threshold specific to this study) and at a nominal significance threshold of p < 0 . 05 for HT. Six of these display no evidence against colocalisation (all posterior predictive p > 0 . 01), the exception being 2q33.2/ CTLA4 / ICOS in which the ppp value for the BMA approaches is 6 × 10 − 3 (two SNP models) or 8 × 10 − 5 (three SNP models). In this region, the profile of the single SNP p values do differ (Supplementary Figure 11), but it would require larger sample sizes to confidently conclude that the two diseases have different causal variants in this region given the number of tests completed. The coefficient of proportionality, η , can be usefully interpreted when analysing two diseases. Two values of particular interest are η = 0 which would indicate no effect in HT given an effect in GD and η = 1 which indicates equal effects in each disease. In most of the seven regions, the credible interval for η includes 1 (Figure 5), the exceptions being 2q33.2 and 10p15.1, where it ends just below 1 using a PCs approach, and 3q27.3/3q28/ LPP where it starts just above 1 on either BMA approach. Turning to the the six regions where there is evidence of association in only GD, we do not expect to see any departure from the null of colocalisation, without evidence of association to both traits, and indeed all posterior predictive p > 0 . 01. However, our estimate of η helps infer whether this reflects a lack of power or genuine absence of association for HT. We evaluated the credible intervals for η in each region and across four of the six regions, the credible interval for η includes 0, whilst in only one does the credible interval include 1 for all approaches. In one 14q31.1/ TSHR , the credible interval ends just below 0 for the BMA approaches, whilst for 6q27/ CCR6 , it starts just above 0 and includes 1 for all methods. TSHR represents the primary autoantigen in hyperthyroidism of GD [Brand and Gough, 2010], so is unlikely to be involved in HT. There are two sources to the bias in colocalisation testing presented above. The problem of variable selection is well studied in statistics generally [Miller, 1984] but has perhaps been neglected in statistical genetics, where the aim has been to detect convincing association to a region, rather than pinpoint the causal variant, particularly as most datasets to date have included an incomplete selection of variants in any region. Selecting SNPs which do not fully capture the trait association Discussion 14