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Highlights of the Theory (4)

Topino 106

This post is dedicated to whoever, at night, encounters scientific articles purporting to show that the people of Bergamo are a superior race.

After reading Imbens & Rubin’s book on Causality, I finally feel entitled to criticize any causal inference study. Since most scientific questions irradiate a blatant causal nature, any “just an association” disclaimer is a vane attempt at stopping me. I’ll rip through all of your puny inferences. Let’s go!

Assortative mating on blood type: Evidence from one million Chinese pregnancies

While in Italy we assign to newborns the Scorpion, the Torus, the Cat etc. based on the month of birth plus some cryptographically secure date shift, in China, Japan, and possibly other countries that in my mind are a haze over that side of the globe, they use the blood type as a safe source of entropy. Things like: if you are A-blooded, you can’t control well your emotions, or something. If you are B-blooded, you are predisposed for math. If you are AB-blooded, you can’t control your emotions about math, and get into hot debates about using $\pi$ versus $\tau$. I’m making this up because I don’t want to contaminate my mind with actual information on what someone else may try to predict from my blood group, not any more than I want to know what combination of polygenic scores proves that Bergamo means big mickeys.

Anyway, this article by Yao “Crazy Regressor” Houa, Ke “Wild Predictor” Tang, Jingyuan “Big Bias” Wang, Danxia “Tempest of Correlations” Xiea, and Hanzhe “Secret Move of the Invisible Matching Hand” Zhang, reports to us noble readers that:

Blood type is one of the most fundamental phenotypes in biological, medical, and psychological studies. Using a unique dataset of one million Chinese pregnancies, we find strong evidence from a group of statistical tests for assortative mating on blood type. After controlling for anthropometric and socioeconomic confounders, assortative mating remains robust.

Id est, those bloody B-blooders mate between themselves like incestuous monkeys. Luckily I’m A-blooded and have relations only with other As.

*puts down silly hat*

*puts down frequentist hat*

*eh, forgot to hang that 5 years ago*

*what is this other “feed the mice hat” beneath? they died in 200-something*


*puts on serious hat*

They say:

The raw dataset consists of 1,137,010 couples


For convenience of our later analysis, we removed observations with incomplete information related to the couple’s blood types, living areas, birthplaces, ethnicity, and marital status. We obtained a sample of 931,964 couples with complete personal information to serve as our full sample.

I can’t help but notice the absence of a giant neon disclaimer pledging for forgiveness and assuring us well-read readers that later they’ll show how removing >10% of the sample because of missing data has no influence on their “robust” results. We’ll see if and when they say something about it.

As the contingency table reports, […] spousal pairs with the same blood type are more likely to marry each other. Pearson’s chi-square test on the full sample (chi-square statistic: 4020.942, P-value: 0.000, degree of freedom: 9, Cramer’s V: 0.038) further validates non-random mating.

My feral instincts trained by years of experimental Physics immediately tells me that a chi-squared of 4000 (pardon: 4020.942) is what you get if your experiment is not totally perfect in every aspect and you have all source of systematic errors under control, and does not otherwise imply that you have proven wrong the laws. The laws here being a strong a priori expectation of no causal effect of your blood group on who you want to marry. The effects are on the order of 10%, referred to the percentage by which the number of same-blood group couples is above the expected one if people where mating randomly.

What about confounders, videlicet, hidden common causes? This chi-squared above 4000 implies an association between blood type and mating, but does not tell us if the blood type is the cause. This kind of thing would either be filed under “systematics”, “you are dumb”, or “do the $\chi^2$ hack and get it over with” if I was still in Physics. Anyway, they say:

Individuals from subpopulations with residential proximity may naturally have more opportunities to mate. Moreover, they usually share similarities in their blood types because of their similar ethnic backgrounds. Without controlling for population stratification, we may overestimate the degree of assortative mating. Local subsample analysis is therefore proposed to relieve the estimation bias of assortative mating induced by population stratification. We identified locally matched observations by birthplace information and living area information provided by Chinese prepregnancy checkup data. Meta-analysis is carried out at city level (that is, we evaluate assortative mating within a city).

Interlude: in what Fisherian hell does the vocabulary assign “meta-analysis” this meaning? Whatever.

We report statistical results for the 16 cities whose sample sizes (i.e., number of pregnant couples) are larger than 10,000 (Table 2 and Fig. 1). In 13 of the 16 cities, Pearson’s chi-square statistics indicate that mating choice is nonrandom at the 5% level of significance.

