more reasonable case fatality rate (1.17% in areas with no deficiency to 3.16% in severely deficient areas, P = 0.002). (Note: several authors on that paper are also named Zhang, but I assume that’s because it’s a common name in China).

Some pharma company thinks selenium is promising enough to launch a trial for it, although recruitment hasn’t started yet.

The pre-print servers are littered with natural experiments highlighting correlations that failed as interventions, but this is very strong for a correlation.

Niacin just generally seems to help lung damage

That is indeed what their citation says, however that paper’s only source looked at the effect of niacin on lung damage in hamsters deliberately induced with a chemotherapy drug, and it’s not obvious to me that that translates to damage from infection or immune reaction. There are some other scattered studies in rodents, combining niacin with other substances, none of which looked at damage from infectious disease.

The treatment for NAD+ deficiency is niacin

Their citation backs this up: niacin supplementation led patients (n=5) and controls (healthy people given the same supplementation, n=8) to increased NAD+ levels, and arguably increased strength, although with that much variation and such a small sample size I’m not convinced. Martens et al supports this with modest benefits seen in n=24 subjects.

A few minutes investigation found some other studies:

  • Dietary niacin deficiency led to NAD+ deficiency in baby rats. This paper works damn hard to hide its sample size but I think it was 10-15 per treatment group.
  • The same author exposed some rats (n=6 per treatment group) to excess oxygen and found that those with a niacin deficient diet had less NAD+ in the lungs and responded less to the damage caused by excess oxygen, but had the same wet/dry ratio as their well-fed friends (wet/dry ratio is a measure of lung health).
  • Ng et al found that in catfish liver NAD increased linearly with dietary niacin supplementation, but health returns like size and mortality dropped off between 6 and 9 mg/kg. They further found that tryptophan supplementation could not make up for a niacin deficiency (in catfish).

Plus niacin is so well established as a treatment for pellagra that no one bothers to cite anything for it, and that does seem to mediate through NAD+.

Nicotinic acid may act as a one of a kind bioenergetic “pump” of inflammatory molecules out of cells

They link to a preprint which has since been taken down, and I could not find it on my own. 

NAD+ problems have been indicated in chronic fatigue syndrome

Everything has been indicated in chronic fatigue syndrome; I’m not looking this up.

Low serotonin -> mast cell activation -> histamine release

Mast cells indeed produce serotonin, in mice. Note that that paper highlights fluoxetine as a way to reverse serotonin deficiency in mast-cell-deficient mice, and since the article was published fluoxetine has shown promise as a covid treatment. However this study says that while serotonin-producing mast cells are common, humans in particular don’t have them while healthy (although it still shows serotonin affecting mast cell movements). This appears to be an area of some controversy.

Mast cells releasing histamine in response to allergens is uncontroversial. Moreover, histamines and serotonin are stored in the same compartments (in mice). Second source (still in mice). 

Some Guy did an informal study based on this theory and it worked

Some guy (Birth name: Gez Mendinger) did indeed report this, and I have to say, for an uncredentialed dude on youtube recommending OTC supplements to treat a nebulously defined disease, this guy looks really credible, and his reasonably good analysis was quite promising. He shared his results with me, and it continued to look promising when I first dug into it with assistance from a statistician, but the deeper we drilled the less promising it looked (details). By the end, the most I could say is “yeah, worth a harder look”, but the history of things that look promising in small, poorly organized studies that wilt under large, well-organized ones is just too dismal to ignore. 

Mouse study shows low NAD+ hurts you via SIRT1

The interview also cites this mouse study featuring a direct NAD+ drip and a slightly different coronavirus. They show improved symptoms but not viral load. They don’t list the sample size anywhere I can find, judging from the low-resolution graph it looks like 7 mice in the control group and maybe 12 in the treatment group? Except for the embolism test which had many more mice.

(apologies for poor image quality, the PDF was crap)

(note: that article was up when I started this post but disappeared before I verified the SIRT1-specific part of the claim)

Quercetin increases NAD+ levels 

Yes, in rats and mice. Specifically, it speeds up the transition from NADH to NAD+

Male pattern balding and low vitamin D are both associated with poor covid outcomes and low NAD+.

The balding citation does indeed say that, but it only looked at hospitalized patients so it’s useless. Moreover, balding is associated with a testosterone derivative, and testosterone weakens the immune system. But when I went to find some cites for those, I found that within hospitalized patients, low testosterone was associated with worse outcomes. However these patients were already hospitalized, so the causality could easily go the other way.

Meanwhile I found several folk-wisdom level comments indicating a link between NAD+ and male pattern balding, but nothing rigorous.

Low vitamin D does seem to be associated with poor covid outcomes, maybe, but treatment doesn’t seem to help (at least not if you wait until patients are hospitalized). 

