Testing and correcting for weak and pleiotropic instruments in two-sample multivariable Mendelian randomization

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Abstract

Multivariable Mendelian Randomisation (MVMR) is a form of instrumental variable analysis which estimates the direct eect of multiple exposures on an outcome using genetic variants as instruments. Mendelian Randomisation and MVMR are frequently conducted using two-sample summary data where the association of the genetic variants with the exposures and outcome are obtained from separate samples. If the genetic variants are only weakly associated with the exposures either individually or conditionally, given the other exposures in the model, then standard inverse variance weighting will yield biased estimates for the effect of each exposure. Here we develop a two-sample conditional F-statistic to test whether the genetic variants strongly predict each exposure conditional on the other exposures included in a MVMR model. We show formally that this test is equivalent to the individual level data conditional F-statistic, indicating that conventional rule-of-thumb critical values of F > 10, can be used to test for weak instruments. We then demonstrate how reliable estimates of the causal effect of each exposure on the outcome can be obtained in the presence of weak instruments and pleiotropy, by re-purposing a commonly used heterogeneity Q-statistic as an estimating equation. Furthermore, the minimised value of this Q-statistic yields an exact test for heterogeneity due to pleiotropy. We illustrate our methods with an application to estimate the causal effect of blood lipid fractions on age related macular degeneration.
Original languageEnglish
Pages (from-to)5434-5452
Number of pages19
JournalStatistics in Medicine
Volume40
Issue number25
Early online date2 Aug 2021
DOIs
Publication statusPublished - 10 Nov 2021

Bibliographical note

Funding Information:
information Medical Research Council, MC_UU_00011/1; MC_UU_00011/2; Wellcome Trust, 108902/B/15/ZWe are grateful for helpful discussions with Frank Windmeijer and Zoltan Kutalik during the development of this article. We are extremely grateful to all the families who took part in the ALSPAC study, the midwives for their help in recruiting them, and the whole ALSPAC team, which includes interviewers, computer and laboratory technicians, clerical workers, research scientists, volunteers, managers, receptionists, and nurses. ES is funded through the MRC Integrative Epidemiology Unit (grant codes MC_UU_00011/1, MC_UU_00011/2). WS is supported by a Wellcome Trust studentship (108902/B/15/Z). JB is funded by an Expanding Excellence in England (E3) grant awarded to the Diabetes research group at the University of Exeter. The UK Medical Research Council and Wellcome (Grant ref: 217065/Z/19/Z) and the University of Bristol provide core support for ALSPAC. The collection of the ALSPAC data used in this publication was funded by Wellcome (Grant ref: 093820/Z/19/Z). This publication is the work of the authors and they will serve as guarantors for the contents of this article.

Funding Information:
We are grateful for helpful discussions with Frank Windmeijer and Zoltan Kutalik during the development of this article. We are extremely grateful to all the families who took part in the ALSPAC study, the midwives for their help in recruiting them, and the whole ALSPAC team, which includes interviewers, computer and laboratory technicians, clerical workers, research scientists, volunteers, managers, receptionists, and nurses. ES is funded through the MRC Integrative Epidemiology Unit (grant codes , ). WS is supported by a Wellcome Trust studentship (108902/B/15/Z). JB is funded by an Expanding Excellence in England (E3) grant awarded to the Diabetes research group at the University of Exeter. The UK Medical Research Council and Wellcome (Grant ref: 217065/Z/19/Z) and the University of Bristol provide core support for ALSPAC. The collection of the ALSPAC data used in this publication was funded by Wellcome (Grant ref: 093820/Z/19/Z). This publication is the work of the authors and they will serve as guarantors for the contents of this article.

Publisher Copyright:
© 2021 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Keywords

  • Cochran's Q-statistic
  • instrument strength
  • instrument validity
  • multivariable Mendelian randomization
  • two-sample Mendelian randomization

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