Relaxing parametric assumptions for non-linear Mendelian randomization using a doubly-ranked stratification method

Non-linear Mendelian randomization is an extension to standard Mendelian randomization to explore the shape of the causal relationship between an exposure and outcome using an instrumental variable. A stratification approach to non-linear Mendelian randomization divides the population into strata and calculates separate instrumental variable estimates in each stratum. However, the standard implementation of stratification, referred to as the residual method, relies on strong parametric assumptions of linearity and homogeneity between the instrument and the exposure to form the strata. If these stratification assumptions are violated, the instrumental variable assumptions may be violated in the strata even if they are satisfied in the population, resulting in misleading estimates. We propose a new stratification method, referred to as the doubly-ranked method, that does not require strict parametric assumptions to create strata with different average levels of the exposure such that the instrumental variable assumptions are satisfied within the strata. Our simulation study indicates that the doubly-ranked method can obtain unbiased stratum-specific estimates and appropriate coverage rates even when the effect of the instrument on the exposure is non-linear or heterogeneous. Moreover, it can also provide unbiased estimates when the exposure is coarsened (that is, rounded, binned into categories, or truncated), a scenario that is common in applied practice and leads to substantial bias in the residual method. We applied the proposed doubly-ranked method to investigate the effect of alcohol intake on systolic blood pressure, and found evidence of a positive effect of alcohol intake, particularly at higher levels of alcohol consumption.Author summary: Various exposures, such as alcohol consumption, may exhibit different effect sizes on health outcomes at different exposure levels. Studying the non-linear shape of these effects can provide valuable insights to predict the impact of interventions for different individuals. Mendelian randomization is an epidemiological approach to make causal inferences from observational data. It uses genetic variants to divide the population into subgroups which behave similarly to arms of a randomized trial. The current residual stratification method most often implemented for non-linear Mendelian randomization relies on strong parametric assumptions and can yield misleading results when these assumptions are violated. We propose a new stratification method that relaxes these assumptions. Our new doubly-ranked method demonstrates superior performance over the residual method across a wide range of simulation scenarios. Furthermore, in cases where the exposure is coarsened (for example, its value is rounded, say to the nearest whole number), the doubly-ranked method achieves good results while the residual method fails to handle such situations adequately. The doubly-ranked method can test the assumptions underlying the residual method, thereby assessing the validity of previously published results. We advocate for the doubly-ranked method to be used in preference to the residual stratification method for non-linear Mendelian randomization.