Chang and Kim assert that Vitamin D activates the NAD-SIRT1 pathway in fat cells in vitro, which if it held up elsewhere would be even stronger evidence for the overall theory than this claim attempts. Byers et al found that vitamin D did not protect guinea pigs against the NAD+ depleting effects of mustard gas. This is not a slam dunk.

Covid depletes NAD+ by activating PARP

Curtin et al lay out a theoretical case for using PARP-inhibitors to treat covid-caused ARDS.

Heer et al “we show that SARS-CoV-2 infection strikingly upregulates MARylating PARPs and induces the expression of genes encoding enzymes for salvage NAD synthesis from nicotinamide (NAM) and nicotinamide riboside (NR), while downregulating other NAD biosynthetic pathways” (notably, the forms not used in the protocol), “overexpression of PARP10 is sufficient to depress cellular NAD and that the activities of the transcriptionally induced enzymes PARP7, PARP10, PARP12 and PARP14 are limited by cellular NAD and can be enhanced by pharmacological activation of NAD synthesis”, “MHV induces a severe attack on host cell NAD+ and NADP+.” (MHV being used as a model)

Long covid and Pellagra share a lot of symptoms, including hyponosmia

Scattered claims pellagra causes hyponosmia but you have to look really hard, it doesn’t show up on any of the common descriptions. I checked in Spanish and didn’t find anything either.

Sen (published only last month) suggests that serotonin deficiency causes anosmia and other neuro symptoms in covid. They propose a different method for the depletion (ACE2 is a mechanism for moving serotonin into the cell), but it’s not mutually exclusive with Wentzel’s theory (that NAD+ depletion causes the body to use up tryptophan trying to produce more NAD+).

Your body hijacks tryptophan to make NAD+ at the expense of serotonin

Tryptophan can indeed be used to make NAD (albeit niacin is better) and serotonin. How your body prioritizes under a given set of circumstances is anyone’s guess.

NAD+ and the immune system

Probably at least some of long covid stems from autoimmune issues, as witnessed by the fact that it’s much more common in women and sometimes helped by steroids. The post and paper don’t make any claims on this beyond the effect of NAD+ on mast cells, which are implicated in autoimmune disorders, but out of curiosity I did some quick googling and found that NAD+ downregulate inflammation via CD4 cells (in mice) and activating SIRT1, the pathway mentioned previously (still in mice).

The Paper

Not that good. Feels associational rather than mechanistic. However Bordoni et al (published after the cited paper) found covid-19 was associated with diminished SIRT1- but Pinto et al found covid-19 upregulated SIRT1 and cite another study claiming that under conditions of energetic stress (which would imply low NAD+), SIRT1 substitutes for ACE2 (the receptor covid uses to enter the cell. Smith suggests that downregulating SIRT1 is good for fighting covid. So SIRT1, NAD+, and covid are probably related, but the first two items are very common so this isn’t damning.

Notably, this paper doesn’t explain why covid would deplete NAD+ more than other infectious diseases, which is an enormous hole.

Does it work? 

The mechanism and empirical data are definitely enough to merit more rigorous follow-up studies (which are in progress) and definitely not slam dunks. But you may need to make a decision before that’s in, so the real question is “should I take this stack if I get sick? Should my parents?”

My tentative answer is: the prescribed stack probably won’t physically hurt you (but see the next section), and it’s fairly cheap, so the limiting factor is probably “what do you have the energy to try”. This is a better thing to try than the interventions whose proof was actively made up or have been investigated and discarded, but there undoubtedly are or will be equally probable things floating around, and choosing between them will be a matter of taste..  

If you do end up giving this a shot, for covid long or acute, I invite you to preregister your complaints and intention with me (a comment here or email elizabeth@acesounderglass.com), so I can create my own little study. If you don’t feel like doing that I still encourage you to announce the intention somewhere, as a general good practice (I did so here). 

So you’re saying it’s safe then?

Anything that does anything is dangerous to you in sufficient dosages. If you’re considering an unverified supplement stack, you should carefully investigate the potential side effects of each substance and consider it in light of what you know of your own health (especially other medications you’re taking). Consider talking to a doctor, if you have a good one.

If any of you are thinking “oh niacin’s a water-soluble vitamin it must be fine”: that’s a pretty good heuristic but it doesn’t hold for niacin in particular.

My experience

As mentioned previously, I acquired lingering progressive chest congestion/inflammation from (probably) my covid vaccine. It’s always possible there was another reason but the timing and symptoms really do not match anything else. 

Since I never had covid (probably), my reaction can’t come from the infection itself, only my immune response to it. Since the theory doesn’t specify a mechanism that’s not disqualifying, but they do make it sound like it starts as a covid problem not an immune problem.

