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

Research output: Contribution to journalArticle

1 Citation (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

ASJC Scopus subject areas

  • Epidemiology

Cite this

Schmidt, A. F., Hingorani, A. D., Jefferis, B. J., White, J., Dudbridge, F., Groenwold, R. H. H., ... Whincup, P. (2016). Comparison of variance estimators for metaanalysis of instrumental variable estimates. International Journal of Epidemiology, 45(6), 1975-1986. [dyw123].