Cross-fitted instrument: A blueprint for one-sample Mendelian randomization.

Bias from weak instruments may undermine the ability to estimate causal effects in instrumental variable regression (IVR). We present here a new approach to handling weak instrument bias through the application of a new type of instrumental variable coined 'Cross-Fitted Instrument' (CFI). CFI splits the data at random and estimates the impact of the instrument on the exposure in each partition. These estimates are then used to perform an IVR on each partition. We adapt CFI to the Mendelian randomization (MR) setting and term this adaptation 'Cross-Fitting for Mendelian Randomization' (CFMR). We show that, even when using weak instruments, CFMR is, at worst, biased towards the null, which makes it a conservative one-sample MR approach. In particular, CFMR remains conservative even when the two samples used to perform the MR analysis completely overlap, whereas current state-of-the-art approaches (e.g., MR RAPS) display substantial bias in this setting. Another major advantage of CFMR lies in its use of all of the available data to select genetic instruments, which maximizes statistical power, as opposed to traditional two-sample MR where only part of the data is used to select the instrument. Consequently, CFMR is able to enhance statistical power in consortia-led meta-analyses by enabling a conservative one-sample MR to be performed in each cohort prior to a meta-analysis of the results across all the cohorts. In addition, CFMR enables a cross-ethnic MR analysis by accounting for ethnic heterogeneity, which is particularly important in meta-analyses where the participating cohorts may have different ethnicities. To our knowledge, none of the current MR approaches can account for such heterogeneity. Finally, CFMR enables the application of MR to exposures that are either rare or difficult to measure, which would normally preclude their analysis in the regular two-sample MR setting.