I started this supplement stack before doing any deep verification. The original blog post pattern matched to the kind of thing that was worth trying, everything on the list I either knew was generally safe or confirmed with a quick check (my doctor later confirmed my opinion on safety without endorsing the stack for any particular use), and I had a lot of client work to do. Shoemaker’s children go barefoot, and all that.  So by the time I was writing this I had been on the recommended supplement stack (and some other things besides) for 3 weeks, and was beginning to wean down. 

Overall: my chest pain got better but the timing fits better with attribution to a different intervention. The rash I got on matches very well with the supplement stack. I nonetheless was craving it after I weaned off, so probably there’s at least one thing in it I need, which hopefully isn’t the same as the thing causing the rash. 

[Alert twitter readers may have questions, since I previously was more positive on the stack. I had a major regression when I got a non-covid cold, and had to go back on the other treatment]

Interestingly, my tolerance for niacin increased and then plummeted. Originally I could take 250mg (the smallest size I could find in the right form) with only very mild flush, and that got better over time, to the point I tried 500 mg once (a mistake). But around week 3 my flush was getting worse. Lowering the dose helped, but it’s getting worse again, so I’m continuing to titrate down. This is extremely consistent with filling up NAD+ reserves over time, although very far from conclusive.

Meta

I was originally much more positive on this treatment/theory. I gave it more credit on Twitter, but that’s nothing compared to the excited messages I sent a few friends after an initial lit review. I wrote several much more positive versions of this post (and the forthcoming study analysis), but there kept being one more thing to check, until I talked my way down to what you see here. Some of my downgrade stemmed from asking better statistical questions, but some of it was just the emotional process of talking myself down from something that initially looked so promising, but ultimately had a similar amount of holes to many other things that looked equally promising and failed to pay off. This represents dozens of hours of work from me and my statistician, for the very disappointing result of “fringe treatment probably doesn’t do very much but can’t rule it out”. Reality is infinitely disappointing

Thanks to Alex Ray and my Patreon Patrons for partially funding this investigation, and Miranda Dixon-Luinenburg⁩ for copyediting.

Alternate Views On Long Covid

Scott Alexander has published a post on long covid, which he rates as much more frequent and dangerous than I do. Scott and I spent a while hashing this out in private, and our cruxes seem to come down to:

  1. I think his studies are too small and sample-biased to be meaningful.
  2. He thinks my studies (especially Taquet) didn’t look at the right sequelae.
  3. I was only looking at cognition (including mood disorders), whereas he looked at everything.

Scott also didn’t do age-specific estimates, although that’s not a crux because I expect other post-infection syndromes to worsen with age as well.

I intended to include fatigue in my analysis of cognitive symptoms but in practice the studies I weighted most highly didn’t include them. Scott’s studies, which he admits are less rigorous although we differ on how much, did include them. Why the hell aren’t the large, EHR-based studies with control groups looking at fatigue?

Also, this isn’t relevant to the covid disagreement, but I baffled by the medical systems’ decision to declare chronic Lyme in particular as the definitely psychosomatic syndrome, given that Lyme is closely related to syphilis, which we know damn well has a long dormant period and a stunning array of possible long term consequences.

Although I didn’t update much on this particular disagreement, I have a lot of respect for Scott and encourage anyone making decisions based on bloggers’ estimates of the risk of long covid to check out his post as well.

Long Covid Is Not Necessarily Your Biggest Problem

Introduction

At this point, people I know are not that worried about dying from covid. We’re all vaccinated, we’re mostly young and healthy(ish), and it turns out the odds were always low for us. We’re also not that worried about hospitalization: it’s much more likely than death, but maintaining covid precautions indefinitely is very costly so by and large we’re willing to risk it.

The big unknown here has been long covid. Losing a few weeks to being extremely sick might be worth the risk, but a lifetime of fatigue and reduced cognition is a very big deal. With that in mind, I set out to do some math on what risks we were running. Unfortunately baseline covid has barely been around long enough to have data on long covid, most of it is still terrible, and the vaccine and Delta variant have not been widespread long enough to have much data at all. 

In the end, the conclusion I came to was that for vaccinated people under 40 with <=1 comorbidiy, the cognitive risks of long covid are lost in the noise of other risks they commonly take. Coming to this conclusion involved reading a number of papers, but also a lot of emotional processing around risk and health. I’ve included that processing under a “personal stuff” section, which you can skip if you just want the info but I encourage you to read if you feel yourself starting to yell that I’m not taking small risks of great suffering seriously. I do encourage you to read the caveats section before deciding how much weight to put on my conclusions.

