Biostatistical problems with the Canadian fluoride/IQ study

There are insights in there somewhere. Image Credit: DATA ANALYTICS COMES TO THE LEGAL PROFESSION

There has been widespread scientific criticism of the recently published Canadian fluoride-IQ study of Green et al., (2019). Most recently Dr. René F. Najera (a Doctor of Public Health, an epidemiologist and biostatistician) has critiqued the statistical analysis. He finds a number of faults and concludes by hoping “public health policy is not done based on this paper:”

 “It would be a terrible way to do public health policy. Scientific discovery and established scientific facts are reproducible and verifiable, and they are based on better study designs and stronger statistical outcomes than this. “

Dr. Najera’s critiques the biostatistics is in his article The Hijacking of Fluorine 18.998, Part Three. This follows his previous critique (Part 1 and Part 2) of the epidemiological issues which I reviewed in Fluoridation – A new fight against scientific misinformation.

Dr. Najera starts by stressing the important role of biostatistics in epidemiological studies. After all the planning and measurement:

“.. we hand off the data to biostatisticians, or we do the work with biostatisticians. Doing this assures us that we are measuring our variables correctly and that all associations we see are not due to chance. Or, if chance had something to do with it, we recognize it and minimize the factors that lead to chance being a factor in and of itself.”

I agree completely. In my experience statisticians play a critical role in research and should be involved even at the planning stage. Further, I think the involvement of experienced biostatisticians is invaluable. Too often I see papers where the authors themselves relied on their own naive statistical analyses rather than calling on experience. Perhaps they are being protective of their own confirmation bias.

The specific study Dr. Najera critiques is:

Green, R., Lanphear, B., Hornung, R., Flora, D., Martinez-Mier, E. A., Neufeld, R., … Till, C. (2019). Association Between Maternal Fluoride Exposure During Pregnancy and IQ Scores in Offspring in Canada. JAMA Pediatrics, 1–9.

For my other comments on the Candian fluoride/IQ research see:

• If at first you don’t succeed . . . statistical manipulation might help
• Politics of science – making a silk purse out of a sow’s ear
• More expert comments on the Canadian fluoride-IQ paper
• An evidence-based discussion of the Canadian fluoride/IQ study
• Fluoridation – A new fight against scientific misinformation

No comparison group

One problem with this study is that a number of mother-child pairs were excluded and, in the end, the sample used was not representative of the Canadian population. Najera summarises the “main finding of the study as “that children of mothers who ingested fluoride during pregnancy had 4 IQ points lower for each 1 mg of fluoride consumed by the mother:”

“If you’re asking yourself, “Compared to whom?” you are on the right track. There was no comparison group. Women who did not consume tap water or lived outside a water treatment zone were not included, and that’s something I discussed in the previous post. What the authors did was a linear regression based on the data, and not much more.”

In fact, while the sample used was unrepresentative the study did compare the IQs of children whose mothers had lived in fluoridated and nonfluoridated areas. There was no statistically significant difference – an important fact which was not discussed at all in the paper. This table was extracted from the paper’s Table 1.

What about that regression?

While ignoring the mean values for fluoridated and nonfluoridated areas the authors relied on regression analyses to determine an effect.

But if you look at the data  in their Figure 3A reproduced below you can see problems:

“. . . you can see that the average IQ of a child for a mother consuming 1.5 mg of fluoride is about 100. You also see that only ONE point is representing that average. That in itself is a huge problem because the sample size is small, and these individual measurements are influencing the model a lot, specially if their value is extreme. Because we’re dealing with averages, any extreme values will have a disproportionate influence on the average value.”

Several scientific commenters on this paper have noted this problem which is important because it should have been dealt with in the statistical analysis:

“When biostatisticians see these extreme values popping up, we start to think that the sample is not what you would call “normally distributed.” If that is the case, then a linear regression is not exactly what we want to do. We want to do other statistical analyses and present them along with the linear regressions so that we can account for a sample that has a large proportion of extreme values influencing the average. Is that the case with the Green study? I don’t know. I don’t have access to the full dataset. But you can see that there are some extreme values for fluoride consumption and IQ. A child had an IQ of 150, for example. And a mother consumed about 2.5 milligrams of fluoride per liter of beverage. Municipal water systems aim for 0.7 mg per liter in drinking water, making this 2.5 mg/L really high.”

