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[R-meta] Intuitive explanation of BLUPs

4 messages · Emily Russell, Michael Dewey, Dr. Gerta Rücker

Emily Russell
# 
Dear All

Sorry if this question is too simple, but could anyone give me an intuitive explanation of best linear unbiased prediction (BLUP) applied to meta-analysis?  Everything I can find seems to refer to genes, and I can't quite make the connection to meta-analysis.

Thanks

Emily
Dr. Gerta Rücker
# 
Hi Emily,

What you observe in a meta-analysis are the random means (or whatever effect measure is used) of the chosen endpoint in each study. If your model is the random effects model, this means that these observations randomly deviate in one or the other direction from the true means in each study. The random effects model provides an estimate of tau^2, the variance of the means between the studies. Moreover, using the tau estimate, it allows estimating the true expectations for each study. These are called BLUPs.

Best,
Gerta


-----Urspr?ngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> Im Auftrag von Emily Russell via R-sig-meta-analysis
Gesendet: Donnerstag, 15. Februar 2024 09:35
An: r-sig-meta-analysis at r-project.org
Cc: Emily Russell <emilyrussell99 at outlook.com>
Betreff: [R-meta] Intuitive explanation of BLUPs

Dear All

Sorry if this question is too simple, but could anyone give me an intuitive explanation of best linear unbiased prediction (BLUP) applied to meta-analysis?  Everything I can find seems to refer to genes, and I can't quite make the connection to meta-analysis.

Thanks

Emily


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Michael Dewey
# 
Dear Emily

It is always hard to give intuitive explanations as our intuitions 
differ so much. That seems pusilanimous though, so here goes.

Suppose you are interested in getting the best estimate for one of the 
studies in your meta-analysis. If there is no heterogeneity then the 
best estimate is the overall mean, the summary estimate. Suppose there 
is substantial heterogeneity then you need an estimate somewhere between 
the overall mean and the actual observed value in that study because you 
know there is much between study variation. That estimate is the BLUP.

Michael
On 15/02/2024 08:35, Emily Russell via R-sig-meta-analysis wrote:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Dr. Gerta Rücker
    

    

      
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pusillanimous - a great word to know, thank you, Michael :-)



-----Urspr?ngliche Nachricht-----
Von: Michael Dewey via R-sig-meta-analysis <r-sig-meta-analysis at r-project.org> 
Gesendet: Donnerstag, 15. Februar 2024 14:39
An: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Cc: Michael Dewey <lists at dewey.myzen.co.uk>; Emily Russell <emilyrussell99 at outlook.com>
Betreff: Re: [R-meta] Intuitive explanation of BLUPs

Dear Emily

It is always hard to give intuitive explanations as our intuitions 
differ so much. That seems pusilanimous though, so here goes.

Suppose you are interested in getting the best estimate for one of the 
studies in your meta-analysis. If there is no heterogeneity then the 
best estimate is the overall mean, the summary estimate. Suppose there 
is substantial heterogeneity then you need an estimate somewhere between 
the overall mean and the actual observed value in that study because you 
know there is much between study variation. That estimate is the BLUP.

Michael

        
On 15/02/2024 08:35, Emily Russell via R-sig-meta-analysis wrote: