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Genetic studies of disease progression can be used to identify factors that may influence survival or prognosis, which may differ from factors that influence on disease susceptibility. Studies of disease progression feed directly into therapeutics for disease, whereas studies of incidence inform prevention strategies. However, studies of disease progression are known to be affected by collider (also known as "index event") bias since the disease progression phenotype can only be observed for individuals who have the disease. This applies equally to observational and genetic studies, including genome-wide association studies and Mendelian randomisation (MR) analyses. In this paper, our aim is to review several statistical methods that can be used to detect and adjust for index event bias in studies of disease progression, and how they apply to genetic and MR studies using both individual- and summary-level data. Methods to detect the presence of index event bias include the use of negative controls, a comparison of associations between risk factors for incidence in individuals with and without the disease, and an inspection of Miami plots. Methods to adjust for the bias include inverse probability weighting (with individual-level data), or Slope-Hunter and Dudbridge et al.'s index event bias adjustment (when only summary-level data are available). We also outline two approaches for sensitivity analysis. We then illustrate how three methods to minimise bias can be used in practice with two applied examples. Our first example investigates the effects of blood lipid traits on mortality from coronary heart disease, while our second example investigates genetic associations with breast cancer mortality. [ABSTRACT FROM AUTHOR]