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[R-meta] Include a study with point estimate and 95% CI into a meta-anlaysis for incidence rates

5 messages · Thao Tran, Wolfgang Viechtbauer

Thao Tran
# 
Dear,
I want to perform a meta-analysis for some studies with the interest lies
in incidence rates.
Many of them, the data on the number of positive cases and person-time are
available.
However, I have one study where the authors only reported point estimate
with its 95%CI.
How do I include this study into the meta-analysis using the *metafor *
package?

Here is an example code.


load("dat2C.RData")
datx <- subset(dat2C, point == 1)
estimS <- escalc(measure="IRLN", xi=Num, ti=py2/1000,
                 data=datx, slab=paste(Cite))
summary(estimS, transf=exp)[8:13]
resS <- rma( yi, vi, data=estimS, method="ML")
hetS <- cbind(round( resS$QE,1),round( resS$QEp,2), round( resS$I2))
hetS # 96%

## However, how to include this study where point estimate (Inc)
## and 95% CI (Incll = lower bound, Incul = upper bound) were reported
xx <- subset(dat2C, point==0); dim(xx)


I look forward to hearing from you.
Regards,
Thao
Wolfgang Viechtbauer
# 
Dear Thao,

You could try to back-calculate the number of cases and total person time from the reported results. Do you have any information how the CI (16.2 to 23.6) was computed? It is not symmetric around the point estimate (19.6), so it might have been computed based on the log incidence rate or a Poisson regression model using a log link. But there are other ways of computing such a CI, for example using the square-root transformed rate or using the Freeman-Tukey transformation. So, any indication how the authors actually computed the CI would be useful.

Best,
Wolfgang
Thao Tran
# 
Hi Wolfgang,
I looked back to the paper, there they used Poisson regression with
analytic weights, offsets, and robust variance estimation to implement the
extrapolation and standardization procedures for estimating seasonal
incidence and 95% confidence intervals (CIs).
I will need to lookup more. But my guess is it is not straightforward to
trace back these two pieces of information.

Best,

On Mon, Jun 15, 2020 at 4:44 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Wolfgang Viechtbauer
    

    

      
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Dear Thao,

Could you please properly register yourself on this mailing list? This was now the 4th post of yours that had to manually approved by the mailing list admins and this is creating extra work for us.

If the authors used Poisson regression (assuming a log link, which is the default), then this would be identical to computing the CI based on the log(rate) and then exponentiating. The use of robust variance estimation though implies that the SE used for constructing the CI is not the one we would construct based on theory, so this introduces a bit of an inconsistency. Ignoring this for now, the SE of a log(rate) is sqrt(1/numer_of_cases). We know the rate per 1000py (19.6) and the corresponding CI (16.2 to 23.6), so if we assume 5.5 * 1000py, we then get roughly the same CI:

round(exp(log(19.6) + c(-1,1) * qnorm(.975) * sqrt(1/(19.6*5.5))), 2)

(this gives 16.23 to 23.67 -- you can play around with the 5.5 a bit more to see if you can find a better approximation).

So, this implies 19.6 * 5.5 = 107.8 =~ 108 cases in 5500 person-years.

I don't know if these numbers are realistic based on how the study was conducted (that's a rather high number of PYs compared to the other studies), but this is what the CI implies.

Best,
Wolfgang

            

      
      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Thao Tran
    

    

      
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Hi Wolfgang,
I believe that I am now properly registered to the mailing list.
Thanks for your clarification. It helps a lot.

Have a good day.
Thao

On Tue, Jun 16, 2020 at 11:38 AM Viechtbauer, Wolfgang (SP) <

        
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote: