The effect of heteroscedasticity on the prediction efficiency of genome-wide polygenic score for body mass index

Globally, more than 1.9 billion adults are overweight. Thus, obesity is a serious public health issue. Moreover, obesity is a major risk factor for diabetes mellitus, coronary heart disease, and cardiovascular disease. Recently, GWAS examining obesity and body mass index (BMI) have increasingly unveiled many aspects of the genetic architecture of obesity and BMI. Information on genome-wide genetic variants has been used to estimate the genome-wide polygenic score (GPS) for a personalized prediction of obesity. However, the prediction power of GPS is affected by various factors, including the unequal variance in the distribution of a phenotype, known as heteroscedasticity. Here, we calculated a GPS for BMI using LDpred2, which was based on the BMI GWAS summary statistics from a European meta-analysis. Then, we tested the GPS in 354,761 European samples from the UK Biobank and found an effective prediction power of the GPS on BMI. To study a change in the variance of BMI, we investigated the heteroscedasticity of BMI across the GPS via graphical and statistical methods. We also studied the homoscedastic samples for BMI compared to the heteroscedastic sample, randomly selecting samples with various standard deviations of BMI residuals. Further, we examined the effect of the genetic interaction of GPS with environment (GPS×E) on the heteroscedasticity of BMI. We observed the changing variance (i.e., heteroscedasticity) of BMI along the GPS. The heteroscedasticity of BMI was confirmed by both the Breusch-Pagan test and the Score test. Compared to the heteroscedastic sample, the homoscedastic samples from small standard deviation of BMI residuals showed a decreased heteroscedasticity and an improved prediction accuracy, suggesting a quantitatively negative correlation between the phenotypic heteroscedasticity and the prediction accuracy of GPS. To further test the effects of the GPS×E on heteroscedasticity, first we tested the genetic interactions of the GPS with 21 environments and found 8 significant GPS×E interactions on BMI. However, the heteroscedasticity of BMI was not ameliorated after adjusting for the GPS×E interactions. Taken together, our findings suggest that the heteroscedasticity of BMI exists along the GPS and is not affected by the GPS×E interaction.