Our analytic result is derived from linear regression models, and is inexact for traits generated under other models13,17. However, in practice our approach only requires that the bias is linear in the incidence effect, which we argue is approximately true for polygenic traits. This linear relationship is estimated from data, and while our theory provides an interpretation for it under some assumptions, our approach requires only that such a relationship exists. The data in our examples used log odds ratios and log hazard ratios, and our simulations suggested the linear approximation was acceptable in these cases.
