<div>In principle score, Wald, and LRT have to give similar answers in non-extreme cases. LRT is theoretically the most superior method (if underlying model assumptions, e.g. normality, hold). Score / Wald are the approximations to LRT derived at the point of null/alternative, respectively. They actually ARE derived from quadratic approximations of the likleihood function derived at these points :) </div>
<div><br></div><div>As for practical advantages/disadvantages of these, may be someone else could comment. I remember there are good/bad sides in both...</div><div><br></div>Re: Wald on 2df - you can not add Walds from individual beta/se, you need to take the covariance into account. For full treatment of the problem, see<div>
<br></div><div><a href="http://www.math.chalmers.se/~wermuth/pdfs/86-95/CoxWer90_An_approximation_to_ML.pdf">http://www.math.chalmers.se/~wermuth/pdfs/86-95/CoxWer90_An_approximation_to_ML.pdf</a></div><div><br></div><div>
For a simple variant, I think our ProbABEL paper does give some details on score/Wald. </div><div><br></div><div>Would that be good idea to put this discussion topic to our "Journal club"? - these are kind of topics of general interest irrespective of GenABEL.</div>
<div><br></div><div>best,</div><div>Yurii<br><br><div class="gmail_quote">On Thu, Jul 11, 2013 at 11:56 PM, L.C. Karssen <span dir="ltr"><<a href="mailto:lennart@karssen.org" target="_blank">lennart@karssen.org</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear all,<br>
<br>
For the upcoming release of ProbABEL I've run into the following. In the<br>
past (~ v 0.1-3) the output of ProbABEL had chi^2 values when doing Cox<br>
regression. These were based on the likelihood ratio test:<br>
2 * (loglik -loglik_null) ~ chi_1^2<br>
However, at some point, when having hamissing data was allowed in<br>
ProbABEL, we ran into the problem that the null model had to be<br>
recalculated for cases with missing genotype data. To do that 'simply'<br>
for each SNP would be time consuming, so the chi^2 values were removed<br>
from the output and replaced by the loglik values for the full model.<br>
(At least, that's how I guess it went).<br>
<br>
Now, I would like to get them back. This can be done in two ways:<br>
1) calculate chi^2 as described above, with some smart way of only<br>
recalculating the null model when a missing value occurs (this shouldn't<br>
be often with today's imputed data).<br>
2) simply calculate the chi^2 value through the Wald test. We have betas<br>
and se_betas, so that is easy.<br>
<br>
Many of you have more knowledge about statistics than I do, so,<br>
statistically, are these methods equivalent? Or is one better (more<br>
precise/unbiased) than the other?<br>
<br>
<br>
Another question:<br>
While testing the Wald-type implementation I ran into the following:<br>
I would assume that for the 2df models (where we get beta_SNP_A1A2 and<br>
beta_SNP_A1A1) the final chi^2 value would be the sum of the individual<br>
Wald statistics, which would be distributed as chi_2^2 (so 2 df). Is<br>
that correct? I ask this because if I compare them with the chi^2 values<br>
from the LRT I get different values. In the example data set I get:<br>
name chi^2_Wald chi^2_LRT<br>
rs7247199 0.880949 0.452465<br>
rs8102643 0.0116651 0.512709 <- here we have a missing value!<br>
rs8102615 1.51434 0.754701<br>
rs8105536 2.56337 1.33223<br>
rs2312724 0.492364 0.256649<br>
<br>
When running the additive model I do get (almost) the same results:<br>
name chi^2_Wald chi^2_LRT<br>
rs7247199 0.0101558 0.01012<br>
rs8102643 0.353168 0.492147 <- here we have a missing value!<br>
rs8102615 0.0181841 0.0180033<br>
rs8105536 0.00222781 0.00222216<br>
rs2312724 0.0412005 0.0401556<br>
<br>
Shouldn't the chi_2 values be equal in both cases? FYI: the LRT chi^2<br>
values are the same as those obtained with ProbABEL v0.1-3.<br>
<br>
<br>
Any suggestions?<br>
Thanks,<br>
<br>
Lennart.<br>
<br>
--<br>
-----------------------------------------------------------------<br>
L.C. Karssen<br>
Utrecht<br>
The Netherlands<br>
<br>
<a href="mailto:lennart@karssen.org">lennart@karssen.org</a><br>
<a href="http://blog.karssen.org" target="_blank">http://blog.karssen.org</a><br>
<br>
Stuur mij aub geen Word of Powerpoint bestanden!<br>
Zie <a href="http://www.gnu.org/philosophy/no-word-attachments.nl.html" target="_blank">http://www.gnu.org/philosophy/no-word-attachments.nl.html</a><br>
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