No one suggests such outliers be removed from the analyses (although the authors did remove some). But they “should be looked at closely, through statistical analysis that is not just a linear regression.”

This is frustrating because while the authors did not do this they hint that it was considered (but do not produce results)  when they say:

“Residuals from each model had approximately normal distributions, and their Q-Q plots revealed no extreme outliers. Plots of residuals against fitted values did not suggest any assumption violations and there were no substantial influential observations as measured by Cook distance. Including quadratic or natural-log effects of MUFSG or fluoride intake did not significantly improve the regression models. Thus, we present the more easily interpreted estimates from linear regression models.”

As Dr. Najera comments, this is “.. worrisome because that is all they presented. They didn’t present the results from other models or from their sensitivity analysis.”

Scientific commenters are beginning to demand that the authors make the data available so they can check for themselves. My own testing with the data I extracted from the figure does show that the data is not normally distributed. Transformation produced a normal distribution of the data but the relationship was far weaker than for a straight linear regression. Did the authors reject transformations simply because they  “did not significantly improve the regression models?”

That suggests confirmation bias to me.

Confidence intervals

In their public promotions, the authors and their supporters never mention confidence intervals (CIs)- perhaps because the story does not look so good when they are considered. Most of the media coverage has also ignored these CIs.

A big thing is made for the IQ score of boys dropping by 4.49 points with a 1 mg/L increase in  mother’s urinary fluoride, but:

“Based on this sample, the researchers are 95% confident that the true drop in IQ in the population they’re studying is between 0.6 points and 8.38 points. (That’s what the 95% CI, confidence interval, means.)”

In other words:

“In boys, the change is as tiny as 0.6 and as huge as 8.38 IQ points.”

For girls the change:

“is between -2.51 (a decrease) and 7.36 (an increase). It is because of that last 95% CI that they say that fluoride ingestion is not associated with a drop in IQ in girls. In fact, they can’t even say it’s associated with an increase. It might even be a 0 IQ change in girls.”

Dr. Najera asks:

“Is this conclusive? In my opinion, no. It is not conclusive because that is a huge range for both boys and girls, and the range for girls overlaps 0, meaning that there is a ton of statistical uncertainty here. “

This is why the epidemiological design used by the authors is worrying. For example:

” The whole thing about not including women who did not drink tap water is troubling since we know that certain drinks have higher concentrations of fluoride in them. If they didn’t drink tap water, what are the odds that they drank those higher-fluoride drinks, and what was the effect of that?”

This comes on top of the problems with the regression models used.

Transformation to normalise the data and inclusion of other important facts may have produced a non-significant relationship and there would be no need for this discussion and speculation.

What about those other important factors?

Green et al (2019) included other factors (besides maternal urinary fluoride) in their statistical model. This “adjustment” helps check that the main factor under consideration is still statistically significant when other factors are included. In this case, the coefficient (and CIs) for the linear association for boys was reduced from -5.01  (-9.06 to -0.97) for fluoride alone to -4.49 (-8.38 to -0.60) when other considered factors were included. In this case, the other factors included race/ethnicity, maternal education, “city”, and HOME score (quality of home environment).

Dr. Najera questions the way other factors, or covariates, were selected for inclusion in the final model. He says:

“The authors also did something that is very interesting. They left covariates (the “other” factors) in their model if their p-value was 0.20. A p-value tells you the probability that the results you are observing are by chance. In this case, they allowed variables to stay in their mathematical model if the model said that there was as much as a 1 in 5 chance that the association being seen is due to chance alone. The usual p-value for taking out variables is 0.05, and even that might be a little too liberal.

