A data-adaptive method for investigating effect heterogeneity with high-dimensional covariates in Mendelian randomization.

"the fitted data used for generating the results in both the simulation and applied example are provided at https://github com/hdtian/rfqt/tree/main/data0 ."

"the code for implementing the effect heterogeneity analysis in mr is available at https://github com/hdtian/rfqt .; the fitted data used for generating the results in both the simulation and applied example are provided at https://github com/hdtian/rfqt/tree/main/data0 .; 4 2 2 mit license) is available at https://github com/hdtian/rfqt .; the illustration codes are provided on https://github com/hdtian/rfqt/tree/main/illustration_sim_real which allows the reader to reproduce all results and adapt the presented methodology to their own research."

"Declarations Ethics approval and consent to participateThe UK Biobank study has approval from the North West Multicentre Research Ethics Committee (11/NW/0382). Participants provided written informed consent to the use of their medical records and samples to be used for health-related research purposes: see https://www.ukbiobank.ac.uk/media/05ldg1ez/consent-form-uk-biobank.pdf for consent statement. This study was conducted in accordance to relevant guidelines and regulations. Consent to publicationNot applicable. Competing interestsThe authors declare no competing interests. Competing interests The authors declare no competing interests."

"Funding This work was supported by the Wellcome Trust (225790/Z/22/Z) and the United Kingdom Research and Innovation Medical Research Council (MC_UU_00002/7). B.D.M.T. is supported through the United Kingdom Medical Research Council programme grant MC_UU_00002/2. S.B. is supported by a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (204623/Z/16/Z). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The research has been conducted using the UK Biobank Resource under Application Number 98032."