Prediction Bias

Bias

Let Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \u<\math> be the true progeny difference (TPD) and <math>\hat y} be our estimate (EPD). From this we could estimate the degree of bias in our estimate by determining the difference in the mean u and mean u^. However, we never observe the TPD. Instead we estimate it using pedigree, performance, and genomic data.

We can approximate the degree of bias and under/over dispersion of EPD by using regression techniques. One such way to do this is to regress the EPD with more information (e.g., genomic EPD) on the EPD with less information (e.g, pedigree-based EPD). Our expectation is that the intercept from this regression is 0 (no bias) and the slope of the regression is 1 (no over or under dispersion). Our expectations come from the theory of BLUP where u^ is an unbiased estimator of u and that

Covar (EPD, EPD)/Var (EPD) = Covar (1/2a,1/2a)/Var(1/2a) = Var(1/2a)/Var(1/2a) = 1

A fundamental assumption is that the ratio of variance components used to generate both sets of EPD are the same. if they are not, then the expectation of the regression coefficient being 1 no longer holds.

Another approach is to regress phenotypes after being corrected for systematic effects on EPD. Here the expectation of the regression coefficient is 2.

Covar (corrected phenotype, EPD)/var (EPD) = Covar (a +e, 1/2a)/var (1/2a) = 1/2 var (a) /1/4 var (a) =2

If EBV were used instead of EPD the expectation of the regression coefficient would be 1.

A key assumption is that the phenotype of the individual is not included in the EPD of that individual. Consequently, this approach lends itself to cross-validation or forward in time validation strategies whereby some set(s) of animals have their phenotypes masked in the genetic evaluation.

In similar fashion, average progeny performance (corrected for systematic effects) can be regressed on parent (sire) EPD. This is done annually at the US Meat Animal Research Center as part of the process to update across-breed EPD adjustment factors. The expectation of the regression coefficient is 1 in this case and assumes that the progeny information used is not part of the sire's EPD. A regression coefficient of less than 1 suggests that the EPD are over-dispersed meaning that a one unit change in EPD will generate less than a one unit change in progeny phenotypes.