we would expect the association between smoking and having qualifications to be positively biased (i.e. we would expect to see a more positive association between genetic variants positively associated with smoking and whether participants had educational qualifications in UK Biobank than in the UK population). The problem is possibly compounded in genetic studies using the first release of genome-wide association data in UK Biobank, which used two genotyping arrays, one of which was applied to a nested case-control study of smoking and lung function (UK BiLEVE).41 The first release genetic data are therefore further subject to selection bias relative to UK Biobank as a whole (although this will no longer be the case when the full release of genome-wide association data becomes available).Box 2). However, it is often assumed that although selection bias will have a strong effect on prevalence estimates, it should not have a strong impact on observed associations between variables.8 This overlooks the fact that selection can induce collider bias (see Figure 1), which can lead to biased observational and genetic associations. This bias can be towards or away from any true association, and can distort a true association or a true lack of association.
