[GenABEL-dev] faster polygenic

[Yurii Aulchenko]

Dear All,

Some of you may know, that MixABEL::FastMixedModel by William Astle
first does polygenic model estimation (e.g. h2-estimate is given by
FastMixedModel(...)$null.herit), though it is build 'within' GWA and
it is not yet possible to get hold on all necessary 'null'
heritability estimates.

Still, given the differences we observed between old 'polygenic' and
Xia's 'polygenic_hglm', I though that trying MixABEL::FastMixedModel
may tell us more on which procedure may be more 'correct'.

I attach the test-script FYI. Results are quite interesting.

First, MixABEL::FastMixedModel (fmm for short) seems to work even
faster than polygenic_hglm, and achieved speed-up is x100, with range
x50-x150 (vs. polygenic_hglm mean speed-up of x30, with range from x10
to x70). Of cause, this numbers are preliminary -- e.g. polygenic_hglm
may gain speed because I did some parts in very 'naive' way, while
MixABEL::FastMixedModel does not report a number of things, and
computing these may take extra time. Nevertheless, I think when
William takes null heritability apart from the GWAS of
MixABEL::FastMixedModel, we have another great alternative to the old
'polygenic'!

Anyways, I have a very good feeling about both polygenic_hglm and
polygenic_fmm -- these are going to provide a real speed-up and a very
important solution -- at the moment with few thousands of people
'polygenic' may be running for weeks, and will run in few hours using
either polygenic_hglm or fmm-based solution!

Second, the squared correlation of h2-estimates was higher between
MixABEL::FastMixedModel and old-polygenic (0.999), compared to
correlation between polygenic_hglm and old-polygenic (0.962), which I
take as a sign that the problem of the 'curved' relation between
h2-estimates is in polygenic_hglm. Also Lambda-graphs (see my previous
e-mail on the topic) were consistent (single line) between
old-polygenic+mmscore and MixABEL::FastMixedModel (see attached
graphs), though there was some offset from a line with a=0 and b=1,
meaning that MixABEL::FastMixedModel h2's are consistently lower than
'polygenic' h2's. Different estimates of h2 (plots a,b) translated to
consistent differences in Lambdas (c). I have a feeling that old
polygenic+mmscore does a better job (in terms of Lambda) than
MixABEL::FastMixedModel, cause Lambdas from MixABEL::FastMixedModel
was significantly over 1 (p-value 1e-11) while from old polygenic, the
results were conservative, but less significant (p=0.0004). I presume,
slight conservativity of mmscore is expected as this is a score test.

William -- thumbs up! -- we look very much forward for the next
version of MixABEL with 'null' heritability estimation procedure
separated from the GWAS part. My results suggest that you may be
slightly under-estimating the heritability in fmm.

best wishes,
Yurii

On Fri, Feb 25, 2011 at 10:37 PM, Yurii Aulchenko
<yurii.aulchenko at gmail.com> wrote:
> Thanks, Xia!
>
> Did what you suggested and just submitted the code to the repository
>
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