Cochran's Q statistic

Heterogeneity statistic for IVW model. 

If Q much larger than its degrees of freedom (No. of IVs minus 1), this provides evidence for heterogeneity and invalid instruments. Assumes genetic IVs are uncorrelated. Individual contribution of each IV to Q can be used to detect individual invalid IVs. An extended version of Q statistic necessary when genetic instruments are weak. 

References

• Greco M FD, Minelli C, Sheehan NA, Thompson JR. Detecting pleiotropy in Mendelian randomisation studies with summary data and a continuous outcome. Statistics in Medicine 2015;34:2926-2940.
• Bowden J, Del Greco M F, Minelli C et al. Improving the accuracy of two-sample summary-data Mendelian randomization: moving beyond the NOME assumption. International Journal of Epidemiology 2018:dyy258-dyy258.

Other terms in 'Heterogeneity and outlier detection methods for two-sample MR':

• HEIDI (heterogeneity in dependent instruments)
• MR-PRESSO
• MR-TRYX (Treasure your exceptions)
• Radial MR (MR pleiotropy residual sum and outlier)