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July 11, 2011

The Misbehaving Signal of Sherman & Mangano

By: Aaron Datesman

The point I tried to make in this post about the Sherman/Mangano study is probably not very clear, so I made an example to clarify it. The graph below examines four cases, read from bottom to top, which correspond reasonably closely to the actual data from Sacramento.

PNW Graph.png

1. In the base case (blue), the typical level of infant mortality is 1/week. After the fallout from Fukushima arrives, I assume that the infant mortality rate jumps by 50%, to 1.5/week. While this is an idealized "signal" - nature will never give us data this clearly - it defines the underlying structure of the noisy and corrupted data we ultimately have available to interpret.

2. In the second case (red), I added a slight temporal variation to the typical rate of infant mortality. The additional variability is not large; I chose 10% of the typical level, or 0.1/week, similar to the 1979 data from Pennsylvania I cited earlier. The temporal variation repeats every twenty weeks, which is about what I found from analysis of the 2008-2010 Sacramento data.

3. In the third case (green), I increased the temporal variation to be equal in magnitude to half of the average, or base, level of infant mortality. This is similar to the Sacramento data.

4. The fourth case (purple) is just the third case shifted by five weeks. This is useful to think about because there is no reason to anticipate a disaster at a nuclear plant at any particular point in the temporal cycle. (Although Three Mile Island, Chernobyl, and Fukushima all occurred in the spring, come to think of it…..)

Sherman and Mangano reached their conclusion of increased infant mortality by comparing average rates of infant mortality in intervals prior to (represented by points AB) and after (CD) the arrival of fallout from Fukushima in the Pacific Northwest. Point B represents the last data point prior to the arrival of fallout, while C represents the first measurement of infant mortality after. The locations of both B and C are fixed in time. Points A and D may be freely chosen according to whatever statistical criteria are judged relevant, which allows us to decide whether to evaluate average values of infant mortality over 2, 4, 10 or any desired number of weeks.

It's clear from the figure that adding a 10% variation to the base signal (which contains a 50% increase after Week 0) doesn't hinder our ability to discern the increase. Furthermore, the locations of points A and D don't matter very much. If the intervals examined are long enough to contain a statistically significant number of mortality incidents, then the answer obtained by averaging in this case will be correct.

I think the critiques of the Sherman/Mangano study miss this point: their results would be correct if the underlying signal "behaved" itself. The additional curves investigate the ramifications of nature's misbehavior. We find that, if the temporal variation is large, you can obtain essentially any result by choosing different intervals for evaluation.

For instance, by placing A at the peak and D at the trough of the green curve, you would reach the conclusion that the average rates prior to the arrival of fallout and after were just about identical - obscuring the 50% rise entirely. And the 4 week/10 week intervals chosen by Sherman and Mangano applied to the purple curve (shown in the figure) would reveal that infant mortality decreased after Week 0, which in this example is exactly wrong.

The takeaway here is that averaging over arbitrary intervals can't be applied: it's wrong when Sherman and Mangano apply it, and it's wrong when their critics use it to dispute their conclusions. When the temporal variation is large compared to the average level, no analysis can be considered correct or even useful without firmly establishing how the signal varies with time.

I already posted the answer (the Sacramento Infant Mortality data), but the origin of that graph provides a very interesting illustration of two topics these posts on the dangers of radioactivity have often brushed against: the difference between average and instantaneous rates, and shot noise. My next post will describe how the raw CDC infant mortality data (which appears to be quite random in character) actually contains a very strong temporal signal. If math makes your eyes bleed, you might wish to skip that post.

— Aaron Datesman

Posted at July 11, 2011 09:49 PM

I wonder what radiation levels in the New Orleans area is about now. I wonder how far along Japan has gotten to resolve its reactor leakage issues?

Posted by: Mike Meyer at July 12, 2011 12:20 AM

What are the specific causes of infant mortality and why should they be linked to fallout?

