Stats Challenge Answered: Study Of PFAS & Vaccine Antibodies

Stats Challenge Answered: Study Of PFAS & Vaccine Antibodies

I trust you have read the original post (Blog, Substack). If not, do so, because I won’t repeat any of it here. However, even if you haven’t, you might still profit from the discussion of the paper.

The paper in the Challenge was the influential 2020 “Internal exposure to perfluoroalkyl substances (PFASs) and biological markers in 101 healthy 1-year-old children: associations between levels of perfluorooctanoic acid (PFOA) and vaccine response” by Klaus Abraham and others in Archives of Toxicology. It is online.

The paper says that increased amounts of PFOA in both the blood of kids (and mothers) reduced antibody levels associated with vaccines for Hib, tetanus and diphtheria.

In the Challenge, there were two behaviors, U (Unnatural) and N (natural), which are now revealed to be formula feeding (U) and breast feeding (N). It was alleged that more PFOA, and similar substances, was found in kids who were breastfed, because (they say) mothers also ingested these substances and passed them on to the kiddies.

The “bad things” were PFOS and other substances, and the treatment was vaccines. The “B” in the blood was the level of antibodies related to these vaccines.

It is likely true that PFOS and others perfluoroalkyl substances are passed on from mother to child, but what is strange is the acceptance that bottle feeding would not pass on these substances, too. After all, “formulas” (mostly soybean oil?) are mass produced in factories where “substances” of all kinds are used in the manufacturing equipment, not to mention the multifarious chemical substances in the formulas themselves.

Here are the ingredients for powdered Enfamil, for instance.

I find it most difficult to believe bottle feeding would be better for a child than natural breast feeding. Of course, they didn’t say anything about which is better overall, but instead only in terms of PFOS and other things (but see the end).

Now before we go further, it is well to acknowledge what is true: these perfluoroalkyl substances were indeed found in the blood of infants, and it likely got there mostly by eating. These are foreign, which is to say, man-made substances. And that certainly sounds scary, or at least suspicious.

It could be that PFAS (PFOS is among them) and all the rest are up to no good when ingested. It could be that they are mostly harmless and pass from the body quickly. I do not know which of these is true, and take no position. My instinct is to suspect harm over harmless. But it has to be proven.

It was not proven here. The study has many weaknesses, which, I am proud to say, readers identified. But I hope you see now why I masked the details. Saying the study involved perfluoroalkyl substances would have prejudiced a great many people, who share the same suspicions I have.

Before we get into the details, I remind you scientists are usually (well, in the old days anyway) smart people. And smart people are better than average people at finding evidence which fits their belief. Smart people should be better at finding evidence which contradicts their belief, which is a power just as important as the former. Alas, this power has largely atrophied in the great race to Find Results. And Results leads to “Follow The Science!”

All right, to the study itself.

The authors recruited only healthy kids, taking pains to exclude sick ones. Yet if you want to prove perfluoroalkyl and polyfluoroalkyl substances (PFAS) cause sickness in kids, a far better study is to survey a broad range of kids, healthy and sick. And sick with diseases PFAS allegedly cause, like diphtheria or one of the other maladies vaccinated against. Merely making claims about changes in antibody concentration, from one vax dose to the next or in time, is far from sufficient.

For one, antibody levels for diphtheria (and the others) naturally decrease, by which I mean decrease for causes other than PFAS. This is why kids get “boosters” for certain vaccines. So when you look at only changes in antibody level, it’s far too easy to get spurious correlations, which when combined with wee Ps and the epidemiologist fallacy [Blog, Substack], results in false claims of cause.

Another problem with excluding sick kids (like “chronic diseases including atopic eczema”) is we can’t see if formula-feeding is causing any grief. Some say seed oils lead to allergic reactions or inflammation. We wouldn’t see that here.

The kids recruited here all had to have “two vaccinations against diphtheria and tetanus”, which is the usual schedule.

There was a problem with the protocol, and many saw it. For instance, of the recruits “ten children could not be examined due to infections existing in the time window”. What caused these? Formula? Something else? This biases the study, but in an unknown direction. And anyway, 10 from the 101 original is a big chunk.

Ignoring all this, we come to the strange, and I think disqualifying, statistical analysis (emphasis original):

A linear model was fitted for each of the plasma antibody concentrations, taking into account the time since last vaccination and, if significant, the number of vaccinations. Using this model, the antibody response was then expressed using the regressed values at the time of vaccination. Further analyses were performed on these data which are referred to as adjusted values. The possible influence of other contaminants was analysed using the stepwise inclusion–exclusion process based on AIC (R function ‘stepAIC’), starting with the full model explaining the respective adjusted antibody concentration.

This is what I meant when I explained we do not, after the initial blood comparisons between formula and breast-fed kids, see the original data. It’s all modeled data! Or, to use the euphemism, adjusted values.

