Meta analysis of paired counts

[rollanders]

I have data from 70 studies reporting number of observed events in two similar time periods, one before Covid and one during the Covid pandemic. The duration of the timeperiods and the size of the population were the events occurred varies between the reports but are corresponding for the paired data within each study. There is no information about the size of the population so cannot use incidence rates.

The hypothesis is that the number of events would be the same in these periods. How can I do the analysis? The problem is the denominator. Can I use the total number of events and estimate the RiskRatio as (percovid numbers/total numbers)/(precovid numbers/total numbers) ? Or simply use the Odds (percovid numbers)/(precovid numbers)? How can I estimate the CI for the estimates?

And how can I do it in Stata?

[Joseph Coveney]

How can I estimate the CI for the estimates?

Well, naively, if it's counts that you're interested in comparing, and if the exposures (time interval and population) are essentially the same between the two conditions within each study, then why not use a count regression model that takes study as the unit of analysis? Maybe something like the following?

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿinputÿbyteÿsidÿintÿ(count0ÿcount1)

ÿÿÿÿÿÿÿÿÿÿsidÿÿÿÿcount0ÿÿÿÿcount1
ÿÿ1.ÿ1ÿÿ100ÿ1000
ÿÿ2.ÿ2ÿ2000ÿ1800
ÿÿ3.ÿ3ÿ5000ÿ4000
ÿÿ4.ÿ4ÿÿÿ10ÿÿÿ15
ÿÿ5.ÿend

.ÿ
.ÿlabelÿvariableÿsidÿ"StudyÿID"

.ÿ
.ÿquietlyÿreshapeÿlongÿcount,ÿi(sid)ÿj(tim)

.ÿlabelÿvariableÿtimÿPeriod

.ÿlabelÿdefineÿPeriodsÿ0ÿ"BeforeÿCOVID"ÿ1ÿ"DuringÿCOVID"

.ÿlabelÿvaluesÿtimÿPeriods

.ÿ
.ÿtempnameÿCounts

.ÿtabulateÿsidÿtimÿ[fweight=count],ÿrowÿnokeyÿÿmatcell(`Counts')

ÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿPeriod
ÿÿStudyÿIDÿ|ÿBeforeÿCOÿÿDuringÿCOÿ|ÿÿÿÿÿTotal
-----------+----------------------+----------
ÿÿÿÿÿÿÿÿÿ1ÿ|ÿÿÿÿÿÿÿ100ÿÿÿÿÿÿ1,000ÿ|ÿÿÿÿÿ1,100ÿ
ÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿ9.09ÿÿÿÿÿÿ90.91ÿ|ÿÿÿÿ100.00ÿ
-----------+----------------------+----------
ÿÿÿÿÿÿÿÿÿ2ÿ|ÿÿÿÿÿ2,000ÿÿÿÿÿÿ1,800ÿ|ÿÿÿÿÿ3,800ÿ
ÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿ52.63ÿÿÿÿÿÿ47.37ÿ|ÿÿÿÿ100.00ÿ
-----------+----------------------+----------
ÿÿÿÿÿÿÿÿÿ3ÿ|ÿÿÿÿÿ5,000ÿÿÿÿÿÿ4,000ÿ|ÿÿÿÿÿ9,000ÿ
ÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿ55.56ÿÿÿÿÿÿ44.44ÿ|ÿÿÿÿ100.00ÿ
-----------+----------------------+----------
ÿÿÿÿÿÿÿÿÿ4ÿ|ÿÿÿÿÿÿÿÿ10ÿÿÿÿÿÿÿÿÿ15ÿ|ÿÿÿÿÿÿÿÿ25ÿ
ÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿ40.00ÿÿÿÿÿÿ60.00ÿ|ÿÿÿÿ100.00ÿ
-----------+----------------------+----------
ÿÿÿÿÿTotalÿ|ÿÿÿÿÿ7,110ÿÿÿÿÿÿ6,815ÿ|ÿÿÿÿ13,925ÿ
ÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿ51.06ÿÿÿÿÿÿ48.94ÿ|ÿÿÿÿ100.00ÿ

.ÿmata:ÿst_matrix(st_local("Counts"),ÿcolsum(st_matrix(st_local("Counts"))))

.ÿdisplayÿinÿsmclÿasÿtextÿ%09.7fÿ`Counts'[1,ÿ2]ÿ/ÿ`Counts'[1,ÿ1]
0.9585091

.ÿ
.ÿxtpoissonÿcountÿi.tim,ÿi(sid)ÿfeÿirrÿnolog

Conditionalÿfixed-effectsÿPoissonÿregressionÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿ=ÿÿÿÿÿÿ8
Groupÿvariable:ÿsidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿ=ÿÿÿÿÿÿ4

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿ2
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿ2.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿ2

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿ=ÿÿÿ6.25
Logÿlikelihoodÿ=ÿ-499.79462ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿ=ÿ0.0124

-------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿcountÿ|ÿÿÿÿÿÿÿÿIRRÿÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
--------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿtimÿ|
DuringÿCOVIDÿÿ|ÿÿÿ.9585091ÿÿÿÿ.016249ÿÿÿÿ-2.50ÿÿÿ0.012ÿÿÿÿÿÿ.927185ÿÿÿÿ.9908915
-------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[rollanders]

Thanks a lot.
Now I want to move one step further. The studies can be grouped according to some characteristics - three agegroups, singlecenter/multicenter, emergent/delayed, and maybe more. How can I include these variables into the analysis and determine their impact? I can of course do subgrups analysis but would also like to do a multivariable analysis.

In meta-analysis it is convention to graph the estimates for each study and their confidence interval. Can this be done?