Simulation using incidence risk ratio

[Chang Xu]

Hi everyone,

I'm trying to simulate aggregated binary data for meta-analysis, which consider the follow-up in both groups as the effect modifier. The Poisson mixed model will be used to see the performance. I use the following code to simulate, by setting fixed irr value and varied sample size parameters (n1, n2), varied incidence of control group (p2), varied follow-up parameter; but I found in few cases, the estimated incidence (p1) in intervention group would exceed 1. Can I just remove those exceed 1? Or is there any better data generation mechanism? Thanks

clear
***set random numbers of obs
set obs 1
gen agen=round(runiform(40,100))
set obs `=agen'

***simulate
gen studyid=_n

***********************************************************************************************************
**** n1 is the treatment arm and n2 is the control arm*****
gen n1vsn2=runiform(0.84, 2.04)
gen logn2 = rnormal(3.353662,0.99993511)
gen n2=round(exp(logn2),1)
replace n2=25 if n2==0
gen n1=round(n2*n1vsn2,1)

***p2 is the incidence in control arm***
gen p2 = runiform(0.01,0.05)
gen r2`s' = rbinomial(n2, p2)

****irr refers to incidence risk ratio
gen tau = 0.2
gen logirr = rnormal(log(0.8), tau^2)

***t1 and t2 refer to follow up time in two arms
gen t1 = runiform(1,500)
gen t2 = runiform(1,500)

***using above parameters to generate p1 and r1
gen p1 = exp(logirr)*p2/(n2*t2)*(n1*t1)
gen r1`s' = round(p1*n1)
drop if p1 > 1

[Maarten Buis]

That is the limitation of using IRRs for binary data: it does not guarantee that the upper bound of 1 is respected. If the event under study is rare, then you are probably fine, but in your case that is apparently not the case. In that case you can use odds ratios and logistic regression.

[Chang Xu]

Thanks Buis.

Yes, this is a big problem when we using RR/RD/IRR as true effect. For OR, it can avoid such a problem, but seems cannot use OR to define a true IRR?

Kind regards
Chang