Not only that, but the more variables you have in your model, the more you mess with the overall p-value of your entire model because you’re going to find a statistically significant association (p-value less than 0.05) if you throw enough variables in there. Could this be a case of P Hacking, where researchers allow more variables into the model to get that desired statistical significance? I hope not.”

Good point. I myself was surprised at the use of such a large p-value for selection. And, although the study treats fluoride as the main factor and inclusion of the other factors reduces the linear coefficient for maternal urinary fluoride, I do wonder why more emphasis was not put on these other factors which may contribute more to the IQ effect than does fluoride.

Perhaps this paper should have concentrated on the relationship of child IQ with race or maternal education rather than with fluoride.

Padding out to overcome the poor explanation of IQ variance

Another point about the inclusion of these covariates. As well as possible improving the statistical significance of the final model they may also make the model look better in terms of the ability to explain the variance in IQ (which is very large – see figure above).

In my first critique of the Green et al (2019) paper (If at first you don’t succeed . . . statistical manipulation might help) I pointed out that the reported relationship for boys, although statistically significant, explained very little of the variance in IQ. I found only 1.3% of the variance was explained – using data I had digitally extracted from the figure. This was based on the R-squared value for the linear regression analysis.

Unfortunately, the authors did not provide information like R-squared values for their regression analysis (poor peer review in my opinion) – that is why I, and others, were forced to extract what data we could from the figures and estimate our own. Later I obtained more information from  Green’s MA thesis describing this work (Prenatal Fluoride Exposure and Neurodevelopmental Outcomes in a National Birth Cohort). Here she reported an R-squared value of 4.7%. Bigger than my 1.3% (my analysis suffered from not having all the data) but still very small. According to Nau’s (2017) discussion of the meaning of R-squared values (What’s a good value for R-squared?), ignoring the coefficient determined by Green et al (2019) (5.01) and relying only on the constant in the relationship would produce a predicted value of IQ almost as good (out by only about 2%).

That is, simply taking the mean IQ value (about 114.1 according to the figure above) for the data would be almost as good as using the relationship for any reasonable maternal urinary fluoride value and OK for practical purposes.

But look at the effect of including other factors in the model. Despite lowering the coefficient of the relationship for fluoide it drastically increases the R-squared value. Green reported a value of 22.0% for her final model. Still not great but a hell of a lot better than 4.7%.

Perhaps the inclusion of so many other factors in a multiple regression makes the final model look much better – and perhaps that perception is unjustly transferred to the relationship with fluoride.

Are other more important factors missed?

Almost certainly – and that could drastically alter to conclusions we draw from this data. The problem is that fluoride can act as a proxy for other factors. City location and size are just one aspect to consider.

In my paper Fluoridation and attention deficit hyperactivity disorder a critique of Malin and Till (2015), I showed inclusion of altitude as a risk-modifying factor completely removed any statistical significance from the relationship between ADHD prevalence and fluoridation – despite the fact Malin & Till (2015) had reported a significant relationship with R-squared values over 30%!

Malin & Till (2015) reported these relationships as statistically significant. However, when altitude was included in the multiple regressions by Perrott (2018) no significant relationships were fluoridation were found.

So you can see the problem. Even though authors may list a number of factors or covariates they “adjusted” for, important risk-modifying factors may well be ignored in such studies. This is not to say that inclusion of them “proves” causation any more than it does for fluoride. But if their inclusion leads to the disappearance of the relationship with fluoride one should no longer claim there is one (reviewers related to the group involved in the Green et al., 2019 study still cite Malin & Till 2015 as if their reported relationship is still valid).

In effect, the authors acknowledge this with their statement:

“Nonetheless, despite our comprehensive array of covariates included, this observational study design could not address the possibility of other unmeasured residual confounding.”

