Calculating statistical power in Mendelian randomization studies.
Open accessAbstract
In Mendelian randomization (MR) studies, where genetic variants are used as proxy measures for an exposure trait of interest, obtaining adequate statistical power is frequently a concern due to the small amount of variation in a phenotypic trait that is typically explained by genetic variants. A range of power estimates based on simulations and specific parameters for two-stage least squares (2SLS) MR analyses based on continuous variables has previously been published. However there are presently no specific equations or software tools one can implement for calculating power of a given MR study. Using asymptotic theory, we show that in the case of continuous variables and a single instrument, for example a single-nucleotide polymorphism (SNP) or multiple SNP predictor, statistical power for a fixed sample size is a function of two parameters: the proportion of variation in the exposure variable explained by the genetic predictor and the true causal association between the exposure and outcome variable. We demonstrate that power for 2SLS MR can be derived using the non-centrality parameter (NCP) of the statistical test that is employed to test whether the 2SLS regression coefficient is zero. We show that the previously published power estimates from simulations can be represented theoretically using this NCP-based approach, with similar estimates observed when the simulation-based estimates are compared with our NCP-based approach. General equations for calculating statistical power for 2SLS MR using the NCP are provided in this note, and we implement the calculations in a web-based application.
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Analysis was limited to phecodes that had 200 or more cases to generate improved statistical power for consequent MR analyses.
“Analysis was limited to phecodes that had 200 or more cases in order to generate improved statistical power for consequent MR analyses (S1 Text) [22,23].”
From Associations of genetically determined iron status across the phenome: A mendelian randomization study (2019) · cites this paper as [23]
The Introduction says MR often requires large sample sizes because statistical power is a challenge, and Applying power calculations treats sample size as a factor in power. The paper does not address phecodes or establish a 200-case cutoff; its calculations concern continuous variables, so it supports the general rationale but not the specific restriction. (LLM, conf=0.84)
Experimental — accuracy not yet measuredIn a one-sample MR setting with weak genetic variant-exposure associations, chance variation causes genetic associations with the exposure and outcome to be correlated in the direction of the confounded association between the two.
“In a one-sample setting, if the genetic variant–exposure associations are weak, then chance variation means that genetic associations with the exposure and outcome are correlated in the direction of the confounded association between the two.”
From Guidelines for performing Mendelian randomization investigations (2020) · cites this paper as [41]
In a one-sample MR setting with weak instruments, instrumental variable estimates are biased in the direction of the confounded association, and false positive (type 1 error) rates are inflated, particularly when more than one variant is included.
“This results in instrumental variable estimates that are biased in the direction of the confounded association, and inflated false positive (type 1 error) rates, particularly when more than one variant is included in the analysis 41 .”
From Guidelines for performing Mendelian randomization investigations (2020) · cites this paper as [41]
If genetic variants are selected based on their associations with the exposure in the dataset under analysis, weak instrument bias is exacerbated (in the direction of the observational association in a one-sample setting, and in the direction of the null in a two-sample setting).
“If genetic variants are selected based on their associations with the exposure in the dataset under analysis, weak instrument bias is exacerbated (in the direction of the observational association in a one-sample setting, and in the direction of the null in a two-sample setting) 41 .”
From Guidelines for performing Mendelian randomization investigations (2020) · cites this paper as [41]
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- Authors
- Brion, M.-J. A., Shakhbazov, K., & Visscher, P. M.
- Affiliations
- Broad Institute (US)
- Corresponding author
- Brion, Marie-Jo A
- Venue
- International Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2012-10-23
- Volume
- 42
- Issue
- 5
- Pages
- 1497-1501
- ISSN
- 0300-5771 (ISSN-L)
- 1464-3685
- PMC
- PMC3807619
- OpenAlex
- W2118008714
- Cited by
- 1,751
- References
- 8
- Citations by year
- 2026: 98 · 2025: 214 · 2024: 454 · 2023: 301 · 2022: 222 · 2021: 138 · 2020: 122 · 2019: 72 · 2018: 49 · 2017: 33 · 2016: 20 · 2015: 11 · 2014: 14 · 2013: 1
- FWCI
- 5.00
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- International Journal of Epidemiology (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- HighWire Press Open Archive (submittedVersion)
- Funders
- Wellcome Trust (WT085515)
- European Commission (247642)
- Fondation Leducq
- Seventh Framework Programme
- Medical Research Council
- National Health and Medical Research Council (613601)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- Mendelian randomization, statistical power, two-stage least squares, noncentrality parameter, asymptotic theory, single nucleotide polymorphisms, genetic instruments
- MeSH terms
- Humans, Statistics as Topic, Causality, Sample Size, Mendelian Randomization Analysis
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