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

Eleanor Sanderson; Wes Spiller; Jack Bowden

doi:10.1002/sim.9133

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

Eleanor Sanderson, Wes Spiller, Jack Bowden

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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 language	English
Pages (from-to)	5434-5452
Number of pages	19
Journal	Statistics in Medicine
Volume	40
Issue number	25
Early online date	2 Aug 2021
DOIs	https://doi.org/10.1002/sim.9133
Publication status	Published - 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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This research was funded in whole, or in part, by the Wellcome Trust [093820/Z/19/Z]. For the purpose of Open Access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.
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@article{57962af57f934434a3a3d6fa80ce22a3,

title = "Testing and correcting for weak and pleiotropic instruments in two-sample multivariable Mendelian randomization",

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.",

keywords = "Cochran's Q-statistic, instrument strength, instrument validity, multivariable Mendelian randomization, two-sample Mendelian randomization",

author = "Eleanor Sanderson and Wes Spiller and Jack Bowden",

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: {\textcopyright} 2021 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.",

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doi = "10.1002/sim.9133",

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T1 - Testing and correcting for weak and pleiotropic instruments in two-sample multivariable Mendelian randomization

AU - Sanderson, Eleanor

AU - Spiller, Wes

AU - Bowden, Jack

N1 - 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.

PY - 2021/11/10

Y1 - 2021/11/10

N2 - 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.

AB - 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.

KW - Cochran's Q-statistic

KW - instrument strength

KW - instrument validity

KW - multivariable Mendelian randomization

KW - two-sample Mendelian randomization

U2 - 10.1002/sim.9133

DO - 10.1002/sim.9133

M3 - Article (Academic Journal)

C2 - 34338327

VL - 40

SP - 5434

EP - 5452

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 25

ER -

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

Abstract

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Keywords

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