We have retreated to the safe and homely havens of 5% significance. No more $p=0.00000000$ juvenile adventures. How interesting. To be honest, their chi-squareds in Table 2 are still somewhat large, however… a huge drop! We have lost 3 of them, and many others are in critical conditions! The erratic nature of happenstance. One day you are hovering over fortunes of thousands, and the next, it all comes crashing down. They continue their attempt:

Therefore, we perform regression analysis to isolate the effect of assortative mating on spousal concordance on blood type from that of relationship maintenance as well as that of subpopulation structure. […] Specifically, we regress an individual’s blood type on their partner’s blood type and incorporate a group of control variables in the regression, which includes the share of the individual’s blood type in the population in their birthplace, the share in their ethnicity, the length of the marriage, and its interaction term with the partner’s blood type (see Methods for details). For comparison, we also run regressions without controlling for other factors.

The Methods inform us that the regression is a logistic linear regression. Since I don’t particularly expect the relationship to be linear, this fit may be taking license to extrapolate with some freedom. Yes, comparing linear trends if 1) you have not checked they are actually linear, 2) you have not checked if you are extrapolating, could be bad. Also, they are bold enough to start investigating different possible causal mechanisms before making sure there is a real causal effect to explain. In particular, they regress on marriage length, which is a TOTALLY POST-TREATMENT variable, the treatment being spouse’s blood type. Not that all the other variables are truly 100% verified pre-treatment, pure as melted snow, but at least they try. Do you know what happens when you try simultaneously to adjust for confounding and study mediation, assuming linear trends and regressing on causally downstream quantities? Well, I don’t! If you do know, please tell me where you live, such that I can move to the opposite side of the globe, and avoid being touched by this dark mastery! Result:

After incorporating control variables, […] the magnitudes of indicator variables’ coefficients decline considerably, and most control variables show statistical significance; this validates that estimates of assortative mating can be biased by confounding factors such as population stratification and relationship maintenance.


After incorporation of a group of control variables, the coefficients of the partner’s blood type are still statistically significant at the 1% level, which indicates highly nonrandom matching on blood type.


To estimate the increase in the probability of matching between individuals that can be explicitly attributed to blood type assortative mating, we repeated the above regression analysis using a linear regression model […] If one’s partner is of a specific blood type, the probability of having the same blood type will increase by approximately 1.6% for those with type A blood, 1.3% for those with type B blood, 1.2% for those with type AB blood, and 4.4% for those with type O blood (Tables 5 and 6). Again, linear regression analysis provides clear evidence to support assortative mating on blood type.

I don’t really know how to interpret causally the coefficients of these regressions, because it’s a mess. But: if you have “validated that that the estimate can be biased by confounding factors,” are adjusting for literally TWO potential confounders (and a post-treatment, aagh), which anyway have already trimmed some of your effect coefficients by more than 10x, then where in the galaxy are you getting the “clear evidence”?

Having shown robust evidence for assortative mating on blood type, we investigate potential reasons.



In summary, we provide evidence of assortative mating on blood type.


To mitigate the estimation bias caused by population stratification, we restrict our analysis to locally matched subsamples to perform meta-analysis. We further address this concern by running regressions with control variables. Other possible mechanisms are also controlled for in our analysis. Our robust results show causal evidence for assortative mating on blood type.


We acknowledge the limitations of our study. First, couples who are lost to follow-up or fail to become pregnant after the prepregnancy examination are missing from our dataset. Selection into the sample introduced by the two kinds of prescreening could be (but does not appear to be) a potential source of bias.


Finally, we sought to avoid our estimates of the degree of assortative mating from being confounded by other factors […] We acknowledge that it is difficult to infer a causal relationship between blood type similarity and mate choice. As previously noted, when a latent subpopulation structure underlies the observed sample, the positive association of blood type within spousal pairs can be attributed to systematic differences among subpopulations that arise from the ancestral differences they inherit.


We strove to control for confounding factors by incorporating a group of control variables to indicate the blood type distribution of subpopulations and the length of couples’ relationship when estimating the extent of assortative mating on blood type using regression models. However, there might still be concern regarding whether confounding factors have been effectively ruled out and a causal relationship between blood type concordance and mate choice is clearly identified.

Wait. So. You knew all along. You held back until the conclusion to keep up some dramatic tension, I guess.

This is the all too common practice of asserting strong results right from the abstract, and then disavowing it somewhere. More sophisticated writers, though, would have avoided very explicit expressions as “our robust results show causal evidence,” and implied it strongly and constantly, but with weasel vocabulary, throughout the whole paper, to claim both fame and prudence.

