Abdulmajeed Jazeel, Chivese Tawanda, Doi Suhail A R
Department of Population Medicine, College of Medicine, QU Health, Qatar University, Doha, Qatar.
Division of Sciences and Mathematics, School of Interdisciplinary Arts and Sciences, University of Washington Tacoma, Tacoma, WA, USA.
BMC Med Res Methodol. 2025 Apr 5;25(1):89. doi: 10.1186/s12874-025-02527-z.
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.
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).
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.
The results suggest that the Freeman-Tukey transform is to be preferred over the logit transformation in the meta-analysis of prevalence.
传统统计方法假定连续变量呈正态分布，这使得它们不适用于患病率比例分析。为解决这一问题，本研究对两种常用的方差稳定变换（对数变换和弗里曼 - 图基变换）进行了实证评估，以便为研究人员明确这些变换中最优选择的相关情况。
使用多次蒙特卡罗模拟创建模拟数据集，通过改变输入参数来检验不同情况下变换估计量的性能。此外，该研究还深入探讨了样本量和比例如何影响弗里曼 - 图基变换的变异性。对单一患病率比例（覆盖率、区间宽度和样本量变化）以及患病率的荟萃分析（合并比例的绝对平均偏差、覆盖率和区间宽度）的性能进行了评估。
对于极端比例，我们发现与对数变换相比，弗里曼 - 图基变换提供了更好的覆盖率和更窄的区间；对于非极端比例，两种变换在单一比例方面表现出相似的性能。只有当所研究比例范围非常小（约0.005）时，弗里曼 - 图基变换比例随样本量的变异性才会显现，且弗里曼 - 图基变换值的变异性出现在小数点后第三位（0.007）。在荟萃分析中，与使用对数变换的相同荟萃分析相比，弗里曼 - 图基变换始终显示出与总体参数的绝对偏差更低、置信区间更窄且覆盖率更高。
结果表明，在患病率的荟萃分析中，弗里曼 - 图基变换比对数变换更可取。
