Inferring on joint associations from marginal associations and a reference sample

We present a method to infer on joint regression coefficients obtained from marginal regressions using a reference panel. This type of scenario is common in genetic fine-mapping, where the estimated marginal associations are reported in genomewide association studies (GWAS), and a reference panel is used for inference on the association in a joint regression model. We show that ignoring the uncertainty due to the use of a reference panel instead of the original design matrix, can lead to a severe inflation of false discoveries and a lack of replicable findings. We derive the asymptotic distribution of the estimated coefficients in the joint regression model, and show how it can be used to produce valid inference. We address two settings: inference within regions that are pre-selected, as well as within regions that are selected based on the same data. By means of real data examples and simulations we demonstrate the usefulness of our suggested methodology.