Here a “Gelman’s disclaimer” is due: I don’t really know what blood type does. I have a generic prior distrust about effects claimed by crappy articles, and on topics tied to popular mysticism like zodiacal blood groups. The point is that this article does not really provide the information it claims to provide on the topic; after reading it, I feel I know as much as before on the effect of blood type on spousal choices, due to the flaws I pointed out.


The article ends with

Data, Materials, and Software Availability. We used 2014 to 2015 Chinese prepregnancy checkup data available from the Institute of Science and Technology of the NHC of the People’s Republic of China. Data and code have been deposited in (48).

Aaaaah they provide raw data and code! Best article ever! <3 uuuuu! I’ll go mate with my fellow X-blooded!

Di-(2-ethylhexyl) phthalate and autism spectrum disorders

Plastic pollution causes cancer, small balls and God knows what, right? Could it be that it also causes autism? Abstract:

ASDs (autism spectrum disorders) are a complex group of neurodevelopment disorders, still poorly understood, steadily rising in frequency and treatment refractory. Extensive research has been so far unable to explain the aetiology of this condition, whereas a growing body of evidence suggests the involvement of environmental factors. Phthalates, given their extensive use and their persistence, are ubiquitous environmental contaminants. They are EDs (endocrine disruptors) suspected to interfere with neurodevelopment. Therefore they represent interesting candidate risk factors for ASD pathogenesis. The aim of this study was to evaluate the levels of the primary and secondary metabolites of DEHP [di-(2-ethylhexyl) phthalate] in children with ASD. A total of 48 children with ASD (male: 36, female: 12; mean age: $11\pm5$ years) and age- and sex-comparable 45 HCs (healthy controls; male: 25, female: 20; mean age: $12\pm5$ years) were enrolled. A diagnostic methodology, based on the determination of urinary concentrations of DEHP metabolites by HPLC-ESI-MS (HPLC electrospray ionization MS), was applied to urine spot samples. MEHP [mono-(2-ethylhexenyl) 1,2-benzenedicarboxylate], 6-OH-MEHP [mono-(2-ethyl-6-hydroxyhexyl) 1,2-benzenedicarboxylate], 5-OH-MEHP [mono-(2-ethyl-5-hydroxyhexyl) 1,2-benzenedicarboxylate] and 5-oxo-MEHP [mono-(2-ethyl-5oxohexyl) 1,2-benzene-dicarboxylate] were measured and compared with unequivocally characterized, pure synthetic compounds (.98%) taken as standard. In ASD patients, significant increase in 5-OH-MEHP (52.1%, median 0.18) and 5-oxo-MEHP (46.0%, median 0.096) urinary concentrations were detected, with a significant positive correlation between 5-OH-MEHP and 5-oxo-MEHP ($r_s=0.668$, $P <0.0001$). The fully oxidized form 5-oxo-MEHP showed 91.1% specificity in identifying patients with ASDs. Our findings demonstrate for the first time an association between phthalates exposure and ASDs, thus suggesting a previously unrecognized role for these ubiquitous environmental contaminants in the pathogenesis of autism.

They say “association.” Prudent people. However, what we actually care about is causation! I guess nobody would like to write in their article “we did a causal study but it’s crappy.” The other thing I notice in the abstract is the control group: how was it selected? This surely isn’t a randomized study, and the first key step is selecting controls which have a chance of being comparable after some adjustment.

A dramatic increase in frequency of ASDs has been reported over the last 20 years (Weintraub, 2011; Kim et al., 2011). Nevertheless, it is difficult to determine how much of this increase may be due to actual increase in the incidence or to increased awareness and diagnosis.

Right, let’s be prudent and remember there’s a huge confounding due to strongly varying spread and criteria of diagnosis.

Although it is widely recognized that ASDs may have a strong genetic component (Risch et al., 1999; Anney et al., 2011). To the best of our clinical experience, not more than 5% of all autism cases appear to be due primarily to single gene mutations. In particular, syndromic ASD accounts for 15–20% of ASDs, and other complex genetic factors appear to play a major role in non-syndromic forms of autism. World literature evidence seems to indicate that autism has a strong genetic component (10–20%, Geschwind, 2011) which, by itself, does not fully explain the prevalence of the disorder exponentially increasing over the last two decades. It is quite likely that exposure to potential environmental factors has differential effects depending on genetic background.