Scientists are pack animals just as much as non-scientists, and maybe even more so in their areas of specialty. For whatever reason, PFAS and changes in antibody levels for certain vaccinations became a “thing”, and there were many papers on the subject. Another is “Serum Vaccine Antibody Concentrations in Adolescents Exposed to Perfluorinated Compounds” by Philippe Grandjean and others in Environmental Health Perspectives. That paper shares the same flaw as Abraham, in that we never see the actual data.

What we should see are plots of serum PFAS levels and actual antibody levels, or the actual changes in antibody levels. It’s not enough to get a “significant” regression, especially when the analysis uses a technique which is not reproducible (step-wise). We don’t, in the end, know just what went into the model. (Step-wise is notorious for over-fitting.)

Grandjean contents themselves with showing the results (wee Ps) from structural equation models, which are even dicier than step-wise.

These papers are all awfully shy about presenting the raw data. Why?

Here’s more on the modeling in Abraham.

To explore a dose–response relation between levels of contaminants and antibodies, several methods were applied. First, a linear model was fitted to confirm possible associations. Then a LOESS smoother was applied as it was judged that such moving average might reveal a trend in the data. Furthermore, the data were divided in PFAS quintiles and deciles. Plots were drawn as box-plots and as plots contrasting the empirical distribution to the normal distribution of the PFOA quintiles. If an ANOVA showed differences between the quintile/decile groups, a no observed adverse effect concentration (NOAEC) was derived as the highest-dose quantile below the first one showing a significant difference to the lowest-dose quantile. Furthermore, the breakpoint of a piecewise linear regression with two segments and left slope null (‘knee’ function) was estimated (least squares estimate by R package ‘segmented’).

Don’t divide your data into quintiles and deciles. Nature doesn’t. It smacks of attempts to find “significance”. And there is almost never (and maybe never) a good reason to do so. You have the real data: use that.

Here are the main plots the authors used to argue increasing PFAS lead to decreased antibody. I showed a doctored version of the middle plot.

See the description and note the y-axis, which is not (log) antibody concentration. It is the adjusted (log) antibody concentration. Adjusted by those models, which we cannot reproduce or see. We cannot see the formula- or breast-fed kids anymore either; they disappear into the model.

There is nothing inherently wrong about using logged data, especially when the values modeled vary so greatly. But here the scatter is already enormous, the “knees” wholly artificial. Even with logged values, the model is only weakly predictive. If it wasn’t for those “knees”, it would not be predictive at all. But think what those “knees” are supposed to represent. It is saying the body has a point at which PFAS levels start doing their dirty work, and they do it linearly (in log space) after that point. Is that how bodies work? Who knows.

The whole thing with the “knees” might be due to correlations of PFOS with other things in the blood, too, which are (maybe) the real causes of antibody suppression. We can’t know because we can’t see the data!

Why not show the plot of actual antibody concentration and PFOS level? Color the dots by type of feeding, maybe. And vary the plot symbol by number of vaccinations, which is surely causative.

As it is, we cannot tell what is happening. The whole thing is far too vague to make any decision.

Curiously, none of these kids had diphtheria or any of the other maladies, even at what seem—and only seem because these are adjusted and not actual values—to be low values of antibodies. What could that mean?

Who knows. It could mean herd immunity, since these kids are surrounded by other kids who don’t have these diseases. Or it could mean antibody levels don’t need to be as high as suspected to be preventative. But, really, we can’t know, because this study excluded all sick kids.

Really we can’t know much of anything, because we never see what happened in the real world. Yet the authors boast

The significance of our results is unambiguous especially due to the high stability of the associations found using different methods of evaluation and due to considering the broad spectrum of other contaminants also measured in this study as possible confounders.


It’s well the authors admit this:

In our study, no associations were observed between levels of PFOA/PFOS measured at the age of 1 year (postnatal exposure) and the number of infections within the first year of life. This may be due to levels of PFASs being not high enough to cause this effect or due to a protective influence of the long duration of breastfeeding in the higher exposed children, if indeed an impact on the occurrence of infections is to be expected at higher levels of exposure.

Yet this is evidence against their theory, not for it. And earlier they showed breast-fed kids had higher levels of PFAS!

There is certainly much more to all this, and we only hit what is considered to be the main evidence.

I want everybody who is, I think rightly, suspicious about PFAS to note what I am claiming and what I am not claiming. I say we can’t know anything useful from this study, one way or the other. I do not say PFAS has no effect. We just can’t tell.

It would be best if the authors shared their data and we can all have a go at it. Who knows what we can find.

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  1. The first principle is that you must not fool yourself and you are the easiest person to fool. –Richard Feynman

  2. JH

    Nothing wrong with plotting adjusted values, though it was clear how the adjusted values are calculated. Just a scatter plot. However, let’s note that the gray bands are not confidence intervals.

