Seriously misleading results using inverse of Freeman‐Tukey double arcsine transformation in meta‐analysis of single proportions

Standard generic inverse variance methods for the combination of single proportions are based on transformed proportions using the logit, arcsine, and Freeman‐Tukey double arcsine transformations. Generalized linear mixed models are another more elaborate approach. Irrespective of the approach, meta‐analysis results are typically back‐transformed to the original scale in order to ease interpretation. Whereas the back‐transformation of meta‐analysis results is straightforward for most transformations, this is not the case for the Freeman‐Tukey double arcsine transformation, albeit possible. In this case study with five studies, we demonstrate how seriously misleading the back‐transformation of the Freeman‐Tukey double arcsine transformation can be. We conclude that this transformation should only be used with special caution for the meta‐analysis of single proportions due to potential problems with the back‐transformation. Generalized linear mixed models seem to be a promising alternative.

[1]  Theo Stijnen,et al.  The binomial distribution of meta-analysis was preferred to model within-study variability. , 2008, Journal of clinical epidemiology.

[2]  John J. Gart,et al.  The bias and higher cumulants of the logarithm of a binomial variate , 1986 .

[3]  R. Newcombe.  Two-sided confidence intervals for the single proportion: comparison of seven methods. , 1998, Statistics in medicine.

[4]  J. Berkson.  Application of the Logistic Function to Bio-Assay , 1944 .

[5]  A. Agresti,et al.  Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions , 1998 .

[6]  Jan J Barendregt,et al.  Meta-analysis of prevalence , 2013, Journal of Epidemiology & Community Health.

[7]  Hannah R Rothstein,et al.  A basic introduction to fixed‐effect and random‐effects models for meta‐analysis , 2010, Research synthesis methods.

[8]  T. Vos,et al.  prevalence of anxiety disorders : a systematic review and meta regression , 2013 .

[9]  Theo Stijnen,et al.  Random effects meta‐analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data , 2010, Statistics in medicine.

[10]  L. Abu-Raddad,et al.  The Epidemiology of Hepatitis C Virus in the Fertile Crescent: Systematic Review and Meta-Analysis , 2015, PloS one.

[11]  T. Jaeger,et al.  Categorical Data Analysis: Away from ANOVAs (transformation or not) and towards Logit Mixed Models. , 2008, Journal of memory and language.

[12]  Ralf Bender,et al.  Methods to estimate the between‐study variance and its uncertainty in meta‐analysis† , 2015, Research synthesis methods.

[13]  J. Tukey,et al.  Transformations Related to the Angular and the Square Root , 1950 .

[14]  Francis K C Hui,et al.  The arcsine is asinine: the analysis of proportions in ecology. , 2011, Ecology.

[15]  F. J. Anscombe,et al.  THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATA , 1948 .

[16]  Lorie A. Kloda,et al.  The Seroprevalence of Hepatitis C Antibodies in Immigrants and Refugees from Intermediate and High Endemic Countries: A Systematic Review and Meta-Analysis , 2015, PloS one.

[17]  J. Miller,et al.  The Inverse of the Freeman – Tukey Double Arcsine Transformation , 1978 .