[GenABEL-dev] ProbABEL, chi^2, Wald and log-likelihood

[L.C. Karssen]

Dear all,

For the upcoming release of ProbABEL I've run into the following. In the
past (~ v 0.1-3) the output of ProbABEL had chi^2 values when doing Cox
regression. These were based on the likelihood ratio test:
 2 * (loglik -loglik_null) ~ chi_1^2
However, at some point, when having hamissing data was allowed in
ProbABEL, we ran into the problem that the null model had to be
recalculated for cases with missing genotype data. To do that 'simply'
for each SNP would be time consuming, so the chi^2 values were removed
from the output and replaced by the loglik values for the full model.
(At least, that's how I guess it went).

Now, I would like to get them back. This can be done in two ways:
1) calculate chi^2 as described above, with some smart way of only
recalculating the null model when a missing value occurs (this shouldn't
be often with today's imputed data).
2) simply calculate the chi^2 value through the Wald test. We have betas
and se_betas, so that is easy.

Many of you have more knowledge about statistics than I do, so,
statistically, are these methods equivalent? Or is one better (more
precise/unbiased) than the other?


Another question:
While testing the Wald-type implementation I ran into the following:
I would assume that for the 2df models (where we get beta_SNP_A1A2 and
beta_SNP_A1A1) the final chi^2 value would be the sum of the individual
Wald statistics, which would be distributed as chi_2^2 (so 2 df). Is
that correct? I ask this because if I compare them with the chi^2 values
from the LRT I get different values. In the example data set I get:
name      chi^2_Wald        chi^2_LRT
rs7247199 0.880949           0.452465
rs8102643 0.0116651          0.512709   <- here we have a missing value!
rs8102615 1.51434            0.754701
rs8105536 2.56337            1.33223
rs2312724 0.492364           0.256649

When running the additive model I do get (almost) the same results:
name       chi^2_Wald        chi^2_LRT
rs7247199  0.0101558          0.01012
rs8102643  0.353168           0.492147  <- here we have a missing value!
rs8102615  0.0181841          0.0180033
rs8105536  0.00222781         0.00222216
rs2312724  0.0412005          0.0401556

Shouldn't the chi_2 values be equal in both cases? FYI: the LRT chi^2
values are the same as those obtained with ProbABEL v0.1-3.


Any suggestions?
Thanks,

Lennart.

--
-----------------------------------------------------------------
L.C. Karssen
Utrecht
The Netherlands

lennart at karssen.org
http://blog.karssen.org

Stuur mij aub geen Word of Powerpoint bestanden!
Zie http://www.gnu.org/philosophy/no-word-attachments.nl.html
------------------------------------------------------------------

-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 230 bytes
Desc: OpenPGP digital signature
URL: <http://lists.r-forge.r-project.org/pipermail/genabel-devel/attachments/20130711/72c25c38/attachment.sig>