I have a hard time following the thread of this paragraph. Why is a small prevalence of single-gene causation an avversative, like we were expecting it to be the case? In general I expect something like ASD to be partially heritable but to depend on a unfathomable combination of genes. The same for heritability not explaining the “exponential increase,” which seems to implicitly lead to environmental factors as what must be missing, while the elephant in the room is increase of diagnosis, as mentioned above. I guess I’m nitpicking, this paragraph just conveys “there’s room for environmental effects,” the precise logical structure is not important, it is a rhetorical flow from ASD to plastic.

Next there’s a summary of why phthalates are suspects. Its strength is the number of its citations, so I can’t say much because I know nuthing about the topic. I feel in my head a higher probability of phthalates causing ASD, but still small due to generic priors on anything causing anything.

Next come our protagonists:

A total of 48 children with ASD (male: 36, female: 12; age at examination: $11.0\pm5$ years) were recruited from the staff of Children Neuropsychiatric Department, Siena, Italy. All the 48 patients with ASD, diagnosed by DSM IV (Diagnostic and Statistical Manual of mental disorders) and evaluated using ADOS (autism diagnostic observation schedule), ABC (autism behaviour checklist) and CARS (childhood autism rating scale) scores entered the study. Patients with Rett syndrome, X-fragile syndrome, inborn errors of metabolism, 21 trisomy, tuberous sclerosis and gene microdeletions were excluded from the present study. […] Forty-five gender- and age-comparable HCs (healthy controls) [male: 25, female: 20; age at examination: $12\pm5$ years] were randomly chosen from outpatients who had no pathological symptoms.

“All the 48 patients with ASD […] entered the study.” What does that mean, exactly? ALL the patients with ASD out of all the patients of the hospital? ALL of the ones whose parents consented? ALL of the ones not excluded due to genetic illness? How many were excluded, at what step? “Healthy controls […] were randomly chosen from outpatients who had no pathological symptoms.” What does randomly mean? Did they make a lottery? Or does it just mean the staff picked them however they felt?

After one paragraph on unit selection, there goes one page about the analysis of urines to measure phthalates:

Determining secondary metabolites in urine

Urine from children with ASD and HCs were collected in polypropylene specimen cups, divided into aliquots (1.0 ml) and frozen at –20 ̊C until analysis. Field blanks consisted in purified water collected in polypropylene tubes and frozen at –20 ̊C.

The metabolites measured in this study included: MEHP [mono-(2-ethylhexenyl) 1,2-benzenedicarboxylate] and 6-OH-MEHP [mono-(2-ethyl-6-hydroxyhexyl) 1,2-benzenedicarboxylate], 5-oxo-MEHP [mono-(2-ethyl-5-oxohexyl) 1,2-benzenedicar- boxylate] and 5-OH-MEHP [mono-(2-ethyl-5-hydroxyhexyl) 1,2-benzenedicarboxylate]. All these metabolites were synthesized in the Laboratory of Peptide and Protein Chemistry and Biology (PeptLab) following their previously described procedure (Nuti et al., 2005). The unequivocally characterized synthetic metabolites were used as pure analytical standards (.98% purity) for quantitative determination in urine from ASD children and HCs.

All the solvents (acetonitrile, water, buffers, etc.), labware (polypropylene vials containing urine, solvent bottles, SPE (solid phase extraction) cartridge, Teflon capped-glass bottles, pipettes) and instrumentation used during SPE procedure and the HPLC-ESI-MS (HPLC electrospray ionization MS) analytical process, to detect MEHP and/or secondary metabolites in ASD patients and HCs, were verified to be MEHP– and secondary oxidative metabolites-free. The internal standards were prepared in acetonitrile and were used as reported in the literature (Blount et al., 2000; Kato et al., 2004).

First morning urine specimens were collected. All specimens displayed urinary creatinine in the children reference value range, dependent on age and lean body mass (0.5–4.0 mg/kg per 24 h). For creatinine measurement, we used a Synchron AS/ASTRA clinical analyser (Beckman Instruments). We used values (μg/l) for creatinine and (g/l) for dilution correction in the analyses.

For SPE treatment of urine, we prepared the following buffers: ammonium acetate buffer 1 M, pH 6.5; acid buffer, pH 2.0 by preparing a solution of NaH2PO4 (0.14 M) and 1% of 85% H3PO4; basic buffer was prepared by adding concentrated ammonium hydroxide (1 ml of 30% NH3 solution) to a 50:50 acetonitrile/water (200 ml). All buffers were stored in sealed bottles at room temperature (20 ̊C): basic buffer was discarded after 1 week, acid buffer after 1 month.

