Fig 1.
Schematics for the association measure for 2-order interaction with binary and multiple outcome classes.
With binary outcome, phenotype is observed as either case or control for each sample, sorted by the multifactor class, and cumulated separately for case and control. Risk status (Ri) for each multifactor class is classified as high (H) or low (L) by comparing the ratio nicase/nicontrol with a certain threshold. With multi-class outcome, only the sorted and cumulated numbers of samples (nij) for each multifactor class are required, where i and j represent the genotypic and phenotypic class, respectively.
Fig 2.
Penetrance assigning scheme in simulation I.
Five risk status patterns for 3-class phenotype were devised in [15]. Pattern tells which of the 3-classes has the largest odds ratio. One of the specific set of the odds ratios that satisfies the pattern 1 is shown here. With fixed prevalence for each class, a set of penetrance can be determined.
Fig 3.
Comparison of performance (simulation dataset I).
Performances of GIDS and OMDR as well as χ2 are compared for the simulation datasets of fifteen models grouped in five patterns. All models are designed to have a single causal pair with two-way interactions and three phenotypic classes. Hit ratio is defined as the ratio identifying the causal pair correctly in “Two-Locus”. In “Single-Locus” it is the ratio identifying either of the causal pairs. The ratio identifying the combination that includes the causal pair is plotted in “Three-Locus”.
Fig 4.
Comparison of performance (simulation dataset II).
A simulation dataset whose quantitative phenotype distribution was made out of three Gaussians was analyzed for the 2-order interaction. Hit ratios were obtained using several methods and compared (A) using the same dataset. GIDS-J2, -J3, and -J4 use the phenotypes of two, three, and four classes categorized beforehand. GMDR and QMDR accept the quantitative phenotype but perform a dichotomous categorization of their own. Only m-spacing analyzes the quantitative simulation dataset in its original form. Hit ratios from GIDS and χ2 are also compared (B).
Table 1.
Type I error estimation with a significance level (α) of 0.05.
Table 2.
Classification of blood pressure (BP) with simultaneous consideration of systolic (SBP) and diastolic (DBP) blood pressure.
Fig 5.
Top associated SNPs and SNP pairs with BP.
Applying GIDS to the KARE dataset with the nine composite classes of BP identified the top associated SNPs in the one-locus model (A) and the interacting SNP pairs in the two-locus model (B).
Table 3.
Top associated SNPs in the one-locus model with permutation p-values.
Table 4.
Top associated interacting SNP pairs in the two-locus model with permutation p-values.