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

[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,
>
> Thank you for your reply!
> 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,
>>
>> I read this thread and I still am not clear about the nature of the 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,
>>
>> Thank you for your reply!
>>
>> 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 answered
>> 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
>>
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>> --
>> Michael
>> http://www.dewey.myzen.co.uk/home.html
>>
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>> --
>>
>> 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