Comparison of variance estimators for metaanalysis of instrumental variable estimates

A. F. Schmidt*, A. D. Hingorani, B. J. Jefferis, J. White, F. Dudbridge, R. H H Groenwold, Y. Ben-Shlomo, N. Chaturvedi, J. Engmann, A. Hughes, S. Humphries, E. Hypponen, M. Kivimaki, D. Kuh, M. Kumari, U. Menon, R. Morris, C. Power, J. Price, G. WannametheeP. Whincup

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)


Background: Mendelian randomization studies perform instrumental variable (IV) analysis using genetic IVs. Results of individual Mendelian randomization studies can be pooled through meta-analysis. We explored how different variance estimators influence the meta-analysed IV estimate. Methods: Two versions of the delta method (IV before or after pooling), four bootstrap estimators, a jack-knife estimator and a heteroscedasticity-consistent (HC) variance estimator were compared using simulation. Two types of meta-analyses were compared, a twostagemeta- analysis pooling results, and a one-stage meta-analysis pooling datasets. Results: Using a two-stage meta-analysis, coverage of the point estimate using bootstrapped estimators deviated from nominal levels at weak instrument settings and/or outcome probabilities ≤ 0.10. The jack-knife estimator was the least biased resampling method, the HC estimator often failed at outcome probabilities ≤ 0.50 and overall the delta method estimators were the least biased. In the presence of between-study heterogeneity, the delta method before meta-analysis performed best. Using a one-stage metaanalysis all methods performed equally well and better than two-stage meta-analysis of greater or equal size. Conclusions: In the presence of between-study heterogeneity, two-stage meta-analyses should preferentially use the delta method before meta-analysis. Weak instrument bias can be reduced by performing a one-stage meta-analysis.

Original languageEnglish
Article numberdyw123
Pages (from-to)1975-1986
Number of pages12
JournalInternational Journal of Epidemiology
Issue number6
Publication statusPublished - 1 Dec 2016


  • Epidemiology methods
  • Mendelian randomization analysis
  • Statistics


Dive into the research topics of 'Comparison of variance estimators for metaanalysis of instrumental variable estimates'. Together they form a unique fingerprint.

Cite this