Personal Stuff

This post took a long time to write, much longer than I wanted, because this is not an abstract topic to me. I have chronic pain from nerve damage in my jaw caused by medical incompetence, and my attempts to seek treatment for this continually run into the brick wall of a medical system that doesn’t consider my pain important (tangent: if you have a pain specialist you trust, anywhere in the US, please e-mail me (elizabeth@acesounderglass.com)). I empathize very much with the long covid sufferers who are being told their suffering doesn’t exist because it’s too hard to measure and we can’t prove what caused it.

Additionally, I’m still suffering from side effects from my covid vaccine in April. It’s very minor, chest congestion that doesn’t seem to affect my lung capacity (but I don’t have a clear before picture, so hard to say for sure). But it’s getting worse and while my medical practitioners are taking it seriously, this + the experience with dental pain make me very sensitive to the possibility they might stop if it becomes too much work for them. As I type this, I am taking a supplement stack from a high end internet crackpot because first line treatment failed and there aren’t a lot of other options. And that’s just from the vaccine; I imagine if I actually had covid I would not be one of the people who shakes it off the way I describe later in this post. 

All this is to say that when I describe the long term cognitive impact of covid as being too small to measure with our current tools against our current noise levels, that is very much not the same as saying it’s zero. It’s much worse than that. What I’m saying is that you are taking risks of similar levels of suffering and impairment constantly, which our health system is very bad at measuring, and against that background long covid does not make much of a difference for people within certain age and health parameters. 

A common complaint when people say “X isn’t dangerous to the young and healthy” is that it implies the death and suffering of those who aren’t young and healthy don’t matter. I’m not saying that. It matters a lot, and it’s impossible for me to forget that because I’m very unlikely to be one of the people who gets to totally walk covid off if I catch it. But from looking at the data, there don’t seem to be very many of us in my age group.

Caveats

Medical research in general is really bad, research of a live issue in a pandemic is worse, you should assume these are low quality studies unless I indicate otherwise.

This research was compiled for LessWrong and Redwood Research, with the goal of assessing safety for their office spaces populated by mostly-but-not-entirely-healthy people 25-40, who were much more interested in the cognitive and fatigue sequelae than the physical. Much of this research is applicable outside that group or the sources can be used in that way, but you should know that’s what I focused on.

There isn’t any data on long covid in vaccinated people with breakthrough delta-variant infections. Neither vaccines nor delta have been around long enough for that to exist. Baseline covid has barely been around long enough to have long-term data. What I have here is:

  • Data showing that strength of acute infection correlates with long term impact, although not perfectly
  • Data on the long term impact of baseline covid, given the strength of an initial infection
  • Data on how the vaccine impacts the strength of acute infections
  • Data on how delta impacts the strength of acute infections

Data

Long term outcomes correlate with short term outcomes

By far the best study (best does not mean good) comes out of the UK, where the BBC coincidentally started an online intelligence test in January 2020 (giving them a pre-covid baseline) and in May began asking participants if they’d had covid and if so how bad a case. When I said “assume the studies are terrible unless I note otherwise”, this is the study I wanted to highlight as reasonably good. Because they can compare test-takers in a given time period with and without covid they can control for some of the effects of changing a study population over time, which would be the biggest concern. Additionally, my statistical consultant described the paper as “not having any errors that affect the conclusion”, which is extremely good for a medical paper. This study was not ideal for determining sequelae persistence, but they did check if size of effect was correlated with time since symptom onset, and it wasn’t (but their average was only 2 months).

This study showed a very direct correlation between the severity of the acute infection and cognitive decline. I don’t trust its absolute numbers, but the pattern that more severe disease -> more severe persistent effects is very clear

A second study in Wuhan, China (hat tip Connor Flexman) examined long term outcomes of hospitalized patients, based on the intensity of their care (hospitalization, supplemental oxygen, ventilation) found an increase in acute severity was correlated with an increase in sequelae, although it didn’t hold for every symptom (there are a lot of symptoms and the highest-intervention group is small), and they barely looked at cognitive symptoms.

Taquet et al used electronic health records to get a relatively unbiased six figure sample size, that also showed a strong correlation between acute and long term outcomes, which we’ll talk about more below.

From this I conclude that your overall risk of long covid is strongly correlated with the strength of the initial infection.

Odds of acute outcomes

Sah et al estimate that 35% of covid cases (implied to be baseline and pre-vaccination) are asymptomatic, with large variation by age. Children (<18) are 46% likely to be asymptomatic, adults 18-59 are 32% likely, adults >=60 are 20% likely. I’m going to round the non-elderly adult number to ⅓ to make the math easier.