Summary

Dr. Najera summarises his impression of the Green et al (2019) study in these words:

“The big idea of these three blog posts was to point out to you that this study is just the latest study that tries very hard to tie a bad outcome (lower IQ) to fluoride, but it really failed to make that case from the epidemiological and biostatistical approaches that the researcher took, at least in my opinion. Groups were left out that shouldn’t. Outliers were left in without understanding them better. A child with IQ of 150 was left in, along with one mother-child pair of a below-normal IQ and very high fluoride, pulling the averages in their respective directions. The statistical approach was a linear regression that lumped in all of the variables instead of accounting for different levels of those variables in the study group. (A multi-level analysis that allowed for the understanding of the effects of society and environment along with the individual factors would have been great. The lack of normality in the distribution of outcome and exposure variables hint at a different analysis, too.)”

Pretty damning!

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Fluoridation – A new fight against scientific misinformation

Anti-fluoride campaigners think a new Canadian fluoride IQ study is the best thing since sliced bread but the scientific critiques warn they are wrong. Photo Illustration by The Daily Beast/Getty

The new Canadian fluoride-IQ study has certainly created some sensational reporting. On the one hand, anti-fluoride campaigners are lauding the study as the best things since sliced bread and seem sure it will lead to the end of community water fluoridation. Mainstream media have featured the findings – although in most cases warn they are controversial and may be meaningless. As would be expected, alternative health media have been promoting it and repeating the anti-fluoridation arguments.

However, scientific commenters have mainly criticised the study and warned that even if the findings are valid it is just one study and it is far too early to consider stopping community water fluoridation – a health policy which is so far been seen as economical, safe and effective in helping fight tooth decay.

I strongly believe the scientific critiques are important. One should not rely on “authority” statements in such matters – especially statements from well known anti-fluoride activists. But we should also be aware that self-promotion by the authors and journal, and by the authors’ institutions, is also not a reliable indicator of the worth of a study.

In the end, the validity and worth of this study will depend on the data and methodology – and good scientific critiques will look at these, not the status of the journal, institutions or authors. And not the public statements being made to promote the findings.

Some interesting critiques are coming from Dr. René F. Najera who is a Doctor of Public Health, an epidemiologist and biostatistician. These are the very skills essential for a proper critique of the Canadian study.

The specific study Dr. Najera refers to is:

Green, R., Lanphear, B., Hornung, R., Flora, D., Martinez-Mier, E. A., Neufeld, R., … Till, C. (2019). Association Between Maternal Fluoride Exposure During Pregnancy and IQ Scores in Offspring in Canada. JAMA Pediatrics, 1–9.

For my other comments on the Candian fluoride/IQ research see:

• If at first you don’t succeed . . . statistical manipulation might help
• Politics of science – making a silk purse out of a sow’s ear
• More expert comments on the Canadian fluoride-IQ paper
• An evidence-based discussion of the Canadian fluoride/IQ study

The “shenanigans” of activists

In his first article, The Hijacking of Fluorine 18.998, Part One, Dr. Najera gives some background. He says:

“Time after time, epidemiological studies have shown that fluoridated water leads to less tooth decay. Less tooth decay leads to better health outcomes as poor oral health is a risk factor for a variety of conditions. At the same time, all of these studies failed to see any association between bad outcomes and fluoridation done correctly.”

And

” . . those people who were suspicious of putting fluoride in the water did what people who are suspicious of public health interventions often do: they heard of some bad outcome of ingesting fluoride (which is a compound made up of fluorine, the chemical element), amplified it, exaggerated it and showed it as the ultimate example of what fluoride consumption at any concentration can do to a person.”

He compares this to “the shenanigans of the anti-vaccine crowd” and concludes that:

“…just like we had to do in the late 1990s with the Wakefield Fraud “study” that was not a study, here we go fighting a new fight against misinformation…”

He concludes this because:

“In consultation with friends and colleagues, we found a lot to be worried about in the epidemiological design of the study and the biostatistical analysis of the resulting data… And, of course, of the conclusions reached by the authors and the press (with some help from the authors). “

Some epidemiological concerns

In his second article, The Hijacking of Fluorine 18.998, Part Two, Dr. Najera expresses his epidemiological concerns about the research. These include:

1: Unwarranted exclusion of some mother-child pairs:

“For example, some were excluded because they did not drink tap water or lived outside a water treatment zone. Wouldn’t you want to know if not drinking tap water or living outside a water treatment zone led to children with normal-to-high IQs compared to the others?

