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Improving bias and coverage in instrumental variable analysis with weak instruments for continuous and binary outcomes
Author(s) -
Burgess Stephen,
Thompson Simon G.
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4498
Subject(s) - instrumental variable , econometrics , causal inference , mendelian randomization , outcome (game theory) , statistics , context (archaeology) , continuous variable , population , mathematics , medicine , paleontology , chemistry , environmental health , mathematical economics , genetic variants , biology , genotype , gene , biochemistry
Causal estimates can be obtained by instrumental variable analysis using a two‐stage method. However, these can be biased when the instruments are weak. We introduce a Bayesian method, which adjusts for the first‐stage residuals in the second‐stage regression and has much improved bias and coverage properties. In the continuous outcome case, this adjustment reduces median bias from weak instruments to close to zero. In the binary outcome case, bias from weak instruments is reduced and the estimand is changed from a marginal population‐based effect to a conditional effect. The lack of distributional assumptions on the posterior distribution of the causal effect gives a better summary of uncertainty and more accurate coverage levels than methods that rely on the asymptotic distribution of the causal estimate. We discuss these properties in the context of Mendelian randomization. Copyright © 2012 John Wiley & Sons, Ltd.