Description of mathematical variables used in the combined haplotype test
Variable Description
Index variables
\(h\) test number (one per test SNP / target region pair)
\(i\) individual
\(j\) target region
\(k\) SNP within target region
\(m\) test SNP
Latent variables
\(\alpha_h\) molecular phenotype level of the reference allele for test \(h\)
\(\beta_h\) molecular phenotype level of the alternative allele for test \(h\)
\(p_h\) fraction of allele-specific reads expected from reference allele \((p_h = \frac{\alpha_h}{\alpha_h + \beta_h})\)
\(T^{*}_{i,j}\) genotype-independent expected total read count for individual \(i\), target region \(j\)
\(\lambda_{hi}\) expected total read count for test \(h\), individual \(i\)
\(\Omega_i\) overdispersion of read counts for individual \(i\) (across all tests)
\(\phi_j\) overdispersion of read counts for test number \(j\) (across all individuals)
\(\Upsilon_i\) overdispersion of allele-specific reads for individual \(i\)
Observed variables
\(x_{ij}\) number of reads for individual \(i\), target region \(j\)
\(G_{im}\) genotype call for individual \(i\), test SNP \(m\)
\(T_{i}\) total number of genome-wide mapped reads for individual \(i\)
\(n_{ik}\) total number of allele-specific reads for individual \(i\), target SNP \(k\)
\(y_{ik}\) number of allele-specific reads from reference haplotype for individual \(i\), target SNP \(k\)
\(H_{ik}\) probability individual \(i\) is heterozygous for target SNP \(k\)

\label{tab:variables}