Human urines (1 ml) were defrosted, sonicated, mixed and dispensed in glass tubes. Then ammonium acetate buffer (250 μl, pH 6.5) was added. Incubation with β-glucoronidase (5 µl, 200 units/ml, Roche Biochemical) was performed at 37 ̊C for 90 min, resulting in quantitative glucuronide hydrolysis of phthalates and metabolites. Escherichia coli K12 β-glucuronidase has excellent glucuronidase activity and no measurable lipase activity on phthalate diesters (Blount et al., 2000; Kato et al., 2004). After deconjugation, samples were treated with two steps of SPE, using SPE cartridge (3 ml/ 60 mg of Oasis HBL, Waters) to remove any contamination of biological matrix, following the procedure described by Blount et al. (2000). The first cartridge was used to retain hydrophobic compounds while the phthalate metabolites were eluted. The second cartridge was helpful in removing residual salts. Analytes were finally eluted with acetonitrile and ethyl acetate, concentrated, re-suspended in water and transferred into vials. All the samples were analysed by RP- HPLC-ESI-MS (reverse-phase HPLC-ESI-MS). One blank and one QC (quality control) sample were included in each batch of samples. The QC sample was spiked with pooled urine and MEHP and secondary oxidative metabolite standards in known concentration (200 ng/ml). When urine analysis resulted in values for metabolite concentrations exceeding the linear range of the analytical method, we subjected a new aliquot of the same sample to the entire process (deconjugation and SPE) and we analysed again. Before analysis, known concentration samples were treated by SPE and analysed by RP-HPLC-ESI-MS to test SPE efficiency. In our study the efficiency of SPE procedure is in accordance with the literature (Mazzeo et al., 2007). Treated urine samples could be stored at 4 ̊C without degradation. Storage of untreated urines at –40 ̊C for 6 months showed no decrease in phthalate monoester levels.

The analytical methodology adapted for measuring MEHP and secondary oxidative metabolites in urine had already been described in the literature (Blount et al., 2000; Silva et al., 2003a, 2003b; Kato et al., 2005).

In particular, we used an HPLC tandem MS, RP-HPLC-ESI- MS (Waters, Alliance 2695, Waters, Micromass ZQ) equipped with phenyl column (Betasil, 5 µm, 50 mm $\times$ 63 mm, Keystone Scientific) and with a Waters 2996 Photodiode Array Detector. All reagents were of at least analytical reagent grade. The lower LOQs (limits of quantification) were 0.042 µg/l MEHP, 0.048 µg/l 5-OH-MEHP, 0.049 µg/l 5-oxo-MEHP and 0.008 µg/l 6-OH-MEHP. In urine, the LODs (limits of detection) were 0.014 µg/l MEHP, 0.016 µg/l 5-OH-MEHP, 0.016 µg/l 5-oxo-MEHP and 0.002 µg/l 6-OH-MEHP. The chromatographic separations of metabolites were resolved using a linear gradient from 3 to 60% B in 10 min (solvent system A: 0.1% acetic acid in water; B: 0.1% acetic acid in acetonitrile). The flow rate was 0.6 ml/min. The column temperature was 32 ̊C. A guard column (XBridgeTm Phenyl 3.5 µm, 3.0 $\times$ 20 mm) was used to prevent column degradation. Column eluates were monitored at 215, 230 and 254 nm. The mass-specific detection was achieved using a Waters, Micromass ZQ ESI in positive ion mode. The product ion with higher signal intensity was selected for the quantitative analysis for each of the four phthalates. The optimal MS parameters were as follows: the source and desolvation temperature were 120 and 400 ̊C respectively; the capillary voltage was 3.24 kV; cone voltage 30 kV, nitrogen gas was used as desolvatation gas and as cone gas as well; the cone gas and the desolvatation flow was 60 and 800 l/h respectively; the collision gas was argon with a flow of 0.60 ml/min. Data were acquired and processed using MassLynx™ software (Waters).

Calibration curves for the quantitative urine analysis were calculated for all analytes plotting peak area average (y) against concentration of standards (x). Five standard solutions (linear range: 2.5–2500 ng/ml) for calibration curve plotting, were prepared for all the metabolites. Curves with correlation coefficients ($r^2$) greater than 0.998 were generated (MEHP, 5-OH-MEHP, 5-oxo-MEHP 0.999 and 6-OH-MEHP 0.998).