This raised flags with me because I don’t exclude someone from an outbreak investigation if they don’t have a desired exposure. In fact, I want to know if someone who is not exposed to something is less likely to develop the disease or have the condition I’m studying. It would be like saying that I don’t want women who live in air-conditioned apartments in a city included in a study on Zika because they are not likely to have been exposed to mosquitoes like women living in huts in the jungle.”

2: Overlap of groups:

“In the end, they had 369 mother-child pairs with mean urine fluoride (MUF) measurements, IQ measurements and water fluoride data and 400 mother-child pairs with fluoride intake and IQ measurements. But that’s 769 pairs when 610 children were originally considered? Yes, there is some overlap between the two groups. No big deal if they do their biostats right. (Spoiler alert for Part Three: They didn’t.)”

3: Urinary fluoride data questionable:

“They then used data on mean urine fluoride concentrations from spot (one-time) urine samples taken at different points in the mothers’ pregnancies, and they only accepted those who had been tested throughout (i.e. didn’t miss a test). The problem with this is that the standard to really know how much fluoride someone is exposed to — by testing their urine — is a 24-hour collection of urine. In that test, you have someone collect their urine for 24 hours and then we measure the fluoride (or a lot of other chemicals) in that sample. This is because urine concentrations of chemicals vary throughout the day. If you drink a lot of fluoridated water in the morning, then your urine is likely to have higher concentrations shortly thereafter than in the evening, when you’ve been drinking bottled water without fluoride. Or, if you worked out in the morning and drank energy drinks but stuck to only tap water in the evening, your urine fluoride will be different.”

Other scientific commenters have also been critical of the urinary fluoride data.  Dr F. Perry Wilson suggests that blood plasm fluoride would have been a far better indicator of fluoride intake (see More expert comments on the Canadian fluoride-IQ paper).

The World Health Organisation’s (WHO) recommendations on the monitoring total fluoride intake for populations also stress the need for 24-hour collection and warn that “urinary fluoride excretion is not suitable for predicting fluoride intake for individuals.” [WHO’s emphasis] (see Anti-fluoridation campaigner, Stan Litras, misrepresents WHO).

WHO recommends it only for monitoring fluoride intake of groups of people because of the large effects of individual diets (see Basic Methods for Assessment of Renal Fluoride Excretion in Community Prevention Programmes for Oral Health). But in this Canadian study, urinary fluoride values were used to estimate individual intake of fluoride.

4: Fluoride intake assessed via an unvalidated survey:

“This means that it is hard to know if the survey really measures what it is supposed to measure. Still, they used it, and it leaves the study wide open to recall bias, something you want to minimize as much as possible. And they would have minimized it if they used it a more valid survey, or a prospective design to their study.

First, what is a prospective design? Well, this is when you take a group of women and sign them up for the study, then you carefully measure their fluoride intake with more validated laboratory assays and questionnaires, and then you follow their children and measure their IQ periodically. You don’t do it all retrospectively with already collected data. But, sometimes, what you have is what you have.

Next, what is recall bias? Recall bias is this interesting phenomenon we see when we rely on people telling us their story in order to ascertain risks and outcomes of exposures. We epidemiologists have noticed that people who have bad outcomes tend to be more likely to remember significant exposures. For example, parents of children with birth defects are more likely to remember things like exposures to chemicals or a history of disease in the family. While parents of typical children don’t recall similar exposures as much because, well, they aren’t looking to connect any dots.

(You see this all the time in anti-vaccine circles, where parents of autistic children are more likely to recall bad reactions to vaccines in their children.)”

