On Sun, Jul 14, 2013 at 10:00 PM, L.C. Karssen <span dir="ltr"><<a href="mailto:lennart@karssen.org" target="_blank">lennart@karssen.org</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Thanks for the explanation Yurii.<br>
<div class="im"><br>
On 12-07-13 01:41, Yurii Aulchenko wrote:<br>
> In principle score, Wald, and LRT have to give similar answers in<br>
> non-extreme cases. LRT is theoretically the most superior method (if<br>
> underlying model assumptions, e.g. normality, hold). Score / Wald are<br>
> the approximations to LRT derived at the point of null/alternative,<br>
> respectively. They actually ARE derived from quadratic approximations of<br>
> the likleihood function derived at these points :)<br>
<br>
</div>Interesting! I didn't know that.<br></blockquote><div><br></div><div>Yep, this is quite interesting. I think David Clayton's book (Statistical Models in Epi?) gives very simple and clear explanation of how you get to the score and Wald from LRT - very nice reading. </div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div class="im"><br>
><br>
> As for practical advantages/disadvantages of these, may be someone else<br>
> could comment. I remember there are good/bad sides in both...<br>
><br>
> Re: Wald on 2df - you can not add Walds from individual beta/se, you<br>
> need to take the covariance into account.<br>
<br>
</div>I see, I guess adding them is only allowed when the two are independent<br>
(hence no covariance). Right?<br></blockquote><div><br></div><div>True. And zero-covariance is definitely not the case with the 2df test :)</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div class="im"><br>
> For full treatment of the<br>
> problem, see<br>
><br>
> <a href="http://www.math.chalmers.se/~wermuth/pdfs/86-95/CoxWer90_An_approximation_to_ML.pdf" target="_blank">http://www.math.chalmers.se/~wermuth/pdfs/86-95/CoxWer90_An_approximation_to_ML.pdf</a><br>
><br>
<br>
</div>Thanks. Not an easy piece to read...<br></blockquote><div><br></div><div>It is not, but at the end it is simple (see the ProbABEL paper)... unfortunately this is one of these "simple" things which are "so simple" after you have figured them out - and after some time you only remember that they were "simple", but not exact way how it works (this is why I refer you to papers). </div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div class="im"><br>
> For a simple variant, I think our ProbABEL paper does give some details<br>
> on score/Wald.<br>
><br>
> Would that be good idea to put this discussion topic to our "Journal<br>
> club"? - these are kind of topics of general interest irrespective of<br>
> GenABEL.<br>
><br>
<br>
</div>Good idea. I'll see if I can find the time to start the discussion there.<br>
<br>
<br>
Best,<br>
<br>
Lennart.<br>
<div class="im"><br>
<br>
> best,<br>
> Yurii<br>
><br>
> On Thu, Jul 11, 2013 at 11:56 PM, L.C. Karssen <<a href="mailto:lennart@karssen.org">lennart@karssen.org</a><br>
</div><div><div class="h5">> <mailto:<a href="mailto:lennart@karssen.org">lennart@karssen.org</a>>> wrote:<br>
><br>
> 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>
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> --<br>
> -----------------------------------------------------<br>
> Yurii S. Aulchenko<br>
><br>
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<div class="HOEnZb"><div class="h5"><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>
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</div></div></blockquote></div><br><br clear="all"><div><br></div>-- <br>-----------------------------------------------------<br>Yurii S. Aulchenko<br><div><br></div><div>[ <a href="http://nl.linkedin.com/in/yuriiaulchenko" target="_blank">LinkedIn</a> ] [ <a href="http://twitter.com/YuriiAulchenko" target="_blank">Twitter</a> ] [ <a href="http://yurii-aulchenko.blogspot.nl/" target="_blank">Blog</a> ]</div>