I am happy they were so thorough in reporting the procedure. However, what I want to know is: is the person who performed the measurement the same for the two groups of children? Where the two groups measured in different occasions? If your are so accurate in reporting what you know, to be balanced you should also report about what you don’t know. My experience with precision calibration is that, if you have some real independent feedback on the quality of your result, after a while you start wondering if what you ate for breakfast has an influence on the measurement.

To summarize: they want us to savor the details of how they cleaned their beakers, but the sample selection is “the staff found some random guys who were similar.” I think this article is higher quality than the previous one on blood mating, yet this reminds me of Yao “Crazy Regressor” etc. letting us know that their $\chi^2$ is 4020.942, no more, no less, at a point they haven’t even started adjusting for confounders yet.


This table shows how well the urine measurement works as a test of ASD. AUC means “area under curve” and would be 0.5 for a completely ineffective test. The main thing to notice here is that the ALL value (last row, $0.671\pm0.055$) is 3 standard errors away from 0.5. Here my usual inner Physicist suggests that 3σ is not something you can claim a result with, because history has taught us that it’s too low a cutoff, but I’m not a Physicist, so… rejoice and publish! 

The next table contains the raw data, the level of phthalate-related molecules measured in urine, compared between autistic children and controls:

Important to know, the text says

However, the data illustrated in Table 2 are without urinary creatinine correction. Differences between groups by using creatinine-adjusted data were comparable with those employing raw data (data not shown). The statistical significance of variables was independent of effects of urinary creatinine concentration. In fact, it is well known that urine concentration/dilution can affect the results of measurements of urinary metabolites.

Like in the first table, notice that even though the p-values are “statistically significant,” (they are Bonferroni corrected, by the way) the intervals overlap. A p-value may look strong because it’s small, but reality reasons in terms of effects; if a small change on the scale of the measured quantity compared to its variation can make the groups overlap, then it means that any defect in the study could swamp the p-value. (See this post by Gelman for a nice discussion.)

Their “best-performing” molecule is 5-Oxo-MEHP, which is honored with its own private graph:

However, they also look at correlations with autism score, instead of just considering ASD/not ASD, and do not find a clear correlation for 5-Oxo-MEHP:

A positive correlation between CARS scores and urinary MEHP levels was observed ($\rho=0.429$, P=0.0033), whereas no significant relationships with the levels of the other examined metabolites were found (total CARS versus 5-OH-MEHP: $\rho=0.120$, P=0.4298; total CARS versus 5-oxo-MEHP: $\rho=0.127$, P=0.3931; total CARS versus 6-OH-MEHP: $\rho=0.0085$, P=0.9529).

Look at the plot. The level in ASDs is quite higher, isn’t it? However, that could totally be lower variance of the control group, depending on the selection.

Their final discussion begins with:

Our findings, for the first time, demonstrate an association between phthalates and ASDs.

And proceeds for one page on all the biological and medical implications of this finding, weaving together an origin story for autism, up to

As a consequence, the current surge of this disease could be related to transient maternal hypothyroxinemia resulting from exposure to anti-thyroid environmental contaminants.

It ends with:

For the first time in this study we correlated different levels of the primary and secondary metabolites with ASDs compared with HC children. These data generate the idea that either current exposure is higher in children with ASD, or alternatively, and more likely, ASD children may differ in their ability to metabolize phthalates.

This may look like a contradiction to their previous discussion, but it is a sound hypothesis: children genetically predisposed to metabolize slowly phthalates have an higher amount of them in their body at any given time, and phthalates increase the chance of autism.

But the cherry is kept for the very last, waiting for the courageous readers who venture to disclaimer sections:


We gratefully acknowledge Dr R. Zannolli (Dipartimento Materno-Infantile, University of Siena, Siena, Italy) for collecting HC urine samples.

The. Control. Urines. Were. Collected. By. Totally. Another. Guy. What else are you not saying?


Now I’m curious. This article is from 2012, and maybe in the meantime this hypothesis has been either confirmed or disproved (or is being fiercely debated by camps of opposing articles). I’ll check. Gelman’s disclaimer: I don’t know if the effect reported by the article does exist or not, and I have no particular opinion on it. All I’m saying is that the article exudes more confidence than warranted. The study per se is valid, but it’s written in a way that’ll get some people to come to me and say “PLASTIC CAUSES AUTISM” like it was a fact, that’s why I read it in the first place.

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