What to use for ti in back-transforming summary statistics from F-T double square-root transformation in 'metafor'

Dear Chunyan,

One possibility would be to use the harmonic mean of the person-time at risk values. You will have to do this manually though at the moment. Here is an example:

### let's just use the treatment group data from dat.warfarin
data(dat.warfarin)
dat <- escalc(xi=x1i, ti=t1i, measure="IRFT", data=dat.warfarin, append=TRUE)
dat

### check if back-transformation of individual IRFT values works
transf.iirft(dat$yi, ti=dat$t1i)
escalc(xi=x1i, ti=t1i, measure="IR", data=dat.warfarin)$yi

### random-effects models
res <- rma(yi, vi, data=dat)
res

### harmonic mean of the ti's
ti.hm <- 1/(mean(1/dat$t1i))

### back-transformation using the harmonic mean
transf.iirft(res$b, ti=ti.hm)
transf.iirft(res$ci.lb, ti=ti.hm)
transf.iirft(res$ci.ub, ti=ti.hm)

Best,
Wolfgang

--
Wolfgang Viechtbauer, Ph.D., Statistician
Department of Psychiatry and Psychology
School for Mental Health and Neuroscience
Faculty of Health, Medicine, and Life Sciences
Maastricht University, P.O. Box 616 (VIJV1)
6200 MD Maastricht, The Netherlands
+31 (43) 388-4170 | http://www.wvbauer.com

Hi Dr. Viechtbauer,

I'm doing meta-analysis using your package 'metafor'. I used the 'IRFT' to transform the incident rate. But when I tried to back-transform the summary estimates from function rma, I don't know what's the appropriate ti to feed in function transf.iirft. I searched and found your post about using harmonic mean for ni  to back-transform the double arcsine  transformation. I'm hoping I can get your help on ti too.

Thanks.


Chunyan Liu

513-636-9763
Biostatistician II
Department of Biostatistics and Epidemiology
Cincinnati Children's Hospital Medical Center