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[R-meta] Need to specify meta analysis weights

5 messages · Emanuele F. Osimo, Gerta Ruecker, Wolfgang Viechtbauer

Original
Emanuele F. Osimo
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Dear all,
I am conducting a random-effects meta-analysis of 4 longitudinal studies
measuring a blood inflammatory marker earlier on in life, and an unrelated
outcome (measured in an interview) years later.
The studies are not uniform in N (one is about 80k people, the 2 smallest
are about 2k people) and in time to follow up (ranging from 8 to 21 years).
I have odds ratios  and 95% confidence intervals for the outcome based on
cut-offs of the baseline marker (e.g. outcome for inflamed vs outcome for
non-inflamed).

I have 2 questions for you:
1- if I use weighting by N, as recommended by Cochrane, I am basically
reporting the findings of the larger study, which gets 88% of the weight.
The larger study is possibly qualitatively less good than the 2 smallest
studies. What do you suggest to use for weighting? Is there any compound
weighting methods that takes into account, say, study quality, N and
inverse variance?
2- time to follow-up: even if I am not measuring a difference in outcome
over time, but just the risk of an outcome after an exposure, do I need to
adjust for time to follow-up? And how?

Many thanks in advance for your time and thoughts on this.

Best wishes,

Emanuele
Gerta Ruecker
# 
Dear Emanuele,

To your first question: First, Cochrane doesn't recommend weighting by 
N. Cochrane (and others) recommend weighting by inverse variance, and in 
the case of a binary outcome (you mention odds ratios) it is even better 
to use a generalised linear mixed model (GLMM), e.g., logistic 
regression. Also random effect models are available. A random effect 
model is suitable to mitigate the effect of the largest study, or to 
upweight smaller studies, which seems to be desired in your case.

To the second question: One possibility would be meta-regression with 
length of follow-up as a covariate. Is length of follow-up a study-level 
covariate, or an individual-level covariate? There is no problem in the 
first case, but it may be problematic in the second case, when each 
individual has a different length of follow-up.

Best,

Gerta

Am 04.09.2020 um 12:22 schrieb Emanuele F. Osimo:

  
    

      
      
    

  


  


      

    

    
3 days later

    

      
      

        


  

        

      Emanuele F. Osimo
    

    

      
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Dear Gerta,

many thanks for your reply.
A couple of follow-up questions:

1) does using inverse variance to weight studies hold when only few studies
are included, and one is much bigger than the others?
2) why is rma.glmm better than rma.uni which I have used in R to apply
random effect models for ORs? Is there a way to apply rma.glmm using
log(OR) and the standard error of the OR (which is what I have available)
instead of the contingency tables it requires?

Many thanks again for your help.

Best wishes,

Emanuele


On Fri, 4 Sep 2020 at 11:55, Gerta Ruecker <ruecker at imbi.uni-freiburg.de>
wrote:

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

  
  


  


      

    

    

      
      

        


  

        

      Gerta Ruecker
    

    

      
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Dear Emanuele,

My answers see inline below.

Am 07.09.2020 um 15:38 schrieb Emanuele F. Osimo:

            

      
      
      
    

        
Inverse variance weighting is relatively uncontroversial if data are 
continuous and the fixed (more precise: the common) effect model is 
used. (In parentheses: There have been a few controversies with respect 
to the random effects model, but the majority of statisticians would 
recommend it.) For binary data, the inverse variance method had also 
been recommended for a long time, but most of us become more and more 
aware that the two-stage methods are not optimal, particularly in case 
of rare events.

If one study is much bigger than the others, the philosophy of the 
common effect model says that the large study provides the most precise 
estimate, and consequently dominates the result.

The philosophy of the random effects model says that each study somehow 
has it own rights and therefore gives a little more weight to the 
smaller studies. But if there are only few of them, the problem is that 
the heterogeneity variance becomes difficult to estimate.

            

      
      
      
    

        
As I am not very used to metafor (I mostly use meta), there are others 
more qualified to answer this. If I understand this correctly, rma.glmm 
uses a one-stage approach which avoids the problems with two-stage 
approaches mentioned above.

I am not sure whether you make a distinction between OR and logOR? There 
is no difference between the models with respect to this - they all 
model the log of the OR, and the standard errors you have most probably 
also refer to the log OR.

Best,

Gerta

            

      
      
      
    

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Wolfgang Viechtbauer
    

    

      
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Just chiming in briefly here: The answer to 2) is No. If you only have the log odds ratios and corresponding standard errors, then you cannot use rma.glmm(). To fit logistic regression models, you need the 2x2 table counts.

Best,
Wolfgang