Figure 3.
Schematic view of the multivariate linkage analysis strategy. First, we transformed the tumor necrosis factor (TNF) produced in response to BCG vaccine and TNF produced in response to BCG plus interferon-γ into a set of 2 uncorrelated new variables, PC1 and PC2, by means of principal component analysis. Then, univariate quantitative model-free linkage analyses of PC1 and PC2 were conducted using the new maximum-likelihood-binomial method for quantitative traits (nMLB-QTL) approach. A multivariate test statistic T was defined as T = LRTPC1 + LRTPC2, where LRTPC1 and LRTPC2 denote the univariate nMLB-QTL likelihood ratio tests of PC1 and PC2, respectively. Finally we derived the asymptotic distribution of T as being a mixture of 3 χ² distributions with 0, 1, and 2 degrees of freedom. Abbreviations: LRT, likelihood ratio test; nMLB-QTL, new maximum-likelihood-binomial method for quantitative traits; PC, principal component; PCA, principal components analysis; TNF-BCG, tumor necrosis factor induced by BCG vaccine; TNF-BCG + γ, tumor necrosis factor induced by BCG vaccine plus interferon-γ.