A new justification of the Hartung‐Knapp method for random‐effects meta‐analysis based on weighted least squares regression

• Published in: Research synthesis methods Vol. 10; no. 4; pp. 515 - 527
• Main Authors: Aert, Robbie C. M., Jackson, Dan
• Format: Journal Article
• Language: English
• Published: England Wiley-Blackwell 01.12.2019; Wiley Subscription Services, Inc; John Wiley and Sons Inc
• Subjects: Algorithms; Comparative Analysis; Computer Simulation; Confidence intervals; Data Interpretation, Statistical; Guidelines; Hartung‐Knapp modification; Inferences; Least squares method; Least Squares Statistics; Least-Squares Analysis; Linear Models; Medical Research; Meta Analysis; Meta-Analysis as Topic; meta‐regression; Outcomes of Treatment; random‐effects weighted least squares regression; Regression analysis; Regression models; Research Design; Sample Size; Simulation; Statistical analysis; Hartung-Knapp modification; meta-analysis; random-effects weighted least squares regression; meta-regression
• ISSN: 1759-2879; 1759-2887; 1759-2887
• DOI: 10.1002/jrsm.1356

The Hartung‐Knapp method for random‐effects meta‐analysis, that was also independently proposed by Sidik and Jonkman, is becoming advocated for general use. This method has previously been justified by taking all estimated variances as known and using a different pivotal quantity to the more conventional one when making inferences about the average effect. We provide a new conceptual framework for, and justification of, the Hartung‐Knapp method. Specifically, we show that inferences from fitted random‐effects models, using both the conventional and the Hartung‐Knapp method, are equivalent to those from closely related intercept only weighted least squares regression models. This observation provides a new link between Hartung and Knapp's methodology for meta‐analysis and standard linear models, where it can be seen that the Hartung‐Knapp method can be justified by a linear model that makes a slightly weaker assumption than taking all variances as known. This provides intuition for why the Hartung‐Knapp method has been found to perform better than the conventional one in simulation studies. Furthermore, our new findings give more credence to ad hoc adjustments of confidence intervals from the Hartung‐Knapp method that ensure these are at least as wide as more conventional confidence intervals. The conceptual basis for the Hartung‐Knapp method that we present here should replace the established one because it more clearly illustrates the potential benefit of using it.