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

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

-----Original Message-----
From: Thao Tran [mailto:thaobrawn at gmail.com]
Sent: Tuesday, 16 June, 2020 10:36
To: Viechtbauer, Wolfgang (SP)
Cc: r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Include a study with point estimate and 95% CI into

a

meta-anlaysis for incidence rates

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:
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

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-

project.org]

On Behalf Of Thao Tran
Sent: Monday, 15 June, 2020 16:25
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] Include a study with point estimate and 95% CI into a
meta-anlaysis for incidence rates

ATTACHMENT(S) REMOVED: dat2C.RData

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

--
Tr?n Mai Ph??ng Th?o
Master Student - Master of Statistics
Hasselt University - Belgium.
Email: Thaobrawn at gmail.com / maiphuongthao.tran at student.uhasselt.be
Phone number: + 84 979 397 410+ 84 979 397 410 / 0032 488 0358430032 488
035843