Introduction

In the next two chapters, we consider extensions to IV methods to efficiently analyse data typically available in Mendelian randomization investigations. The first extension is the inclusion of multiple instrumental variables in a single analysis model, and the statistical issues arising.We consider the impact on statistical power, and discuss the practical issue of missing data, which can limit power gains.

Key points from chapter

- Use of multiple instrumental variables in Mendelian randomization leads to more precise estimates of causal effects.
- Sporadically missing genetic data may offset this gain, but missing data methods can recover much of the loss.
- Parsimonious models of genetic association, and in particular allele scores, can alleviate the problems of weak instruments which may arise when using large numbers of instrumental variables.
- The procedure for constructing an allele score to be used in an analysis should be made clear, and in particular how variants and weights for the score are chosen, as this has a considerable impact on bias.

Relevant papers to chapter:

Section 8.2 (Allele scores). S. Burgess, S.G. Thompson. Use of allele scores as instrumental variables for Mendelian randomization. Int. J. Epidemiol. 2013; 42(4):1134-1144.

Section 8.2 (Allele scores). N.M. Davies, S.v.H.K. Scholder, H. Farbmacher, S. Burgess, F. Windmeijer, G. Davey Smith. The many weak instruments problem and Mendelian randomization. Statist. Med. 2014.

Section 8.3 (Power of IV estimates). S. Burgess. Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome. Int. J. Epidemiol. 2014; 43(3):922-929.

Section 8.4 (Multiple variants and missing data). S. Burgess, S. Seaman, D. Lawlor, J.P. Casas, S.G. Thompson. Missing data methods in Mendelian randomization studies with multiple instruments. Am. J. Epidemiol. 2011; 174(9):1069-1076.

Section 8.5.2 (Subsample Mendelian randomization). B.L. Pierce, S. Burgess. Efficient design for Mendelian randomization studies: subsample and two-sample instrumental variable estimators. Am. J. Epidemiol. 2013; 178(7):1177-1184.