Cross-fitted instrument: a blueprint for one-sample Mendelian Randomization

Summary Bias from weak instruments may undermine the ability to estimate causal effects in instrumental variable regression (IVR). We present here a simple solution for handling weak instrument bias by introducing a new type of instrumental variable called ‘cross-fitted instrument’ (CFI). CFI splits the data at random and estimates the impact of the instrument on the exposure in each partition. The estimates are then used to perform an IVR on each partition. We adapt CFI to Mendelian randomization (MR) and term this adaptation ‘Cross-Fitting for Mendelian Randomization’ (CFMR). A major advantage of CFMR is its use of all the available data to select genetic instruments, as opposed to traditional two-sample MR where a large part of the data is only used for instrument selection. Consequently, CFMR has the potential to enhance the power of MR in a meta-analysis setting by enabling an unbiased one-sample MR to be performed in each cohort prior to meta-analyzing the results across all the cohorts. In a similar fashion, CFMR enables a cross-ethnic MR analysis by accounting for ethnic heterogeneity, which is particularly important in consortia-led meta-analyses where the participating cohorts might be of different ethnicities. To our knowledge, there are currently no MR approach that can account for such heterogeneity. Finally, CFMR enables the application of MR to exposures that are rare or difficult to measure, which would normally preclude their analysis in the regular two-sample MR setting. Key messages We develop a new method to enable an unbiased one-sample Mendelian Randomization. The new method provides the same power as the standard two-sample Mendelian Randomization approach and does not require summary statistics from a genome-wide association study in an independent cohort. Our approach enables a cross-ethnic instrumental variable regression to account for heterogeneity in a sample consisting of multiple ethnicities.