Meta-analysis without study-specific variance information: Heterogeneity case.

Area of Science:

• Biostatistics
• Medical Statistics
• Meta-analysis Methodology

Background:

• Random effects models are standard for meta-analysis with study heterogeneity.
• Existing frameworks lack methods for meta-analysis with only sample means and sizes, excluding standard deviations.
• This limitation hinders statistical comparison between treatment arms.

Purpose of the Study:

• To develop estimators for key random effects model components: overall mean difference, associated variances, between-study variance, and within-study variance.
• To introduce a novel measure of heterogeneity adjusting Higgins' I² for within-study sample size.
• To evaluate the performance of these proposed estimators.

Main Methods:

• Utilized maximum likelihood estimation to derive estimators for mean difference and variances.
• Investigated standard errors for the proposed estimators.
• Developed and assessed a modified heterogeneity measure (I² adjustment).
• Employed simulation studies to evaluate estimator performance.

Main Results:

• All estimated means converged to true parameter values.
• Standard errors of estimators were small with a large number of studies.
• The proposed heterogeneity measure effectively adjusts for within-study sample size.
• Simulations confirmed the reliability of the new estimators.

Conclusions:

• The proposed maximum likelihood estimators are effective for random effects meta-analysis with incomplete data (missing standard deviations).
• The adjusted heterogeneity measure provides a more refined quantification of study variability.
• These methods can be beneficially applied to meta-analyses, such as comparing surgeries for congenital lung malformations.