    Broad gray band: moving average. Red line: Fitted ‘knee’ function.

    “After the release of the EFSA opinion on PFOA and PFOS in December 2018, we decided to conduct further measurements using two remaining plasma aliquots (125 ?L each, continuously frozen at ? 80 °C).”
    Which is different from saying

    6. After a government report was issued on U and N and the alleged bad things in the blood, the researchers went in and gathered more blood.

    Accurate reporting is important, as in this case, it affects what statistical analyses are appropriate.

  3. JH

    though it was NOT clear

  4. JH

    Antibodies can be transferred through the breast milk, and so can chemicals such as PFOA. Having the antibodies doesn’t imply that breastfed babies don’t get sick. Having PFOA in your blood doesn’t imply that you would get sick from it. If you use Teflon pans and pots, chances are you have PFOA in your blood. If you are sick with no apparent reason, check it out though.

    The authors want to examine the “possible association of PFASs and parameters of immune response to vaccinations.” If sick babies were included, the researchers would have to somehow tease out immune responses due to illness, not vaccinations (is this even possible?). Right?

    Got to pay me for more comments. 🙂

  5. Incitadus

    God help us another indeterminate research project funded by the government. With
    all the other substances the Chemical industry has introduced into the human body I’m
    not sure what difference it makes to tease one out. I suppose it does occupy our time and
    pay the rent, and the camel is strong though his back is broken he moves incrementally

    Any civilization that would allow itself to be systematically poisoned with fluoride based on the wacky
    research of Alcoa Metals and the American Dental Association of 1909 cannot expect a stream of
    high IQ scientists. I think that’s basically what we’re seeing across the board in most fields of research
    where studies are fabricated and tailored solely to obtain government funding. The dumbing down
    of the general population is the cornerstone of a kleptocracy obsessed with depopulation.

    Famine is the final weapon deployed against a population after war and biological interventions
    have been exhausted. They’re itching to unleash a limited nuclear holocaust to refocus hearts and
    minds and provide the rationalization for a multidecadal worldwide famine. The template for this
    can be see in present day China with the intentional destruction of their domestic economy via the
    plandemic. Immediate small business failures ensued followed by large corporate bankruptcies, failing
    banks, implosion of their stock exchange, and the flight of foreign capitol. Before his peasants drag him
    off to an open grave Xi desperately needs a war which his global partners are sure to accommodate.
    Buckle up this is after all the year of the Dragon with Putin chained to a corpse.

  6. Robin

    Bizarre subject and even more bizarre logic.

    There is probably some sort of valuable information in the raw data but the analysis has obscured it. Even so, no matter how thoroughly the data is scrutinised there is still nothing to be said about causation.

  7. Robin

    The best way to write a paper is to let the data speak for itself. If it can’t then there is nothing to write.

  8. I KNEW IT WAS BRESTFEEDING!! Had to be! I’ll now go and read the rest of the article. 🙂 And the “procedure” has to be stopping breastfeeding. I didn’t yet read that far down into the article before commenting. 🙂

  9. Johnno

    Government funded studies into problems government is suspect of having created, like any investigations of themselves, are designed to find nothing.

    Just wait until these studies are outsourced to Google’s A.I.! Assuming by then it is finally capable of finding white people in order to study them.

  10. Milton Hathaway

    One interesting thing about the abstracted versus actual study is that the flaws seem more obvious in the abstracted study. This makes sense, of course, and is the reason given for abstracting the study to begin with – to separate the analysis of it from preconceived notions.

    One aspect of engineering that wasn’t addressed in any of my college classes is checking the accuracy of work product, either my own or others. I can think of few things more stressful in my career than when my boss plopped down a stack of design documents in front of me and asked me to check it, and can I get that done by the end of the day? The work product took weeks or months to produce, and I’m supposed to check it in a few hours?

    So, how does one check work product for accuracy?

    One way is to just repeat the whole process, ala “replicate the study”. That is time-consuming, and if the checker takes the same path, the checker might take the same wrong turns.

    Another generic approach is to do it in reverse, work backwards from a result to the inputs. For an overly simple example, back in the day when I balanced my checkbook with a calculator, I would start from the most recent entry and work back in time, so bills became paychecks and vice-versa. But that approach only helps for very specific problems that are suitably reversible.

    In general, the further one can abstract from the original work product when checking, the more likely flaws are to be visible, I think. One engineer I worked with liked to recast a work product to the point where it accomplished something impossible or proved something ridiculous, then he would go through the details attempting to prove the original work product had the same flaws. This was also very time-consuming for a valid work product, but he was often able to reveal major flaws very quickly, then throw it back to the original engineer without wasting much time.

    Checking work product for accuracy is a such a big deal it seems quite surprising that it is so often so ad-hoc.

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