## Results: 5

1.

2.

The subplots show density histograms for the distribution of LRs achieved by complete (solid red line) and restricted (dotted red line) family history models, and probability density functions for the distribution of LRs achieved by genetic factors accounting for either 10% (dotted blue line), 30% (dashed blue line), or 100% (solid blue line) of the heritability of the disease. As a technical aside, since all plots are shown on a logarithmic scale, the density histograms and density functions shown here were derived for rather than itself (see ).

3.

(A) In the family structure shown, the shaded box represents the index individual, whose risk of developing the disease we wish to predict. (B) There are possible combinations of disease status for the individuals in the family. Using the liability threshold model, we compute the probability of each combination; in this example, we assume and . (C) From the joint distribution, we can then compute the disease risk of the index individual for any given family history pattern, as well as the likelihood of particular family history patterns among cases and controls. (D) These quantities then allow us to construct the receiver operating characteristic (ROC) curve for a complete family history-based classifier, from which sensitivity, specificity, PPV, NPV, and AUC can be computed.

4.

Each cell of the grid corresponds to a different combination of disease characteristics: rows correspond to differing heritabilities () and columns correspond to differing frequencies (). Within each cell, the subplots compare the AUC when using a complete family history model that accounts for the disease status of every individual in the pedigree (solid red line), a restricted family history model that only considers the number (0, 1, or 1) of affected first-degree relatives of the index individual (dashed red line), or genetic risk factors for the index individual only (blue line). For each subplot, the horizontal axis indicates the proportion () of heritability explained by known SNP associations, and the vertical axis indicates the AUC. Arrows indicate points of equivalence—values of and for which family history and SNP-based methods give the same AUC.

5.

Subpanels (A) and (B) contain contour plots showing the proportion of heritability explained () by a complete family history model and a restricted family history model, respectively. Horizontal and vertical axes correspond to varying disease frequency () and heritability (). Lines in each subplot depict the level curves of , i.e., the combinations of and for which the proportion of heritability explained by family history is constant. SNP-based risk models for specific diseases are illustrated by circles (when the SNP-based model outperforms family history) and squares (when family history outperforms the SNP-based model). The circle or square for each SNP-based model has been colored to indicate the estimated proportion of heritability explained by SNPs, using the same color scheme as the contour plot (e.g., blue indicates 25–30% of heritability explained whereas red indicates 5% of heritability explained). Note that the performance of SNP-based models shown here reflects only currently known genetic factors for European populations and will change as more associations are discovered.