The Economist has a great calculator showing your pre-vaccine, pre-Delta risk of hospitalization and death, given your age, sex, and comorbidities. Note that this calculator only includes diagnosed cases, so it excludes both asymptomatic cases and those that did have symptoms but didn’t drive people to seek medical care. Here’s a few sample people:

  • A healthy 30 year old man has a 2.7% chance of hospitalization, and <0.1% risk of death
  • A healthy 30 year old woman has a 1.7% chance of hospitalization, and <0.1% risk of death
  • A 25 year old man with asthma has a 4.2% risk of hospitalization, and <0.1% risk of death
  • A 40 year old woman with obesity has a 6.5% risk of hospitalization, and 0.1% risk of death.
  • Risk of hospitalization rises steadily with age but the risk of death doesn’t really take off until 50, at which point our healthy man has a death risk of 0.4% and our health woman has a risk of 0.2%

If you’d like, you can use your own numbers in this guesstimate sheet.

And again, that’s only for officially diagnosed and registered cases. If you assume ⅓ of infections in that age group are asymptomatic, the risk drops by ⅓.

If you are hospitalized, your risk of being ventilated is currently very, very low even if you’re in a high risk category. The overall average percent of hospitalized patients who were ventilated was 2.0% in the last week for which data was available (2021-03-24), after dropping steadily for most of the plague. We can assume that’s disproportionately among the elderly and people with severe comorbidities, so if that’s not you your odds are better still. I’m going to count the risk of intubation for our cohort as 0.5%, although that’s likely still an overestimate.

How do vaccines change these odds? According to CDC data from a time period ending 2021-05-01 (so before delta took off), 27% of breakthrough infections that reached the attention of the CDC were asymptomatic, and only 7% were hospitalized due to covid (another 3% were hospitalized for non-covid reasons). It’s very likely that the CDC is undercounting asymptomatic cases, so we’ll continue using our ⅓ number for now. The minimum age of reported breakthrough infection deaths was 71, so we’ll continue to treat the risk of death as 0% for our sample subjects. Additionally, given the timing most vaccinated participants would be elderly or front line workers, raising their risk considerably. A CDC press release goes much farther, saying vaccinated people > 65 had 7% of the hospitalizations of age-matched controls. 

How does delta change these odds? A Scottish study estimated delta had 2x the risk of hospitalization as alpha, which a Danish study estimated as having 1.42x the risk of hospitalization as baseline covid. So very roughly, we’re looking at 3x the risk of hospitalization from delta, relative to baseline.

So for our sample cases above, we have the following odds (note I updated these on the night it was posted, due to a math error. Thanks to Rob Bensinger for catching it):

Risk given vaccine, deltaHospitalizedIntubated
Healthy 30yo man0.38% = 2.7*.07*3*2/3.002% = 0.38*.005
Healthy 30yo woman0.24% = 1.7*.07*3*2/3.002% = 0.24*.005
Asthmatic 25yo man0.58% = 4.2*.07*3*2/3.003% = 0.58*.005
Obese 40yo woman0.92% = 6.5*.07*3*2/3.005% = 0.92*.005

That’s not so far from the rate of hospitalization in that age range for the flu (0.6%), with some caveats (the CDC sample includes unvaccinated people and the bucket is 18-49 years old, with the higher end presumably carrying more of the disease burden).

There is concern that vaccine effectiveness wanes over time, which I haven’t incorporated here.

Odds of long term outcomes

In general I ignored studies that merely tracked number of persistent sequelae but not their severity or type, which made it impossible to distinguish between “sense of smell still iffy” from “permanent intellectual crippling”, and studies that didn’t track how long the sequelae persisted. This was, unfortunately, most of them.

We talked about the Great British Intelligence Test above. I initially found this study quite scary. The study used its own tests rather than IQ, but if you assume a standard deviation in their tests is equivalent to a standard deviation in an IQ test, the worst category (ventilation) is equivalent to a 7 point IQ loss. That’s twice as bad as a stroke in this study (although I suspect sampling bias). I suspect the truth is worse still, because the worse your recently acquired cognitive and health issues are, the less likely you are to take a fun internet test advertised as measuring your intellectual strengths. However as I noted above, you are extremely unlikely to be put on a ventilator. 

For people with “symptoms, but not respiratory symptoms”, the cognitive damage is ~equivalent to 0.6 IQ points. For “medical assistance at home”, it’s 1.8 points. These are both likely to be overestimates given that the study only included known (although not necessarily formally diagnosed) cases. Additionally, while the paper claims to control for education, income, etc, bad things are more likely to happen to people in worse environments, and it’s impossible to entirely back that out.

