# Logit or arcsine transformation for proportion in meta-analysis

I am performing a meta-analysis with 137 study arms. From each arm I have extracted a proportion of a disease. Here are my proportions:

[1] 0.002710027 0.000000000 0.000000000 0.000000000 0.017857143 0.000000000 0.010269576 0.000000000 0.000000000 0.000000000 0.000000000
[12] 0.010000000 0.053691275 0.052631579 0.070351759 0.000000000 0.108333333 0.262626263 0.013043478 0.000000000 0.007000000 0.000000000
[23] 0.000000000 0.000000000 0.240000000 0.000000000 0.033333333 0.000000000 0.000000000 0.000000000 0.000000000 0.013201320 0.000000000
[34] 0.005361930 0.002308403 0.000000000 0.000000000 0.000000000 0.030000000 0.046296296 0.000000000 0.020000000 0.045454545 0.161073826
[45] 0.000000000 0.000000000 0.000000000 0.095238095 0.007194245 0.001472754 0.000000000 0.000000000 0.000000000 0.000000000 0.012048193
[56] 0.000000000 0.048780488 0.000000000 0.086253369 0.033898305 0.011966701 0.004162331 0.062790698 0.005555556 0.004451039 0.287356322
[67] 0.083333333 0.000000000 0.000000000 0.014666667 0.006160164 0.023809524 0.000000000 0.000000000 0.000000000 0.001552795 0.102564103
[78] 0.030555556 0.000000000 0.000000000 0.000000000 0.000000000 0.029411765 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
[89] 0.003231018 0.000000000 0.037500000 0.040247678 0.000000000 0.000000000 0.007299270 0.014598540 0.000000000 0.015118790 0.000000000
[100] 0.000000000 0.005555556 0.000000000 0.000000000 0.000000000 0.003039514 0.042145594 0.250000000 0.307692308 0.324444444 0.002057613
[111] 0.008333333 0.000000000 0.027522936 0.022598870 0.000000000 0.000000000 0.000000000 0.135278515 0.033333333 0.000000000 0.000000000
[122] 0.003690037 0.003412969 0.000000000 0.017391304 0.004237288 0.033210332 0.000000000 0.008928571 0.038834951 0.030303030 0.142857143
[133] 0.170000000 0.000000000 0.112903226 0.000000000 0.007299270


A majority of the proportions has zero value. I am struggling with whether I should go for logit or arcsine transformation. One source says that arcsine transformation should not be used (1). On the other hand, I several zero counts. With logit transformation values 0 and 1 are mapped to infinity, and according to another source I should go with arcsine transformation (2). Furthermore, I found another study close to my topic in which they used arcsine transformation. The default in R with metaprop function is logit.

Which one I should go with my data?

## 1 Answer

If all your proportions were in an intermediate range the choice would be quite arbitrary as they are very similar. In your case that is not true as you have many zero counts in the numerator. If you want to do meta-regression and see if your 137 study arms are affected by some covariate then there would be arguments for going with the logit as you cannot then end up with impossible predictions (as you say, it ranges over the whole real line). If you just want an overall summary then arcsine would be fine and would avoid having to make an arbitrary choice about adding a small constant. To add to your collection of refences you might be interested in this article by Rücker and colleagures with the title "Why add anything to nothing? The arcsine difference as a measure of treatment effect in meta--analysis with zero cells".