Posted by: Edward at July 12, 2011 09:29 AM

why should they be linked to fallout?

I should imagine it's for the same reason cigarette smoking was linked to cancer in the absence of a specific cause. And I also imagine your question is raised for the same reason the anti-smoking lobby kept asking its version of that question.

I don't have evidence of that, of course, but it seems a reasonable assumption.

Posted by: NomadUK at July 12, 2011 12:03 PM

Never forget Occam's Razor.

The tobacco companies had more hoops to jump through than a dog and pony show. But alas soon enough, the smoke and mirrors failed, but after millions had died.

The victims should never have the burden of proof when the evidence is in the hands of those who have secreted it away.

Sanity demands it.

Posted by: Dredd at July 12, 2011 02:37 PM

If one googles "Radioactivity in milk and water in Oregon, Washington, California after Fukushima accident", one finds many articles worth reading. Also by adding EPA monitoring, one will find articles claiming EPA stopped monitoring radioactivity levels too soon for many of the watchdog groups' comfort.

One interesting article is...


Rather strange statement from the EPA.....
Earlier in the week, the Environment Protection Agency confirmed radiation was found in air filters in Alabama and in rainwater in Pennsylvania and Massachusetts. Though the trace levels are very low and not hazardous to health, residents have been warned not to use rainwater which has been collected in cisterns.

Physicians for Social Responsibility, a U.S. anti-nuclear group, disputed the food safety assurances and called for a more strict ban on sales of exposed food.
“There is no safe level of radionuclide exposure, whether from food, water or other sources. Period,” said physician Jeff Patterson, a former president of the group.




Posted by: Rupa Shah at July 12, 2011 03:53 PM

Like so many things, this was actually clearer to me when I didn't understand it that well.

(Not that I understand it that well now.)

Posted by: N E at July 12, 2011 10:33 PM


If such a connection exists, there is probably evidence from earlier cases with more severe exposure and longer time periods, such as the Chernobyl accident in its vicinity.


I think the points being made here are that:

1)The mortality data jumps around and by choosing particular time periods you can create the appearance of an increase after the accident.

2)If the noise is too great it will obscure any trends in the data.

On the other hand, what qualifies as noise? The noise will be factors you don't take into account.

Posted by: Edward at July 13, 2011 01:11 AM

@Edward - it's a very fair question, so here's what I think.

1. To a certain extent, asking for a cause gets the process of science backwards. Theory flows down from observation; we're not allowed to disregard observations which don't fit our theories. One of the IAEA critiques of Yablokov et al. is that they described damaging health effects in areas where the calculated doses were below the threshold where models assume no harm can occur. This is unscientific.

2. In a general way, I think it's very sensible that fetuses and infants are extremely sensitive to radiation. Accepting that ionizing radiation damages genetic material, and further that genetic material controls cell division, it follows that health impacts should be most severe in periods of fast cell division (rapid growth). Now, go one step further - unlike an adult, a young fetus does not yet have differentiated organs. Only small groups of cells which will become those organs in the future via cell division exist.

If the genetic material in one of those cells is damaged, to me it's very sensible to conclude that the viability of the infant outside of the womb could be severely impacted. (If the baby comes to term at all. Most pregnancies, in fact, are not viable and are re-absorbed by the body within the first trimester.)

Even Yablokov says that there is not a firm experimental understanding of how ionizing radiation impacts infant mortality. It would be extremely difficult to create a convincing animal study. Nevertheless, we do have epidemiological data.

3. The first person to suggest that infant mortality was increasing due to radiation (fallout, in this case) was Ernest Sternglass. This was highly contentious and a very controversial topic around 1965-75; I'm learning about the history, and find it very fascinating. You can read some of the primary material online through the archives of the Bulletin of the Atomic Scientists. Maybe I'll post something about it.