Taquet et al used electronic health records to get a relatively unbiased six figure sample size, and found unhospitalized diagnosed covid patients (pre-Delta, pre-vaccine) had a 11% likelihood of a new neuro or psych diagnosis after their covid diagnosis, hospitalized patients had a 15% likelihood, and ICU patients had 26% likelihood. The majority of these were mood disorders (3.86%/4.49%/5.82% for home/hospitalized/ICU) and anxiety (6.81%/6.91%/9.79%). This seems quite bad, until you compare it to the overall numbers for depression in the time period, a naive reading of which suggests that covid had a protective effect

These numbers aren’t directly comparable. The second study is much lower quality and includes rediagnoses (although the total depression diagnosis numbers for the covid patients are 13.10%/14.69%/15.43%- still under the total increase in depression in the general population study). 

Overall this seems well within what you’d expect from getting a scary disease at a scary time, and not evidence of widespread neuro or psych impact of covid. Even if you take the numbers at face value, they exclude most people who were asymptomatic or treated at home without a formal diagnosis.

A UK metareview found the prevalence at 12 weeks of symptoms affecting daily life ranged from 1.2% (average age: 20, minimum 18) to 4.8% (average age: 63). The cohort with average age 31 had a mean prevalence of 2.8%., which is is well within the Lizardman Constant. This is based on self-reports on survey data, which will again exclude asymptomatic cases, so even if you treat it as real, you need to discount it down to 2.8%.

On the other hand, medicine is notoriously bad at measuring persistent, low-level, amorphous-yet-real effects. The Lizardman Constant doesn’t mean prevalences below 4% don’t exist, it means they’re impossible to measure using naive tools.

Comparison to other diseases

The Taquet study did compare covid patients to those with other respiratory diseases (including the flu, not controlling for disease severity or patient age), and found covid to be modestly worse except for myoneural junction and other muscular diseases, where covid 5xed the risk (although it’s still quite low in absolute terms). Dementia risk is also doubled, presumably mostly among the elderly.

Additionally, cognitive impairment following critical illness, and especially following intubation, is a well known phenomenon. This puts the Great British Intelligence Test numbers in perspective- being/needed to be ventilated is quite bad, but it’s always been that bad, there doesn’t appear to be any unique-to-covid badness.

Conclusion

My tentative conclusion is that the risks to me of cognitive, mood, or fatigue side effects lasting >12 weeks from long covid are small relative to risks I was already taking, including the risk of similar long term issues from other common infectious diseases. Being hospitalized would create a risk of noticeable side effects, but is very unlikely post-vaccine (although immunity persistence is a major unresolved concern).

I want to emphasize again that “small relative to risks you were already taking” doesn’t necessarily mean “too small to worry about”. For comparison, Josh Jacobson did a quick survey of the risks of driving and came to roughly the same conclusion: the risks are very small compared to the overall riskiness of life for people in their 30s. Josh isn’t stupid, so he obviously doesn’t mean “car accidents don’t happen” or “car accidents aren’t dangerous when they happen”. What he means is that if you’re 35 with 15 years driving experience and not currently impaired, the marginal returns to improvements are minor. 

And yet. I have a close friend who somehow got in three or four moderate car accidents in < 7 years, giving her maybe-permanent soft tissue damage (to answer the obvious question: no, the accidents weren’t her fault. Sometimes she wasn’t even driving). Statistically, that friend doesn’t exist. No one gets in that many car accidents that quickly without it being their fault. And yet the law of large numbers has to catch up with someone. Too small to measure can be very large.


What this means is not that covid is safe, but that you should think about covid in the context of your overall risk portfolio. Depending on who you are that could include other contagious diseases, driving, drugs-n-alcohol, skydiving, camping, poor diet, insufficient exercise, too much exercise, and breathing outside. If you decide your current risk level is too high, or are suddenly realizing you were too risk-tolerant in the past, reducing covid risk in particular might not be the best bang for your buck. Paying for a personal trainer, higher quality food, or a HEPA filter should be on your radar as much as reducing social contact, although for all I know that will end up being the best choice for you personally. 

Change my mind

My own behavior and plans have changed a lot based on this research, so I’m extremely interested in counterarguments. To make that easy, here’s a non-exhaustive list of things that would change my mind:

  1. Evidence that long covid gets worse over time, rather than slowly improving (note that I did look at data from SARS 1 and failed to find this).
  2. New variants increase the risk to what it was or was feared to be in April 2020
  3. Evidence of more severe vaccine attenuation than we’re currently seeing.
  4. Credible paths through which the risk could drop sharply in the next six months.

Thanks to LessWrong and Redwood Research for funding this research, Connor Flexman and Ray Arnold for comments on drafts, and Rob Bensinger and Lanrian for catching errors post-publication that did not affect my overall conclusion.

Exercise Trade Offs

Woman Exercise Bike - Free vector graphic on Pixabay

Update 9/2: A friend pointed out that I was ignoring the time costs of exercise, which ended up being pretty significant. See new numbers here. I then double checked the math on the microlife numbers and the news is not good.

