Most MR studies assume a linear (dose-response) effect of the exposure on the outcome. Methods for exploring non-linear effects in one-sample MR and two-sample MR are available but require very large numbers to be adequately powered and strong assumptions about the relationship between the genetic instrumental variable (IV) and exposure.
In order to estimate the non-linear effect of an exposure on an outcome using two-sample MR with summary-level data, non-linear estimates of the associations between both the single nucleotide polymorpism (SNP) and exposure and the SNP and outcome must be provided. Otherwise, only a linear causal effect between the exposure and outcome can be estimated with two-sample MR. Therefore, in most cases, non-linear effect estimates derived from MR analyses are done so via the use of one-sample MR with individual-level data. However, generally, there may be lack of statistical power to detect non-linear effects given the need to stratify the effect of the exposure on outcome by levels of the exposure. Several methods to estimate the non-linear causal effect of an exposure on an outcome have been developed for individual-level data. One such method uses "instrument-free" exposures, whereby the residuals of the association between the genetic IV and exposure are used as the variable on which the data are stratified when estimating the non-linear effect of the exposure on the outcome. This comes with the additional assumption that there is a constant genetic effect of the genetic IV on the exposure across all strata. Other such method (called the "doubly-ranked" method) is less sensitive to the constant genetic effect assumption, as it allows the validity of this assumption to be assessed and the estimation of a less biased non-linear causal effect. However, this is an ongoing area of research given concerns that both methods may produce biased estimates, especially in situations where the constant genetic effect assumption is violated, and the source(s) of this bias is currently not clear.
References
- Staley JR, Burgess S. Semiparametric methods for estimation of a nonlinear exposure‐outcome relationship using instrumental variables with application to Mendelian randomization. Genet Epidemiol. 2017; 41: 341–352
- Burgess S. Violation of the constant genetic effect assumption can result in biased estimates for non-linear Mendelian randomization. medRxiv 2022; doi: https://doi.org/10.1101/2022.10.26.22280570
- Tian H, Mason AM, Liu C, Burgess S. Relaxing parametric assumptions for non-linear Mendelian randomization using a doubly-ranked stratification method. bioRxiv 2022; doi: https://doi.org/10.1101/2022.06.28.497930
- Burgess S, Davies NM, Thompson SG, Consortium EP-I. Instrumental variable analysis with a nonlinear exposure-outcome relationship. Epidemiology 2014; 25: 877-85.
- Silverwood RJ, Holmes MV, Dale CE, et al. Testing for non-linear causal effects using a binary genotype in a Mendelian randomization study: application to alcohol and cardiovascular traits. Int J Epidemiol 2014; 43: 1781-90.
Other terms in 'Sources of bias and limitations in MR':
- Assortative mating
- Canalization
- Collider
- Collider bias
- Conditional F-statistic for multiple exposures
- Confounding
- Exclusion restriction assumption
- F-statistic
- Harmonization (in two-sample MR)
- Homogeneity Assumption
- Horizontal Pleiotropy
- Independence assumption
- INstrument Strength Independent of Direct Effect (InSIDE) assumption
- Intergenerational (or dynastic) effects
- Monotonicity assumption
- MR for testing critical or sensitive periods
- MR for testing developmental origins
- No effect modification assumption
- NO Measurement Error (NOME) assumption
- Non-overlapping samples (in two-sample MR)
- Overfitting
- Pleiotropy
- Population stratification
- R-squared
- Regression dilution bias (attenuation by errors)
- Relevance assumption
- Reverse causality
- Same underlying population (in two-sample MR)
- Statistical power and efficiency
- Vertical pleiotropy
- Weak instrument bias
- Winner's curse