The goal of my meta-analysis project is to combine proportions from studies without a control group.
In Practical Meta-Analysis, Lipsey and Wilson mentioned that the logit transformation should be used when proportions are less than 0.2 or more than 0.8 instead of using raw proportions. But they didn't mention the double arcsine transformation. Barendregt et al. have claimed the double arcsine transformation to be a preferred option. I wonder which method you guys would prefer to use and how you would do to decide which one to use.
I tried to find out how to determine which method to choose by trying to replicate the results of a handful of studies using both methods (I also used the arcsine square root method). Here is my approach: For each study, I first transformed the original data using the logit and the double arcsine transformation. I then generated Q-Q plots and histograms of these transformed data. After that, I compared their skewness and kurtosis in order to see if they were in the acceptable range. Then I conducted the Shapiro-Wilk test. By now, I would have a basic idea of which method would be better for me to use, but I wonder how you would make the decision.
The thing is, sometimes, both methods could lead to very similar results; sometimes, neither of the methods was able to pass the Shapiro-Wilk test; sometimes, both methods failed to normalize the data; sometimes, the arcsine square root transformation seemed to have done a better job. In these situations, what would you do?
The logit transform does not really stabilize the variance, it just stops the pooled CI from exceeding 0-1. Only the double arcsin square root transform really stabilizes the variance
Dear Naike:
¿Do you mean log transformation instead logit transformation because there are two different procedures?
Base on your question one can imagine that you want to normalize some data distribution.
If so, another question rise, ¿Why do you need a transformation for?
¿What are you trying to do?
¿What is your research question?
Due to you are working with a single proportion, and if you are interesting in testing a statistical significance, you have, at least, two options, both comparing to zero:
1. Normalize the original distribution in order to use parametric procedures, which are robust, or
2. Use non parametric procedures, in order to maintenance the original data.
Both procedures lead to similar results, but the decision is based on, most of the times, in the number of observations you have on hand,
I had another problem. Used 2 different softwares-medcalc vs CMA and they probably use different models. I got different ES and dont know which to use...
- double arcsine transformed proportion is better at stabilizing the variance reference: https://jech.bmj.com/content/67/11/974
- at the same time there is serious effect when such transformed proportion are back-transformed. reference: Schwarzer G, Chemaitelly H, Abu-Raddad LJ, Rücker G. Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions. Res Synth Methods. 2019;
- what to do? just do logit transformation through generlaized linear mixed model. reference: Schwarzer G, Chemaitelly H, Abu-Raddad LJ, Rücker G. Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions. Res Synth Methods. 2019;
In continuation with ( Ibrahim H. Elkhidir ), the logit transformation with GLLMs method is recommended by Schwarzer et al (2019). However, it doesn't provide the study weights. Hence, if you need study weights, can prefer the arcsine transformation.
Alternatively, if the arcsineFreeman-Tukey double arcsine method is used, caution needed - the estimates to be tested using different sample sizes // sensitivity analysis. Naike Wang
Hello,
Does anyone know how to go back easily to a proportion (percentage) from a "double arcsine transformed proportion"?
I am using jamovi and the final result is a "double arcsine transformed proportion" for my meta analysis of proportions, which is not very easy to use...
Thank you for your help
Jasmina Mallet, you can find the answer in [1]. It is implemented in many packages, e.g. metafor (https://www.metafor-project.org/doku.php/analyses:miller1978). Additionally, if you observe the erratic behavior of the back-transformation, you can use suggestions from [2].
[1] Article The Inverse of the Freeman – Tukey Double Arcsine Transformation
[2] Preprint Domain of Inverse Double Arcsine Transformation
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