Tl;dr: under my current conditions, outdoor exercise is slightly safer than indoor for me, but the risks of both are dwarfed by the benefits of exercise.

Recently I’ve been weighing trade offs around exercise. At the gym I’m risking covid exposure. I can reduce that by wearing a mask, at the cost of making the exercise less effective or enjoyable. I could use my friend’s outdoor gym, but it’s fire season here in California so there are prolonged periods where I don’t want to be sucking in all that unfiltered air. This is also addressable with a mask, but at the same cost. I could exercise indoors in my own home, but I do not have that much space and it gets miserable really fast. I could not exercise until conditions improve, but that has its own health costs. So I did some math.

Wikipedia says 10 minutes of exercise = 1 micromort lost (as in, you live longer). That’s obviously going to depend a lot on the type of exercise but we’ll use it.

This calculator translates time * AQI into cigarette equivalents. At 50 AQI, it takes 12 minutes to generate .01 cigarettes. I’m going to treat that as 10 minutes because exercising is slightly worse than merely existing out doors and it makes the math much easier.

Wikipedia lists an equivalent of 1.4 cigarettes = 1 micromort.

N95 masks block 95% of PM2.5 particles (which is what the AQI is based on). I couldn’t immediately find a translation of that to micromorts so let’s assume it’s linear discounting. EDIT: On Twitter Divia Eden points out that 95% assumes a perfect seal, which you probably don’t have. This isn’t material at my current air quality; I did this whole thing without including masks at all and then added them in afterwords, but when you do your own math you should include that.

That means that 10 minutes unmasked outdoor cardio, at 50 AQI = .01/1.4 = .007 micromorts, which is clearly dwarfed by the 1 micromort lost from exercise (even if you assume it’s 10x worse for me due to the existing chest congestion, and don’t give the exercise a corresponding impact bump). If I wear a mask the risk is probably below the significant figures I’m allowed. It’s so negligible compared to the benefits that if allowing myself to go outside increases total exercise by any amount at all, it’s obviously worth it.

How about covid risk?

My gym is personal training focused with a single cardio machine, which you must schedule in advance. If I’m doing cardio there will be at most two clients doing weight training and two trainers in the room, plus me, all > 10 feet away, in a large room with filtration they claim is good. If I’m doing weight training there’s me, my trainer (fairly nearby), and potentially a farther away client and trainer pair. In theory there could be an additional person on the cardio machine but I’ve yet to see it happen.

Under an excessively conservative set of assumptions (City-average vaccination, no mask, constant talking), my cardio scenario is 7 microcovids. If I give everyone masks it’s 0.5. My weight training scenario is <=10 microcovids (7 for the other pair, which may or may not exist, and 3 for my trainer. Note that weight training is 2.5x as long as cardio). But microcovids are not micromorts. The Economist calculator (pre-delta, pre-vaccine) has the risk of dying of acute covid at my age and sex as immeasurably low, despite it being prone to overestimate because its denominator is only diagnosed cases. Long covid is a concern (although I’ve tentatively concluded its overblown: more on that soon hopefully), but lack of exercise is bad for long covid in particular. If we generously use my age/sex hospitalization rate as the discount factor (2.6%), the micromorts from my indoor cardio are <=0.16, and my weight training is <=0.23. These are not quite as negligible as the pollution, but still very safely under the benefits of exercising.

Some caveats: I didn’t examine any of these numbers that closely because the verdict was so overwhelmingly clear; the values would need to be off by orders of magnitude to change my conclusion. But that is always an option, and when I tried to follow up on the 0.1 micromort/minute of exercise number, I hit a dead end.

I’ve made a very crude spreadsheet with sources linked in comments so you can make a copy and play around with your own numbers, based on your local air quality, covid prevalence, etc.

What can a covid test tell you?

The following is extracted from research I did for a client (which I’m sharing with their permission). An important thing to keep in mind while reading this is that the information was gathered to answer particular questions (Primarily “quarantine procedures for very risk sensitive, cost insensitive people”), and that biases what I looked at in weird ways. But I think it’s still much more useful for some set of you to have this information than not, so here it is.

The Tests

Symptoms

Of young, healthy people caught by prophylactic screening (typically contact tracing), 30-50% who test PCR+ will never report symptoms (in some cases these subjects are proactively screened for temperature, in others it’s not clear. Additionally, other studies have found that some percentage of people who report no symptoms will go on to develop CT lung anomalies). Additionally, most people who do develop symptoms spend several days being contagious before they develop symptoms.  So symptoms are not a very good metric at all for determining if someone is infectious.