Dr. Najera also finds this methodology strange because “they multiplied the intake of certain drinks by some factors in order to estimate fluoride intake:”

“This complicates things because, as you saw above, they excluded women who were not in places where the water was being treated and women who didn’t consume tap water. But, come on, have you ever met someone who never consumed tap water? Do we not use tap water to cook foods all the time? What about that fluoride intake? And why just multiply for fluoride in beverages and not, say, that delicious Canadian cheese soup I’ve heard good things about?”

5: Problems with IQ testing of children:

“I’ve asked some friends of mine who are experts in childhood development, and they are skeptical of accurate measurements of IQ in children because children develop at different rates depending on a variety of variables. You may have seen this when you look at a classroom or a school play. Children are on a big spectrum of development, with milestones being really more like average moments.”

6: Sample not representative:

“The sample used in this study is not at all representative of all mothers and their children in Canada, not even close. As we saw in the paper, many women were left out of the study for a variety of reasons, and mother-child pairs were also excluded. I want to believe that there were good reasons for this, but I could not find them in the paper. The authors do mention that they wanted to look only at mothers consuming fluoride, but why not include those who were not expected or outright did not consume fluoride in order to really compare two populations of interest?”

Dr. Najera finishes with a general comment about the way other studies in the scientific literature are used to provide credibility to the findings;

“Finally, the authors mention other studies — some with rats, other purely environmental — where there is some association between fluoride intake and lowered IQ or some sort of negative impact to neurodevelopmental delay. The thing is, public health agencies around the whole world have been looking at these claims and not finding them to be true within their populations. “

I also find the practice concerning, especially as it is relatively common. I think it indicates confirmation bias – the authors making citations that they think support their findings (and purposely refraining from citing studies that don’t). I find this practice disingenuous because it never qualifies the citations with any reference to the applicability to the real-life situation of community water fluoridation. It never points out the high fluoride concentrations used in animal studies or the fact that many research articles on fluoride and child IQ have involved populations in areas of endemic fluorosis where health problems abound.

Dr. Najera is planning a third article discussing the biostatistical issues with the research – a very important issue I have commented on in previous posts. I look forward to it and will do a post on it in due course.

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Paul Connett’s misrepresentation of maternal F exposure study debunked

Title slide for Paul Connett’s presentation to parliament

Anti-fluoride campaigners are misrepresenting a recent Mexican study claiming its findings should cause governments around the world to abandon community water fluoridation (CWF). Their claims are unwarranted because the study has a high degree of uncertainty. Activists are misrepresenting the accuracy of the studies findings. Because Mexico has areas of endemic fluorosis the study itself is not relevant to CWF.

Misrepresentation of the Mexican study was a central argument used by US anti-fluoride activist Paul Connett in his recent New Zealand speaking tour. This is shown in the Powerpoint presentation he prepared for his meeting at parliament buildings last month (see Anti-fluoride activist commits “Death by PowerPoint”).

It may have not been used in the end as only 3 MPs turned up. But, given his status in the anti-fluoride movement, this presentation will present the current strongest arguments against CWF. It is therefore worth critiquing his presentation whether it was given or not.

In this article, I will concentrate on Paul’s presentation of the Mexican study and may deal with other arguments used in the presentation in later articles. The paper reporting the study is:

Bashash, M., Thomas, D., Hu, H., Martinez-mier, E. A., Sanchez, B. N., Basu, N., … Hernández-avila, M. (2016). Prenatal Fluoride Exposure and Cognitive Outcomes in Children at 4 and 6 – 12 Years of Age in Mexico.Environmental Health Perspectives, 1, 1–12.

In Connett’s mind, the study’s results are so overwhelming we should immediately stop fluoridation throughout the world! This was the first and main argument he presented. His title slide and slide no. 10 introducing the study demonstrates the importance to him.

Slide No. 10 introducing Connett’s presentation of the Bashash et al (2017) study.

I have critiqued this study in previous articles – readers can find them at:

Fluoride, pregnancy and the IQ of offspring,
Maternal urinary fluoride/IQ study – an update,
Anti-fluoridation campaigners often use statistical significance to confirm bias and
Paul Connett “updates” NZ MPs about fluoride?

