title: Comparison of variance estimators for meta-analysis of instrumental variable estimates.
abstract: 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.
  
  
  
  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 two-stage meta-analysis pooling results, and a one-stage meta-analysis pooling datasets.
  
  
  
  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 meta-analysis all methods performed equally well and better than two-stage meta-analysis of greater or equal size.
  
  
  
  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.
authors: Institute of Cardiovascular Science.
authors: A F
authors: AF
authors: Schmidt
authors: Institute of Cardiovascular Science.
authors: A D
authors: AD
authors: Hingorani
authors: Department of Primary Care and Population Health.
authors: B J
authors: BJ
authors: Jefferis
authors: UCL Genetics Institute, University College London, London, UK.
authors: J
authors: J
authors: White
authors: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands.
authors: Rhh
authors: R
authors: Groenwold
authors: Department of Non-Communicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK.
authors: F
authors: F
authors: Dudbridge
mesh_terms: D015982:Bias; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D057182:Mendelian Randomization Analysis; D015201:Meta-Analysis as Topic
keywords: Epidemiology methods; Mendelian randomization analysis; statistics