Two-Loci Genetic P-Value Plot

The Two-Loci genetic plot shows the statistical significance of performing associations of pairs of genetic markers with the response variable(s).

Figure 1. Two-loci genetic association plot.

Selecting the Two-Loci option will cause HelixTree to attempt a categorical split upon every possible pair of genetic variables in the node, using the node’s response variable or variables. The resulting p-values are shown on the color axis of a three-axis plot. (If a split cannot be performed, a p-value of one will be assigned.)

In Figure 1 we see that there are a number of significant pairwise associations in the region between markers 25 and 50. You can plot the negative of the base-10 logarithm of the raw p-value, the adjusted p-value, or the Bonferroni adjusted p-value. The Bonferroni adjustment for multiple testing is equal to the number of pairs for which associations are performed.

Technically the two locus association is performed as follows. For a given pair of markers, combine the markers to form a new categorical variable. For instance, suppose marker1 had the value 0_1 for patient 1, and marker2 had the value 2_2 for patient 1. A combined variable is temporarily created, marker1-marker2 with the value 0_1-2_2 for patient 1. Similarly, the combination variables are created for each patient to form a column vector marker1-marker2 that is used as a predictor variable. Then, a categorical split is performed behind the scenes to obtain the p-value of the association. The tree options determine the splitting criteria for the categorical split, including the maximum split cardinality and whether or not you wish to drop missing values.

In principle, with two bi-allelic markers, each having 3 possible values, there are 9 possible combined markers.

Once a plot is generated you can click on any point of interest and statistical information about that point will be displayed in the plot’s lower left hand corner.

Figure 2. Two-loci genetic association spreadsheet.

You can view more specific split information concerning a specific point as seen in Figure 2. This table first summarizes the split groupings in its header area. For each grouping, the average and standard deviation of the response variable are shown, along with the count. The main part of the table then shows each combination of genotypes, giving the response average, the response standard deviation, the count, and which split grouping the combination belongs to.