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

Dr. Gerta Rücker ruecker @end|ng |rom |mb|@un|-|re|burg@de
Tue Mar 8 20:29:47 CET 2022

```Dear Thiago,

I found that, apparently, the result presented by the common effect
model (=fixed effect model) is simply the sum of all entries/events over
all studies, divided by the total sample size (summed up over all
studies). You see this by typing the following after the code in my last
e-mail:

all.equal(sum(out1)/sum(n), plogis(m1\$TE.fixed))
all.equal(sum(out2)/sum(n), plogis(m2\$TE.fixed))
all.equal(sum(out3)/sum(n), plogis(m3\$TE.fixed))

This means that the method is equivalent to considering the data as a
contingency table where the rows correspond to the studies and the
columns to the outcomes. The meta-analytic result corresponds to the
percentages in the column sums, and of course these add to 100%. In fact
this is the easiest way to deal with this kind of data.

@Guido, @Wolfgang: I couldn't find thisinformation on the metaprop or
the rma.glmm help pages. Do you see any problem with interpreting
Thiago's data as a contingency table? I think that, by contrast to
pairwise comparison data, confounding/ecological bias is not an issue here.

Best,

Gerta

Am 08.03.2022 um 19:30 schrieb Dr. Gerta Rücker:
> 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:
>> Dear Gerta,
>>
>> In my systematic review, I have several cross-sectional original
>> studies. In each one of these original studies I have a sample size (n
>> for the total number of suicide cases included in the study), and this
>> number is also classified according to the suicide method (for
>> instance, if n is 100 for the total number of cases, 80% or 80 cases
>> died due to hanging, 10 or 10% died due to firearms, 5 or 5% died due
>> to drug overdose, 3 or 3% died due to pesticides, and so on). The same
>> example applies to other variables such as biological sex, race,
>> suicide site, etc.
>> The idea of my analysis is to pool the proportions of several key
>> characteristics, including suicide methods, across all included
>> studies, so I can report the proportions with 95%CI in the paper.
>> I tried using "metaprop" for the pooling of the proportions of suicide
>> methods, however, when I summed up the pooled proportions, when using
>> the "Inverse" method the sum would give more than 100%, and when using
>> the "GLMM" method it would give less than 100%.
>>
>> That is why I was wondering if it was possible to pool those
>> proportions using "metaprop". If yes, is it OK for the summed pooled
>> proportions to be different than 100%?
>>
>> Thank you,
>>
>> Thiago
>>
>> Em ter., 8 de mar. de 2022 às 09:27, Dr. Gerta Rücker
>> <ruecker using imbi.uni-freiburg.de> escreveu:
>>> Dear Thiago, dear Michael,
>>>
>>> data. Are these really compositional data, or simple proportions?
>>> The difference is:
>>>
>>> Compositional data are characterized by lacking a denominator (no
>>> "n", no sample size). For each study, you have only percentages that
>>> add to 100%. Such data occur in microbioma research (percentages of
>>> species in the microbioma).
>>> By contrast, proportions are given as r (number of events) and n
>>> (sample size, i.e., number of persons/patients/trials/whatever), or
>>> as percentages and n.
>>>
>>> If you have proportions, you may use metaprop. If you have
>>> compositional data, as Michael supposed, you cannot.
>>>
>>> Best,
>>>
>>> Gerta
>>>
>>> Am 08.03.2022 um 12:34 schrieb Thiago Roza:
>>>
>>> Dear Michael,
>>>
>>>
>>> Do you think it would be possible to generate pooled proportions for
>>> at least the most commonly reported suicide method in this case? (I
>>> would organize my dataset in the following format: "suicide by
>>> hanging" vs "other method of suicide", only two categories).
>>>
>>> Thank you,
>>>
>>> Thiago
>>>
>>> Em seg., 7 de mar. de 2022 às 13:40, Michael Dewey
>>> <lists using dewey.myzen.co.uk> escreveu:
>>>
>>> Dear Thiago
>>>
>>> What you have is compositional data which might prove a useful search
>>> term. A common way to analyse such data is by taking the ratios of the
>>> components to a reference one and then taking logs. However that is
>>> about the sum total of my knowledge of compositional data analysis and
>>> as far as I know there is no extant R package which deals with it.
>>> Others on the list may have better ideas.
>>>
>>> For future reference if you post on CrossValidated it is best to put a
>>> link in each of them so people can check if it has already been
>>> in the other place.
>>>
>>> Michael
>>>
>>> On 06/03/2022 16:36, Thiago Roza wrote:
>>>
>>> Dear all,
>>>
>>> I am conducting a meta-analysis about characteristics of suicide
>>> deaths in post-mortem studies. My aim is to describe pooled
>>> proportions of key characteristics (biological sex, suicide site,
>>> race, marital status, suicide method, the proportion of substance use
>>> near death, proportion of psychiatric diagnosis prior to death, etc)
>>> across the included studies. Initially, I thought that "metaprop" from
>>> the package "meta" would be enough to pool all these proportions
>>> across included studies. Nevertheless, some of these variables have
>>> more than one category (i.e. suicide method has more than 10
>>> categories: such as hanging, firearm, poisoning, etc), and the pooling
>>> of the proportion of each suicide method separately produces results
>>> which when summed up give more than 100% for the summed proportion of
>>> all suicide methods. Therefore, my first question is: is it possible
>>> to pool all those proportions using "metaprop"? If yes, could anyone
>>> give an example about the coding for the pooling of proportions in the
>>> case of suicide methods? If not, is there any other package that would
>>> allow me to pool the aggregate proportion of suicide methods?
>>>
>>> Thank you,
>>>
>>> Thiago Roza
>>>
>>> _______________________________________________
>>> R-sig-meta-analysis mailing list
>>> R-sig-meta-analysis using r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>>
>>> --
>>> Michael
>>> http://www.dewey.myzen.co.uk/home.html
>>>
>>> _______________________________________________
>>> R-sig-meta-analysis mailing list
>>> R-sig-meta-analysis using r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>>
>>> --
>>>
>>> Dr. rer. nat. Gerta Rücker, Dipl.-Math.
>>>
>>> Guest Scientist
>>> Institute of Medical Biometry and Statistics,
>>> Faculty of Medicine and Medical Center - University of Freiburg
>>>
>>> Zinkmattenstr. 6a, D-79108 Freiburg, Germany
>>>
>>> Mail:     ruecker using imbi.uni-freiburg.de
>>> Homepage:
>>> https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker
>
--

Dr. rer. nat. Gerta Rücker, Dipl.-Math.

Guest Scientist
Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center - University of Freiburg

Zinkmattenstr. 6a, D-79108 Freiburg, Germany

Mail:     ruecker using imbi.uni-freiburg.de
Homepage: https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker

```