This paper investigates the bias in Mendelian randomization analyses when there is overlap between participants in two datasets. The authors use simulation studies to explore the magnitude and direction of bias, particularly in the context of continuous and binary outcomes. They find that bias in a two-sample Mendelian randomization analysis is linearly related to the proportion of sample overlap. For a continuous outcome, bias increases with the proportion of overlap, while for a binary outcome, bias is negligible if the genetic associations with the risk factor are estimated only in control participants. The paper also provides analytical formulae for calculating expected bias and Type I error rates, which are validated through simulations. Additionally, the authors discuss the implications of sample overlap in large genetic consortia and offer practical recommendations to mitigate bias, such as using genetic associations from non-overlapping data sources or equal weights for genetic variants.This paper investigates the bias in Mendelian randomization analyses when there is overlap between participants in two datasets. The authors use simulation studies to explore the magnitude and direction of bias, particularly in the context of continuous and binary outcomes. They find that bias in a two-sample Mendelian randomization analysis is linearly related to the proportion of sample overlap. For a continuous outcome, bias increases with the proportion of overlap, while for a binary outcome, bias is negligible if the genetic associations with the risk factor are estimated only in control participants. The paper also provides analytical formulae for calculating expected bias and Type I error rates, which are validated through simulations. Additionally, the authors discuss the implications of sample overlap in large genetic consortia and offer practical recommendations to mitigate bias, such as using genetic associations from non-overlapping data sources or equal weights for genetic variants.