A note on using ‘forward prediction’ to assess precision and bias of genomic predictions

Abstract

It has been argued repeatedly that cross-validation (CV) correlations should be used as a benchmark to assess matters of precision and bias of genomic predictions (GEBV) in practical applications. Irrespective of the fact that CV in this discussion is used in the very limited meaning of doing one single forward-prediction, we show by the use of standard formulae and simple simulation techniques that in traits underlying selection correlations derived from these techniques are considerably influenced by effects of selection on observed variances. As a consequence the squared correlations will be underestimations of the true precision of the estimates and the degree of underestimation depends on the number of selection steps, the selection intensity applied in any of them and the selection criteria applied in each step. The underestimation might be severe, so that without some reasonable assumptions about the selective conditions in a validation group no general conclusion about the precision and bias of genomic estimates can be drawn from a forward-prediction or comparable CV procedures. Additionally, we show that although correlation-measures are influenced by the effects of selection, linear combinations of estimates (e.g. differences between genomic predictions and daughter-based conventional estimates) are not much affected by the effects of selection. It is argued that the analysis of these differences could be a helpful extension to common validation tests for GEBV. We suppose that the aspects covered by this investigation will become increasingly important in the near future, when validation groups eventually will consist entirely of animals preselected on GEBV. However, in this case even the underlying conventional breeding value estimation will be influenced by the effects of selection.