Overcoming challenges in prevalence meta-analysis: the case for the Freeman-Tukey transform

Abstract

Background: Traditional statistical methods assume normally distributed continuous variables, making them unsuitable for analysis of prevalence proportions. To address this problem, two commonly utilized variance-stabilizing transformations (logit and Freeman-Tukey) are empirically evaluated in this study to provide clarity on the optimal choice among these transforms for researchers. Methods: Simulated datasets were created using multiple Monte Carlo simulations, with varying input parameters to examine transformation estimator performance under varying scenarios. Additionally, the research delved into how sample size and proportion influenced the variability of the Freeman-Tukey transform. Performance was evaluated for both single prevalence proportions (coverage, interval width and variation over sample size) as well as for meta-analysis of prevalence (absolute mean deviation of pooled proportions, coverage and interval width). Results: For extreme proportions we found that the Freeman-Tukey transform provides better coverage and narrower intervals compared to the logit transformation, and for non-extreme proportions, both transformations demonstrated similar performance in terms of single proportions. The variability of Freeman-Tukey transformed proportions with sample size is only seen when the range of proportions under scrutiny are very small (~ 0.005), and the variability of the Freeman-Tukey transform’s value occurs in the third decimal place (0.007). In meta-analysis, the Freeman-Tukey transformation consistently showed lower absolute deviation from the population parameter, with narrower confidence intervals, and improved coverage compared to the same meta-analyses using the logit transformation. Conclusion: The results suggest that the Freeman-Tukey transform is to be preferred over the logit transformation in the meta-analysis of prevalence.