Calculating statistical power in Mendelian randomization studies

Abstract

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.

Genomics and metabolomics of muscular mass in a community-based sample of UK females

“…As the genotype has been randomly assigned at conception (hence 'Mendelian randomization') it can be used as a proxy for the intermediate variable (instrumental variable) to assess the effect of the exposure on the outcome, not the effect of a gene on an outcome. 24,25 To test the hypothesis of causal effect of the given metabolite, we conducted genetic variance component analysis 26 of RALM, and each of the selected MTBs separately, as implemented in the statistical package MAN, 27 which takes into account familial structure of the sample. Each analysis was conducted with simultaneous testing of the linear regression effect of the SNP, most significantly associated with the corresponding MTB variation.…”

“…The causal effect of the MTB on RALM can be established by the ratio, ρ = β R /β M , where β 2 R and β 2 M are the least squares estimates of the SNP effect on the RALM and the MTB variations in the respective linear regression models. 25 The test for the nullity of the causal effect ρ was based on the following approximation:…”

Assessing the causal association between 25‐hydroxyvitamin D and the risk of oral and oropharyngeal cancer using Mendelian randomization

“…Given this, in the GAME‐ON study for oral ( n  = 2,700 cases, 5984 controls) or oropharyngeal sites ( n  = 2,433 cases, 5984 controls) alone, there was adequate power to detect an OR of 0.67 to 0.74 per SD increase in log 25OHD with power of 0.8 and an alpha of 0.05. For all sites combined ( n  = 5,133 cases, 5984 controls), the study was powered to detect an OR of between 0.74 and 0.79 (http://cnsgenomics.com/shiny/mRnd/) 32…”

The genetic architecture of psychiatric disorders

“…The power in MR studies is a function of the true causal association between exposure and outcome and of the variance explained by the instrumental variables [81]. Since statistically significantly associated SNPs often only explain a small proportion of the genetic variance, for many pairs of traits, very large sample sizes are needed to achieve sufficient power to detect causal associations (see online calculator [81]).…”

“…Since statistically significantly associated SNPs often only explain a small proportion of the genetic variance, for many pairs of traits, very large sample sizes are needed to achieve sufficient power to detect causal associations (see online calculator [81]). …”