 [Full notes and sources]

PCR

PCR tests look for specific viral RNA sequences and amplify them to make them easier to detect. They can vary in a number of ways:

  • Specific sequence searched for
  • Number of amplifications done
  • Collection site and mechanism of sample

PCR false positives are quite rare, and typically have to do with sample contamination. False negatives are more common, and can come from a variety of sources:

  • Covid was present but did not have the particular sequence searched for
  • Did not do enough amplifications to notice effect
  • Patient has covid but the particular site sampled does not.

How common are false negatives? That’s hard to define, because currently a nasopharyngeal PCR is what gets you diagnosed as having covid- if you fail that, you’re assumed to have one of the many things that produces similar symptoms. However, we can make some guesses.

The following graphs show the calculated chance of testing PCR+ on a nasopharyngeal test on a given day after exposure, given frequent testing and an eventual positive result.

But that’s just for nasopharyngeal (NP) tests. Data on sicker patients (the only ones studied) show it’s possible to have a negative NP test while another area of the body (lower respiratory or gut) tests positive.

Figure thumbnail gr1

But these are all people who tested PCR positive eventually. What about people who get sick without ever testing positive? A very small study found that of 24 health care workers who developed positive antibodies over a 3 month period, 10 never had a positive PCR test despite being tested twice weekly. The paper offers multiple explanations for this, and I’m very reluctant to draw conclusions from such a small study, but it is concerning.

[Notes on NP tests]

[Notes on stool tests]

[Notes on spit tests]

[Notes on lung tests]

Antibody tests

Antibody tests look for an immune reaction to viral proteins. They can be negative when a person is contagious (because they haven’t formed a large enough reaction yet) and positive when they are not (because they successfully fought off an infection). 

A reasonable question I have not investigated is “does an antibody+ test mean I’m immune?” 

[Full notes and sources]

LAMP tests

Like PCR, LAMP tests look for specific viral RNA sequences and amplify them to make them easier to detect. LAMP tests go through many fewer amplification cycles, making them less sensitive but much faster: 30 minutes vs 2-3 days for PCR, plus the transit time for the PCR samples. 

A LAMP test every three days is much more valuable than one PCR test, because catching the peak is much more important than the sensitivity. I’m not sure if a LAMP test taken today is more or less useful than a PCR test taken to give results today. I stopped digging into this because there were not yet any LAMP tests on the home market.

[Full notes and sources]

Antigen tests

Antigen tests look for specific viral proteins in a sample. There’s no amplification, which makes them less sensitive, but manufacturers report catching 88% of cases caught by PCR, so maybe this is fine, especially since you get results days faster? 

The 88% sensitivity number is much, much higher than you see in literature (which is something like 20%-50%), I assume because they used more abundant samples. There’s some controversy over whether that’s because many PCR positives are driven by dead virus, in which case the antigen test returning a negative result is a feature, not a bug. This may well be true, however at least one study was able to culture live virus from a PCR+/antigen- sample, so it’s not foolproof.

Of the studies looking at antigen tests, all that I found either started post-symptoms, or took a random sample of people showing up at a sampling site. None were in a position to determine how good antigen tests are as an alarm system for catching an early infection (as opposed to diagnosing symptoms or determining when someone has ceased being contagious)

However antigen tests return results in minutes, while PCR tests take 2-3 days to complete not including shipping time. Given how quickly covid multiplies, it’s possible that an antigen test now is more sensitive than a PCR test from four days ago, especially if the exposure occurred in the intervening time.

[Full notes and sources]

What do any of these mean for contagiousness?

That’s a good question, which with the exception of asymptomatic spread can’t really be answered without human challenge trials, which the entire world declined to do. I would be surprised if any of these tests’ thresholds lined up perfectly with the threshold of infectiousness, because there’s no reason to expect they would. I expect culture tests to be much closer, but still not necessarily exactly on line (plus AFAIK they’re not available for diagnostics, even through a doctor). Given that I asked…

How long do I need to stay in quarantine after potential exposure?

The best data on this is from New Zealand, which has a very strict isolation policy for entrants: 14 days isolation, with PCR tests on days 3 and 12 of isolation (a pre-departure test is required only if you’re coming from the US or the UK). By my earlier estimations, day 3 of isolation is already likely to be past the peak of detectability, unless travellers were exposed right before they left. Nonetheless, New Zealand reports only a handful of import-related covid cases after this policy kicked in, and a model attributes those to people who caught covid in isolation (e.g., a couple who shares a hotel room and one partner gives it to other on day 4), rather than people who entered New Zealand infected.

Transmission type of COVID-19 cases

I did look for similar data from other countries, but NZ had both the best quarantine and the best data.

So despite the tests’ low sensitivity, 14 days + a test at the end really does seem to be a long-enough isolation period.

[Full notes and sources]

Thanks to my original clients for funding this research, and my Patreon patrons for contributing to the cost of preparing this for publication