[GenABEL-dev] Patch bug [#1322] polygenic would not run with a covariate which is non-informative

[pirastu at burlo.trieste.it]

Dear all,

Yurii and I have been working for quite some times on estimating the
regression coefficient of a SNP of a logistic regression from those of a
linear one.

Many of you may think we went mad but the reason for this is that there
are at this moment no methods for doing case control association in
isolated populations which take into account covariates and that gives you
Odds Ratio.
So our thought was to use linear mixed models and to convert the results
into its logistic counter part.

As far as p-values go we are already fine since this approach would be
analitically the same as using trend test.

After trying many different approaches we got probably to the bottom of
the problem with this last version of what we have called LiLog (Linear to
logistic).

I'm attaching the function and a simple simulation script which still does
not take into account kinship, but proves that the general procedure work.

We have pretty good results although they are slightly worse for big Odds
Ratio and standard errors are not completely precise as betas (but they
are quite precise anyways).
The other thing is that this method works only on SNPs and won't work on
other continuous variables as far as betas tranformation (but they can be
included in the model) because of the way we estimate the intercept.

Following the project phylosophy I'm submitting to all of you our work for
mainly two reason:

A. Maybe someone has a better idea (I'm not a statistician afterall)

B. Maybe some one can brake it so we can know what needs improving. From
this side the method starts performing a little worse when prevalence is
more than 50% but I think no one is going to use a study design like that.

Sorry if I was too long.

Best

Nicola


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