Predicting human height by Victorian and genomic methods

Abstract

In the Victorian era, Sir Francis Galton showed that 'when dealing with the transmission of stature from parents to children, the average height of the two parents, ... is all we need care to know about them' (1886). One hundred and twenty-two years after Galton's work was published, 54 loci showing strong statistical evidence for association to human height were described, providing us with potential genomic means of human height prediction. In a population-based study of 5748 people, we find that a 54-loci genomic profile explained 4-6% of the sex- and age-adjusted height variance, and had limited ability to discriminate tall/short people, as characterized by the area under the receiver-operating characteristic curve (AUC). In a family-based study of 550 people, with both parents having height measurements, we find that the Galtonian mid-parental prediction method explained 40% of the sex- and age-adjusted height variance, and showed high discriminative accuracy. We have also explored how much variance a genomic profile should explain to reach certain AUC values. For highly heritable traits such as height, we conclude that in applications in which parental phenotypic information is available (eg, medicine), the Victorian Galton's method will long stay unsurpassed, in terms of both discriminative accuracy and costs. For less heritable traits, and in situations in which parental information is not available (eg, forensics), genomic methods may provide an alternative, given that the variants determining an essential proportion of the trait's variation can be identified.

Figure 1

Rate of regression in hereditary stature (Plate IX, figure a from Galton with superimposed data from the ERF study).

Figure 2

Observed sex- and age-adjusted height vs different predictive profiles. (a) Rotterdam Study, prediction with the genomic profile constructed from 54 loci, (b) ERF study, Galtonian prediction using mid-parental height values and (c) Rotterdam Study, a hypothetical profile explaining 80% of height variance. Red lines: mean residual height in people coming from top and bottom 5% of the profile distribution. Blue line: regression of the height residuals onto profile. In (b), green line has slope of 1, deviation of the blue line from the green showing ‘regression towards mediocrity'.

Figure 3

Accuracy to discriminate the top 5% tallest person, as measured by AUC, using different height profiles. (a) 54-loci genomic profile explaining 3.8% (54 loci, solid red line, AUC=65% in the Rotterdam Study), population-specific 54-loci genomic profile explaining 5.8% in the Rotterdam Study (estimated using the data, red dotted line, AUC=68% in the Rotterdam Study), mid-parental value explaining 40% (blue line, AUC=83% in the ERF study) and a hypothetical profile explaining 80% of height variance (green line, AUC=97%). (b) AUC achieved by a test explaining certain proportion of height variance; red: predicting top 50%, blue: predicting top 5%, green: predicting top 1%. Vertical lines: standard error of the mean.