Sunday, March 30, 2014

Why does GCTA work?

This paper, by two of my collaborators, examines the validity of a recently introduced technique called GCTA (Genome-wide Complex Trait Analysis). GCTA allows an estimation of heritability due to common SNPs using relatively small sample sizes (e.g., a few thousand genotype-phenotype pairs). The new method is independent of, but delivers results consistent with, "classical" methods such as twin and adoption studies. To oversimplify, it examines pairs of unrelated individuals and computes the correlation between pairwise phenotype similarity and genotype similarity (relatedness). It has been applied to height, intelligence, and many medical and psychiatric conditions.

When the original GCTA paper (Common SNPs explain a large proportion of the heritability for human height) appeared in Nature Genetics it stimulated quite a lot of attention. But I was always uncertain of the theoretical justification for the technique -- what are the necessary conditions for it to work? What are conservative error estimates for the derived heritability? My impression, from talking to some of the authors, is that they had a mainly empirical view of these questions. The paper below elaborates significantly on the theory behind GCTA.
Conditions for the validity of SNP-based heritability estimation

James J Lee, Carson C Chow
doi: 10.1101/003160


The heritability of a trait ($h^2$) is the proportion of its population variance caused by genetic differences, and estimates of this parameter are important for interpreting the results of genome-wide association studies (GWAS). In recent years, researchers have adopted a novel method for estimating a lower bound on heritability directly from GWAS data that uses realized genetic similarities between nominally unrelated individuals. The quantity estimated by this method is purported to be the contribution to heritability that could in principle be recovered from association studies employing the given panel of SNPs ($h^2_\textrm{SNP}$). Thus far the validity of this approach has mostly been tested empirically. Here, we provide a mathematical explication and show that the method should remain a robust means of obtaining $h^2_\textrm{SNP}$ under circumstances wider than those under which it has so far been derived.


chartreuse1737 said...

"What are conservative error estimates for the derived heritability?"

but heritability is merely the square of the coefficient of G for the tangent plane to the GxE to trait surface at a particular point. turkheimer's finding and the heteroskedasticity of g vs iq show that this heritability is a local phenomenon, local to the point in the GxE plane.

"In recent years, researchers have adopted a novel method for estimating a lower bound on heritability..."

the lower bound is always 0.

Iamexpert said...

Havent read the paper, but this sounds like a high tech version of kinship-phenotype correlation. Identical twins are phenotypically more similar than regular siblings who are more similar than cousins who are more similar than randomly paired citizens who are more similar than people from different countries etc. But how does that prove heritability? Genetically similar people tend to grow up in similar environment so how does this advance the debate? Now perhaps if you could subtract environmental similarity from genetic similarity, then you could draw conclusions, but since the only environmental effects that appear to matter by maturity (for fluid IQ) are biological (head injuries, prenatal nutrition, alcohol etc), this sounds impossible to measure. But since biological environmental effects are so small within generations (arguabley HUGE between generations-see the Flynn Effect) failing to subtract for environment may work in practice despite being theoretically sloppy.

Abruzzi_spur said...

what exactly are you an expert on?

1. there is no fluid intelligence, just like there are no angels.

2. aside from wk or fas, alcohol and alcoholism have no effect on iq. it can affect performance on some neuropsychological tests, but has no effect on an indivdual's general cognitive ability. this is not a controversial claim. the gross changes in the brains of some heavy drinkers are generally not the result of cell death. at autopsy the brains of heavy drinkers are not significantly lighter than those of abstainers.

James Hedman said...

John von Neumann was a notorious drunkard.

Iamexpert said...

Brain size & alcohol:

With respect to fluid IQ, you're entitled to your opinion.

Abruzzi_spur said...

brain volume yes, brain mass no.

Abruzzi_spur said...

so was alekhine.

James Hedman said...

I was going to mention that too although before a match he usually had only one or two drinks at most if at all. At those levels alcohol has a mildly stimulating effect.

By all accounts von Neumann could drink a whole fifth and remain as brilliant and loquacious as ever. He once downed 16 martinis straight in a row. His friends were constantly covering for him and getting him out of drunken driving jams with the cops when he would run off the road in his car.

Those were different times back then though. It was perfectly legal to drink and drive (none of this open container nonsense we have today) it was only illegal to drive drunk. Of course back then the legal limit for blood alcohol was much higher too. When BAC levels became law in the 1930's they were generally .15%. You might recall early on in Alfred Hitchcock's movie North By Northwest Cary Grant is picked up by the Connecticut cops for driving after being made drunk by nefarious means, and while his credibility about the events is questioned he isn't in much legal trouble.

The damnable Mothers Against Drunk Driving changed all that as the awful wave of 1970's feminism wracked over our society.

Iamexpert said...

Why would the effect be different on volume than on weight? It's probably just that volume studies are more accurate since they use in vivo MRIs. By contrast measuring brain weight is messy considering it increases 9% postmortem. Anyway here's an article about the damaging effects of alcohol on intellect:

Iamexpert said...

Von Neumann probably had a large enough brain that he could afford to lose a little brain mass without jeopardizing his super genius status

Abruzzi_spur said...

there's nothing new for me in that article. the first article you linked to suggested that alcohol dehydrates the brain. but a 1.5% difference in mass may be described as "insignificant" by some researchers.

there are changes in performance on some tests, but general performance (iq) is not affected or the effect is not practically significant (with some rare exceptions). the parts of the brain most atrophied in heavy drinkers are the same areas used in tests of "fluid" intelligence. but again, the effect is generally not practically significant. and it may be that alcohol abuse is more common in those with a lopsided crystallized vs fluid profile. authors are often heavy drinkers.

wk is entirely due to the sequela of thiamine deficiency. it is seen in non-alcoholic beriberi also. cerebellar atrophy and the very rare Marchiafava-Bignami i would suggest are also due to sequela.

in one study in spain half of those who'd consumed an average of 3/4 of a fifth for decades had no detectable cerebellar atrophy. (the cerebellum is more sensitive to alcohol than other parts of the brain.) i for one would get very sick if i drank that much.

i do think that of all drugs alcohol is by far the most likely to cause irreversible brain damage, but at the same time, because etoh is a source of calories, nutritional deficiencies are more likely also. also hypertension and electrolyte imbalances are effected by drinking too much. both can damage the brain. excitotoxicity from alcohol withdrawal though is very rare.

gide07 said...

steve deletes all comments which he disagrees with.

typical chinaman.

CharlesRyder1921 said...

another person whose iq is higher than steve's.

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