Partial Identification of the Average Causal Effect in Multiple Study Populations: The Challenge of Combining Mendelian Randomization Studies

Elizabeth W. Diemer*, Luisa Zuccolo, Sonja A. Swanson

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Background: Researchers often use random-effects or fixed-effects meta-analysis to combine findings from multiple study populations. However, the causal interpretation of these models is not always clear, and they do not easily translate to settings where bounds, rather than point estimates, are computed.

Methods: If bounds on an average causal effect of interest in a well-defined population are computed in multiple study populations under specified identifiability assumptions, then under those assumptions the average causal effect would lie within all study-specific bounds and thus the intersection of the study-specific bounds. We demonstrate this by pooling bounds on the average causal effect of prenatal alcohol exposure on attention deficit-hyperactivity disorder symptoms, computed in two European cohorts and under multiple sets of assumptions in Mendelian randomization (MR) analyses.

Results: For all assumption sets considered, pooled bounds were wide and did not identify the direction of effect. The narrowest pooled bound computed implied the risk difference was between-4 and 34 percentage points.

Conclusions: All pooled bounds computed in our application covered the null, illustrating how strongly point estimates from prior MR studies of this effect rely on within-study homogeneity assumptions. We discuss how the interpretation of both pooled bounds and point estimation in MR is complicated by possible heterogeneity of effects across populations.

Original languageEnglish
Pages (from-to)20-28
Number of pages9
Issue number1
Publication statusPublished - 1 Jan 2023

Bibliographical note

Funding Information:
The Norwegian Mother, Father and Child Cohort Study is supported by the Norwegian Ministry of Health and Care Services and the Ministry of Education and Research. We are grateful to all the participating families in Norway who take part in this ongoing cohort study. We thank the Norwegian Institute of Public Health (NIPH) for generating high-quality genomic data. This research is part of the HARVEST collaboration, supported by the Research Council of Norway (#229624). We also thank the NORMENT Centre for providing genotype data, funded by the Research Council of Norway (#223273), South East Norway Health Authorities and Stiftelsen Kristian Gerhard Jebsen. We further thank the Center for Diabetes Research, the University of Bergen for providing genotype data and performing quality control and imputation of the data funded by the ERC AdG project SELECTionPREDISPOSED, Stiftelsen Kristian Gerhard Jebsen, Trond Mohn Foundation, the Research Council of Norway, the Novo Nordisk Foundation, the University of Bergen, and the Western Norway Health Authorities. We are extremely grateful to all the families who took part in this 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.

Funding Information:
This project is supported by an innovation program under the Marie Sklodowska-Curie grant agreement no. 721567. S.A.S. is further supported by a NWO/ZonMW Veni Grant (91617066). L.Z. was supported by a UK Medical Research Council fellowship (grant number G0902144). L.Z. was also supported by the UK MRC Integrative Epidemiology Unit (grant number: MC_UU_00011/1) and the National Institute for Health Research (NIHR) Bristol Biomedical Research Centre at University Hospitals Bristol National Health Service (NHS) Foundation Trust and the University of Bristol. S.A.S. and E.W.D. are further supported by a US Department of Veterans Affairs Cooperative Studies Program study #2032. The UK Medical Research Council and Wellcome (Grant ref: 217065/Z/19/Z) and the University of Bristol provide core support for ALSPAC. This publication is the work of the authors and E.W.D., L.Z., and S.A.S. will serve as guarantors for the contents of this paper. A comprehensive list of grants funding is available on the ALSPAC website ( ).

Publisher Copyright:
© 2023 Lippincott Williams and Wilkins. All rights reserved.


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