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January 1, 2012

“Doctors don’t cure nothing”

Filed under: Causation,Correlation,Culture,False Positives,Medicine,science — Razib Khan @ 2:00 pm


As I observed before, modern medicine is subject to some of the same statistical issues as social science in its tendency to put unwarranted spotlight on preferred false positive results. Trials and Errors – Why Science Is Failing Us:

This doesn’t mean that nothing can be known or that every causal story is equally problematic. Some explanations clearly work better than others, which is why, thanks largely to improvements in public health, the average lifespan in the developed world continues to increase. (According to the Centers for Disease Control and Prevention, things like clean water and improved sanitation—and not necessarily advances in medical technology—accounted for at least 25 of the more than 30 years added to the lifespan of Americans during the 20th century.) Although our reliance on statistical correlations has strict constraints—which limit modern research—those correlations have still managed to identify many essential risk factors, such as smoking and bad diets.

I need to look at the difference between mortality and morbidity here. The two are clearly related, but if modern medicine has decreased morbidity, then it is still worthwhile to a greater extent than simple life expectancy calculations might indicate. But the reality is that the more and more I look at modern medicine the more worried I get that the age old heuristics and biases which allowed medicine to flourish as a form of counterproductive psychotherapy up until the early 20th century are now coming back to the fore. The issue here is less the profession of medicine, as the incentives and impulses which drive the need for a “cure” from the demand side.

All this brings to mind a passage from the book Religion Explained:

E. E. Evans-Pritchard is famous for his classic account of the religious notions and beliefs of the Zande people of Sudan…one day the roof of a mud house collapses in the village…People promptly explain the incident in terms of witchardcraft…Evans-Pritchard points out to this interlocutors that termintes had undermined the mud house and there was nothing particularly mysterious in its collapse. But people are not interested in this aspect of the situation. As they point out…they know perfectly that termites gnaw at the pillars of mud houses and that decrepit structures are bound to cave in at some point. What they want to find out is why the roof collapsed at the precise time when so-and-so was sitting undernearth it rather than before or after that. This is where witchcraft provides a good explanation.

With all due respect to modern scientifically trained physicians, but the demands that their patients are now making upon them in terms of curing diseases whose causal roots are less than clear are transforming them into latter-day shamans. As it was, it will be?

December 30, 2011

How do relatives correlate in traits?

Filed under: Correlation,Height,Quantitative Genetics — Razib Khan @ 1:24 am

The Pith: Even traits where most of the variation you see around you is controlled by genes still exhibit a lot of variation within families. That’s why there are siblings of very different heights or intellectual aptitudes.

In a post below I played fast and loose with the term correlation and caused some confusion. Correlation is obviously a set of precise statistical terms, but it also has a colloquial connotation. Additionally, I regularly talk about heritability. Heritability is in short the proportion of phenotypic variance which can be explained by genetic variance. In other words, if heritability is ~1 almost all the variation in the trait is due to variation in genes, while if heritability is ~0 almost none of it is. Correlation and heritability of traits across generations are obviously related, but they’re not the same.

This post is to clarify a few of these confusions, and sharpen some intuitions. Or perhaps more accurately, banish them.


The plot above shows relationship between heights of fathers and heights of sons in standard deviation units (yes, I removed some of the values!). You see that the slope is ~0.45, and that’s the correlation. At this point you probably know that heritability of height is on the order of 0.8-0.9. So why is the correlation so low? A simple biological reason is that you don’t know the value of the mothers. If the parents are not strongly correlated (assortative mating) obviously the values of the sons is going to diverge from that of the father. That being said, you probably notice that the correlation here is about 1/2 that of the heritability you know has been confirmed in the literature. That’s no coincidence. One way to estimate heritability is to take the slope of the plot of offspring vs. parents, and multiply that by 2. Therefore, the correlation (which equals the slope) is 1/2 × h2, where h2 represents heritability.

Correlation (parent to offspring) = 1/2 × h2

1/2 turns out to be the coefficient of relatedness of a parent to offspring. I’ll spare you the algebra, but suffice it to say that this is not a coincide. Where r = coefficient of relatedness the correlation between sets of relatives on a trait value is predicted to be:

Correlation (relative to relative) = r × h2

Where r is simply the coefficient of relatedness across the pair of relatives. Here are some values:

r relationship
0.5 (½) parent-offspring
0.25 (¼) grandparent-grandchild
1 identical twins; clones
0.5 (½) full siblings
0.25 (¼) half siblings
0.125 (⅛) first cousins

Here’s the kicker: the correlation coefficient of the midparent value and the offspring value does not equal the slope of the line of best fit. This is why I had second thoughts about using the term “correlation” so freely, and then switching to heritability. The formula is:

Correlation (midparent to offspring) = 1/√2 × h2

So the correlation of midparent to offspring is 0.71 × heritability.

Why is this something you might want to know? I think people are sometimes confused about how an extremely heritable trait, like height, where you’re given heritability values of 0.90, still yields families with such a wide range of heights. Well, recall that the coefficient of relatedness among siblings is 1/2. So their correlation is going to be the same as with parents. Therefore, the magnitude will be half that of the heritability. A correlation of 0.45 is not small, but neither is it extremely tight. The histogram below illustrates this with the above data set. The values are simply the real difference between fathers and sons:

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