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[R-meta] Questions about the use of metaprop for the pooling of proportions

Dear Thiago,

So you have proportions of several mutually exclusive outcomes. Of 
course, these are dependent because the sum is always the total numbers 
of cases in the study (corresponding to 100% in that study). 
Nevertheless, I don't see any reason why not pooling each outcome 
separately using metaprop(). In fact, depending on the transformation, 
the resulting average proportion will not generally sum up to 100%, 
particularly not when using no transformation at all. This raises the 
question which transformation to choose. The default in metaprop() is 
random intercept logistic regression model with transformation logit.

I made an observation that I have to think about, and you may try this. 
If I use the default, the sum of the pooled percentages over all 
outcomes is indeed always 1 for the fixed effect estimate. I used code 
like this (here for 3 outcomes):

#### Random data ####
out1 <- rbinom(10,100,0.1)
out2 <- rbinom(10,100,0.5)
out3 <- rbinom(10,100,0.9)
n <- out1 + out2 + out3
m1 <- metaprop(out1, n)
m2 <- metaprop(out2, n)
m3 <- metaprop(out3, n)
plogis(m1$TE.fixed) + plogis(m2$TE.fixed) + plogis(m3$TE.fixed)

(plogis is the inverse of the logit transformation, often called 
"expit": plogis(x) = exp(x)/(1 + exp(x).) These seem to sum up to 1 for 
the fixed effect estimates, but not in general for the random effects 
estimates, only in case of small heterogeneity (which is rarely the case 
with proportions).

I am interested to hear whether this works with your data. (And I have 
to prove that this holds in general ...)

Best,

Gerta


Am 08.03.2022 um 13:42 schrieb Thiago Roza: