Taxonomy 3. Methods. Log Bayes Factors (LBFs)

Enter/modify the SNP genotypes in the table below for these 5 cases and 7 controls subjects, and click on the button.

LBF : definition and properties for categorical variables (e.g. SNP).

We are using an informal inference technique that filters SNP data to extract meaning. It relies upon a directed discrete multivariate "Bayes Rule" measure of evidence for the SNP distinction of an individual free of genetic assumptions.

The LBFs are the observed difference in log genotype frequencies (between trait cases and controls) or a difference in the relative frequencies of categorical variables between the two groups. This measure transforms the characterisation of people from a binary domain of SNPs to a rapidly calculable continuous measure with simple additive properties.

For subject i, categorical variable j and categorical values k, the lbf value is :

Where:

Si,j,k = {0,1} : presence/absence of the kth categorical value (genotype) of the jth categorical variable (SNP) for the ith subject

nu and theta are bayesian estimates of the genotype frequencies (non-informative beta prior) :

This Bayes Factor or 'diagnostic' likelihood ratio (DLR) is the amount of evidence that the ith case individual is classified as not having the same genome as that of a set of controls. LBFs are a directed or asymmetric measure that indicate the 'case-ness' of an individual i.e. their propensity to be a non-control. In other words, LBF values for each individual (i.e. the individualised difference in information content) represent that person's relative contribution to the 'case-ness' in this overall distinction, or 'index of separation', between the groups.

This extremely simple empirical Bayesian predictive measure is effectively the summation of case-control contrasts (i.e. group by SNP genotype differences or interaction) over genotypes x loci from a log-linear model estimated for each locus on its own (partial log-linear modeling) of all subjects in 2 groups, instantiated by the presence of the SNP genotype markers in that individual.

This method non-linearly deforms or amplifies the SNP data space by re-weighting all subjects with the observed between group differences in order to yield a continuous measure of the genetic model involved in that trait.

This measure has simple additive properties and can be used in any linear algebra tool: addition, averaging, moments, singular value decomposition, eigen analysis, recursive partitioning, ....