[R-meta] Meta-analysis of proportion differences (certain cells frequency)

[Viechtbauer, Wolfgang (NP)]

Dear Jakub,

Proportions like you are describing can be thought of as so-called 'compositional data' (i.e., data that describe to what extent some whole is composed of various subcomponents):

https://en.wikipedia.org/wiki/Compositional_data

For example, one might know that in a given person, 52% of their white blood cells are eutrophils, 36% are lymphocytes, 7% are monocytes, and the remaining 5% are other types. But without an actual count, these cannot be treated as binomial/multinomial counts and are just percentages (or proportions) of the whole.

Compositional data analysis is its own subfield in statistics, but whether the methods described there are relevant in the present context is not clear to me.

Since you mentioned the beta distribution: Yes, one could assume that a percentage/proportion like in the case above (i.e., a proportion of 0.36 of the white blood cells are lymphocytes) is beta distributed. But note that this is a proportion for a single individual. I would assume that there is such a proportion for multiple individuals within a group (e.g., patients). Then what is it that study authors would report? I would assume that they report the mean proportion (with hopefully also the SD of the individual proportions). If so, then one could basically just use methods for meta-analyzing means and mean differences.

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Jakub Ruszkowski via R-sig-meta-analysis
> Sent: Monday, March 11, 2024 17:43
> To: R sig meta analysis <r-sig-meta-analysis using r-project.org>
> Cc: Jakub Ruszkowski <jakub.ruszkowski using gumed.edu.pl>
> Subject: [R-meta] Meta-analysis of proportion differences (certain cells
> frequency)
>
> Dear All,
>
> I am looking for guidance on performing a meta-analysis of the proportions
> difference using R. Specifically, I am interested in analyzing the difference
> in certain cell frequencies: for example, the difference in lymphocyte% among
> all white blood cells between patients and healthy individuals, without having
> information about the total white blood cell count.
>
> I would appreciate it if anyone could provide insights or point me in the
> right direction regarding the appropriate R packages and methods for
> conducting such a meta-analysis. On a related note, I came across information
> suggesting that the difference between two beta distributions (likely
> representing fraction values) does not follow a normal distribution:
> https://blogs.sas.com/content/iml/2023/03/01/distribution-difference-beta.html.
> Because of that, I am afraid that I cannot use rma function.
>
> Thank you in advance for your time and support.
>
> Best regards,
>
> Jakub Ruszkowski
> Department of Nephrology, Transplantology and Internal Medicine
> Medical University of Gdańsk