Non-linear Mendelian randomization is an extension of conventional Mendelian randomization that performs separate instrumental variable analyses in strata of the study population with different average levels of the exposure. The approach estimates a localized average causal effect function, representing the average causal effect of the exposure on the outcome at different levels of the exposure. The commonly-used residual method for dividing the population into strata works under the

more »

... that the effect of the genetic instrument on the exposure is linear and constant in the study population. However, this assumption may not hold in practice. We use the recently developed doubly-ranked method to re-analyse various datasets previously analysed using the residual method. In particular, we consider a genetic score for 25-hydroxyvitamin D [25(OH)D] used in a recent non-linear Mendelian randomization analysis to assess the potential effect of vitamin D supplementation on all-cause mortality. We show that the effect of the genetic score on 25(OH)D concentrations varies strongly, with a five-fold difference in the estimated genetic association with the exposure in the lowest and highest decile groups. Evidence for a protective causal effect of vitamin D supplementation on all-cause mortality in low vitamin D individuals is evident for the residual method, but not for the doubly-ranked method. We show that the constant genetic effect assumption is more reasonable for some exposures, and less reasonable for others. If the doubly-ranked method indicates that this assumption is violated, then estimates from both the residual and doubly-ranked methods can be biased, although bias was smaller on average in the doubly-ranked method. Analysts should compare results from both methods, as well as considering transforming the exposure to reduce heterogeneity in the genetic effect on the exposure.