Basically, Sternglass found that US infant mortality data departed from the long-term trend around the time that atmospheric testing began in Nevada. This was a pretty big conjecture, but in my opinion his data about infant mortality near the Hanford site in Washington in 1944 is quite convincing. (It would be interesting, I think, to go back and examine the big Sternglass conjecture with an addition 40 years of data. Maybe I'll do that. But I have a job.)

Whatever opinion one might hold about that conjecture (and you can read what some very prominent scientists had to say, including Pauling and Dyson), there are supporting findings which are more recent and better-supported. Albert Korblein, for instance, has data from Germany and Poland in the article I linked in a previous post.

I hope that's a sufficient answer.

Also, regarding noise, noise is not just stuff you don't take into account. In this case, the principal source of noise is shot noise - which reflects the basic reality that dead infants come in discrete packets of one.

@NE - Sorry for the confusion. The basic point is that the infant mortality signal has a very strong time variation. No analysis of the data can be valid without first extracting that time variation.

Posted by: Aaron Datesman at July 13, 2011 09:15 AM


Yes, it does sound like radioactive particles should be extra dangerous for a fetis. Perhaps the question then is how likely is it for such particles inhaled or injested by the mother to lodge in the fetis? Also, I think it is worth considering the various causes of infant mortality because some causes may not be linked to radiation damage; actually, you may only want to work with a subset of the mortality data. It may also be easier to analyze the "shot noise" of particular types of mortality rather then combining everything together.

Posted by: Edward at July 13, 2011 02:09 PM

@Edward -

Well, it seems to me that the fetus is built out of the same stuff that the mother is. So, if the mother is building strontium into her bones or cesium into her muscles (they are chemical analogues of calcium and potassium, respectively), then those same processes are occurring in the fetus also.

The argument involves examination of the mortality statistics against a counterfactual (no exposure to radiation) which doesn't exist. This is a pretty subtle thing. Infants who have suffered exposure are weaker than they would have been if that exposure had not occurred. (There is good evidence for this - occurrence of lower birth weights is documented.)

Therefore, the analysis relies on either a) comparison of mortality rates in comparable populations where one suffered exposure but the other did not, or b) deviation in long-term trends of mortality which correspond to exposure onset. I'm not aware of any other way to examine this issue.

This sounds logical, but it means the following: if an infant perishes of pneumonia in her 22nd week, we're choosing to attribute or not attribute that death to radiation based on statistical comparisons between large populations, and upon our knowledge about contamination levels in the relevant geographical areas. This may be too tenuous for many people to accept.

I agree that it's necessary to be careful about what data is combined and what evaluated separately. For instance, I think it was incorrect for Sherman and Mangano to combine eight separate cities in their analysis.

Appreciate your comments. Thanks!

Posted by: Aaron Datesman at July 13, 2011 05:25 PM

Aaron, no need to apologize. You're a great explainer. It's not confusing because you didn't explain it well, and I think I basically get it. It's just complex and so easier to understand superficially without full understanding, which is how I think we all actually understand most things.

Which is why I suppose we're going to be replaced and hunted down by cyborgs or something even cooler.

Posted by: N E at July 13, 2011 09:53 PM

As long as they are wind- or solar-powered, I welcome our incipient cyborg overlords.

Posted by: Aaron Datesman at July 14, 2011 05:27 AM

"As long as they are wind- or solar-powered, I . . ."

What's wrong with geothermal? Or wave power??

As for explaining, well, communication is the art of transferring a thought of idea from one consciousness to another and language sucks at this - i.e., "counterfactual" is not just counter to any old facts, it's a control group. It took me until "The argument involves examination of the mortality statistics against a counterfactual (no exposure to radiation) which doesn't exist" to figger that out. Of course, I are a high school drop out and therefore have no formal education to speak of. I was thinking, "a yellow sky and pink sun" -- that's certainly counter to the facts I'm familiar with.

Posted by: Some guy on the innernet at July 14, 2011 09:56 PM