In this the second of an anticipated four papers, we examine polygenic risk scores from a quantitative genetics perspective. In its most simplistic form, a polygenic risk score (PRS) analysis involves estimating the genetic effects of alleles in one study and then using those estimates to predict phenotype in another sample of individuals. Almost since the first application of these types of analyses it has been noted that PRSs often give unexpected and difficult-to-interpret results, particularly when applying effect-size estimates taken from individuals with ancestry very different than those to whom it is applied (applying PRSs across differing populations). To understand these seemingly perplexing observations, we deconstruct the effects of applying valid statistical estimates taken from one population to another when the two populations have differing allele frequencies at the sites contributing effect, when alleles with effects in one population are absent from the other, and finally when there is differing linkage disequilibrium (LD) patterns in the two populations. It will be shown that many of the seemingly most confusing results in the field are natural consequences of these factors. Given our best current understanding of human demographic history, most of the patterns seen in PRS analysis can be predicted as resulting from systematic differences in allele frequency and LD. Put the other way around, the most challenging and confusing results seen in cross population application of PRSs are likely to be the result of allele frequency and LD differences, not differences in the genetic effects of individual alleles. PRS analysis is an important tool both for understanding the genetic basis of complex phenotypes and, potentially, for identifying individuals at risk of developing disease before such disease manifests. As such it has the potential to be among the most important analysis frameworks in human genetics. Nevertheless, when a PRS is trained in people with one ancestry and then applied to people with another, the PRS’s behavior is often unpredictable, and sometimes is seemingly perverse. PRS distributions are often nearly non-overlapping between individuals with differing ancestry, i.e., odds ratios for unaffected people with one ancestry might be vastly larger than affected individuals from another. The correlation between a PRS and known phenotype might differ substantially, and sometimes the correlation is higher among people with ancestry different than the one used to create the PRS. Naively, one might conclude from these observations that the genetic basis of traits differs substantially among people of differing ancestry, and that the behavior of a PRS is difficult to predict when applied to new study populations. Differing definitions of genetic effect sizes are discussed, and key observations are made. It is shown that when populations differ in allele frequency, a locus affecting phenotype could have equal differences in allelic (additive) effects or equal additive variances, but not both. They cannot have equal additive effects, equal allelic penetrances, or equal odds ratios. PRS is defined, and its moments are derived. The effect of differing allele frequency and LD patterns is described. Perplexing PRS observations are discussed in light of theory and human demographic history. Suggestions for best practices for PRS construction are made. The most confusing results seen in cross population application of PRSs are often the predictable result of allele frequency and LD differences. There is relatively little evidence for systematic differences in the genetic basis of disease in individuals of differing ancestry, other than that which results from environmental, allele frequency, and LD differences.