Paul is clearly aware of these articles because he included a note in his presentation about them. I am honoured (it is the only comment in the presentation) and pleased he has made an effort to engage with my critique.

This is what he says:

“Ken Perrott and those who follow him will claim that the wide degree of scatter in the data means the findings of this study are unreliable.  That is an incorrect interpretation of this graph and the study.  The effect size is very large (decrease by 5-6 IQ points per 1 mg/L increase in urine F) and is highly statistically significant.  The fact that urine F can only explain a small amount of the variation of IQ does not invalidate the finding.  Rather, it is a reflection that there are many other factors that affect IQ, most of which are essentially random with respect to F exposure.  For example, individual genetics plays a huge role in IQ (it explains 80% or more of variation in IQ), therefore it would not be possible for F to explain more than the small remaining portion of variation in IQ.  Most studies of other developmental neurotoxins like Pb and Hg find very similar low correlation coefficients, yet there is no debate that their findings are valid.”

This comment provides me with a basis for a more detailed discussion of his use of the study.

The small amount of variance explained

Connett acknowledges my point that the observed relationship with urinary fluoride can explain only a very small amount of the variation in IQ – only 3%. A bit hard to deny considering the high degree of scatter in the data which is obvious even in the slides Connett uses:

Slide 20 where Connett reproduces Fig 2 from the Bashash et al. paper.

But he claims that this:

“does not invalidate the finding. Rather, it is a reflection that there are many other factors that affect IQ, most of which are essentially random with respect to F exposure.”

Here he is, of course, referring to his own “finding” or conclusion – not the authors.

Notice his assumptions:

• Other factors will be “essentially random with respect to F exposure,” and
• The observed relationship will not be changed by the inclusion of these other factors.

Those are huge assumptions. And they are wrong.

Here is a relevant example illustrating the danger of such assumptions – the association between ADHD prevalence and extent of fluoridation observed by Malin & Till (2015). Their association was able to explain between 22% and 31% of the variance in ADHD, depending on the specific data used. Far more than the 3% for the Bashash et al., (2017) study.

Yet, when other risk-modifying factors were included, in this case, mainly altitude, the significant association with fluoridation disappeared. A model including altitude, but not fluoridation, explained 46% of the variability in ADHD (see Perrott 2017 and a number of articles in this blog).

In this case, the incidence of fluoridation was correlated with altitude – fluoridation was simply acting as a proxy for altitude in the Malin & Till (2015) association. So much for Connett’s assurance that other factors “are essentially random with respect to F exposure.”

Other studies have found an association between symptoms of fluorosis and cognitive deficiencies. Choi et al., (2015), for example, reported an association of child cognitive deficits with severe dental fluorosis, but not with water F concentration. But there is a relationship between fluoride exposure and fluorosis prevalence – ie. fluorosis is not random with respect to F exposure. If the health effects resulting from fluorosis are the prime cause of the cognitive deficiency, the inclusion of fluorosis incidence in the multiple regression could produce a model where there is a statistically significant association with fluorosis but not with fluoride expose. That is, the urinary fluoride values could be simply acting as a proxy of fluorosis incidence.

A similar non-random association of premature births and low birth weight could occur because these problems do occur in areas of endemic fluorosis. These could be two of the health issues related to fluorosis but fluoride intake may not be the prime cause (see Premature births a factor in cognitive deficits observed in areas of endemic fluorosis?).

Connett is completely wrong to assume that other risk-modifying factors not considered in the Bashash study would necessarily be random with respect to fluoride exposure. And he is wrong to assume that inclusion of these factors would not change the association of child IQ with mothers’ urinary fluoride reported in the paper.

Notably, the Bashash et al (2017)study did not include any measure of fluorosis as a risk-modifying factor – despite the fact that Mexico has areas of endemic fluorosis. I believe its consideration of gestation period <39 weeks or >39 weeks was inadequate (the normal average period is 40 weeks). The cutoff point for birth weight (3.5 kg) was also high.

