Discriminatory accuracy from single-nucleotide polymorphisms in models to predict breast cancer risk

Abstract

One purpose for seeking common alleles that are associated with disease is to use them to improve models for projecting individualized disease risk. Two genome-wide association studies and a study of candidate genes recently identified seven common single-nucleotide polymorphisms (SNPs) that were associated with breast cancer risk in independent samples. These seven SNPs were located in FGFR2, TNRC9 (now known as TOX3), MAP3K1, LSP1, CASP8, chromosomal region 8q, and chromosomal region 2q35. I used estimates of relative risks and allele frequencies from these studies to estimate how much these SNPs could improve discriminatory accuracy measured as the area under the receiver operating characteristic curve (AUC). A model with these seven SNPs (AUC = 0.574) and a hypothetical model with 14 such SNPs (AUC = 0.604) have less discriminatory accuracy than a model, the National Cancer Institute's Breast Cancer Risk Assessment Tool (BCRAT), that is based on ages at menarche and at first live birth, family history of breast cancer, and history of breast biopsy examinations (AUC = 0.607). Adding the seven SNPs to BCRAT improved discriminatory accuracy to an AUC of 0.632, which was, however, less than the improvement from adding mammographic density. Thus, these seven common alleles provide less discriminatory accuracy than BCRAT but have the potential to improve the discriminatory accuracy of BCRAT modestly. Experience to date and quantitative arguments indicate that a huge increase in the numbers of case patients with breast cancer and control subjects would be required in genome-wide association studies to find enough SNPs to achieve high discriminatory accuracy.

Figure 1

Cumulative distributions of the log_e relative risk, F_rr(t), for the seven–single-nucleotide polymorphism (SNP) model (thin dashed line), a 14-SNP model with the original seven SNPs plus seven more SNPs with identical characteristics (thin solid line), the Breast Cancer Risk Assessment Tool (BCRAT; thick dashed line), and BCRAT plus the seven SNPs (thick solid line).

Figure 2

Probability that a case patient has a risk greater than t, [1–FD_r(t)], plotted against the probability that a member of the general population has a risk greater than t, [1–F_r(t)], as t (not shown) varies from 0 to 1. Separate curves are shown for the seven–single-nucleotide polymorphism (SNP) model (thin dashed line), a 14-SNP model with the original seven SNPs plus seven more such SNPs (thin solid line), the Breast Cancer Risk Assessment Tool (BCRAT) (thick dashed line), and BCRAT plus the seven SNPs (thick solid line). The areas under these curves are measures of discriminatory accuracy and approximate the areas under the receiver operating characteristic curve.