The performance of polygenic indices is typically assessed in terms of the amount of phenotypic variance they explain in independent prediction samples. For some applications, however, the correct ranking of individuals in the polygenic index distribution is of higher importance. Using simulations and empirical applications, we analyze common approaches of polygenic index construction methods in terms of their concordance in ranking individuals. We find that, even for highly heritable traits, (i) the exact ranking of individuals in the polygenic index distribution is characterized by large uncertainty, and (ii) the ranking is highly unstable across construction methods. The profound consequences for personalized screening are illustrated in simulations and with an empirical application for cardiovascular disease in the UK Biobank.