The size of the IQ effect

We only have the data in the Bashash et al., (2017) study to go with here and the associations they report are valid for that data. But what about the calculations Connett makes from the reported association.

For example, Connett declares:

” The effect size is very large (decrease by 5-6 IQ points per 1 mg/L increase in urine F) and is highly statistically significant.”

Let’s test this claim – using the association represented in Fig 2 from Bashash, which is the figure Connett and other anti-fluoride activists are using (his slide 20 above).

Firstly, we need to calculate prediction intervals from the data (see Confidence and prediction intervals for forecasted values). The shaded region in the figure used by Connett (Fig 2 in Bashash et al., 2017) represents the confidence interval – the region where there is a 95% probability that a best-fit line for the data lies. The region for the prediction intervals is much larger and Connett may be confused because he has interpreted the confidence interval wrongly. Yet, the prediction intervals are the important measure when considering the effect size.

Here are my graphs for the confidence interval and the prediction interval using data I digitally extracted from the paper (see Maternal urinary fluoride/IQ study – an update).

Let’s consider the predicted values of “child IQ” for urinary F concentrations of 0.5 and 1.5 mg/L.

Urine F (mg/L)	Predicted value	Lower	Higher
0.5	99.8	74.4	125.2
1.5	93.0	67.5	118.4

The prediction intervals are very large. This means the real value for “child IQ” at a urine F value of 0.5 mg/L has a 95% probability of being in the range 74.4 – 125.2. The corresponding range for a urine F concentration of 1.5 mg/L is 67.5 – 118.4. When Connett claims that an increase of 1 mg/mL in mother’s urinary F produces a drop of 5 – 6 IQ points he actually means a drop of 5 – 6 ± 26 IQ points which is not statistically significantly different to zero.

The best-fit line for the data may be statistically significant – but Connett is wrong to say this about his predicted effect of urinary F on child IQ. In fact, over the whole range of urinary F measured there is a 95% probability that IQ remains at 100.

Connett’s claim of a “highly statistically significant” effect size is completely false. If he had simply and objectively looked at the scatter in the data points he would not have made that mistake.

Comparing maternal urinary F levels to other countries

Connett makes an issue of the similarity of maternal urinary F levels found in this Mexcian study to levels found elsewhere. One is tempted to say – so what? After all, I showed above that his claim of a “highly statistically significant” drop in child IQ with increases in maternal urinary F is completely wrong.

He does compare the urine F levels reported by Bashash et al., (2017) with some New Zealand data (Brough et al., 2015) and finds them to be very similar. Interestingly, Brough et al., (2015) reported their urinary F values as indicating fluoride intakes were inadequate for the women concerned. They certainly did not indicate toxicity.

The comparison does highlight for me one of the inadequacies in the Bashash (2017) paper – the inadequate measurements of urinary F. Whereas Borough et al., (2015) used the recommended 24-hr urine collection technique, the data used by Bashash et al (2017) relied on spot rather than 24 hr measurements. These spot measurements were only made once or twice during the pregnancy of these women.

Yes, these were the only F exposure measurements Bashash et al., (2017) had to work with but they are far from adequate.

Conclusions

Paul Connett, as a leader of the anti-fluoridation movement, is completely wrong about the Bashash et al., (2017) study. It will not lead to the end of community water fluoridation throughout the world – nor should it.

He has attempted to ignore, or downplay, the high scatter in the data and the low explanatory power of the relationship between children’s IQ and maternal F exposure found in the study (only 3%). His denial that this relationship may disappear when other more important risk-modifying factors are included is also wrong – as other examples clearly show.

Connett’s presentation of a size effect (5-6 IQ points with a 1 mg/L increase in F exposure) as “highly statistically significant” is also completely wrong. In fact, this size effect is more like 5 – 6 ± 26 IQ points which is not significantly different to zero.

The misrepresentation of this study by Paul Connett and other anti-fluoridation activists demonstrates, once again, that their claims should never be accepted uncritically. This is just one more example of the way their ideological and commercial interests drive them to misrepresent scientific finding.

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