Multipoint linkage-disequilibrium-mapping approach based on the case-parent trio design

Abstract

In the present study we propose a multipoint approach, for the mapping of genes, that is based on the case-parent trio design. We first derive an expression for the expected preferential-allele-transmission statistics for transmission, from either parent to an affected child, for an arbitrary location within a chromosomal region demarcated by several genetic markers. No assumption about genetic mechanism is needed in this derivation, beyond the assumption that no more than one disease gene lies in the region framed by the markers. When one builds on this representation, the way in which one may maximize the genetic information from multiple markers becomes obvious. This proposed method differs from the popular transmission/disequilibrium test (TDT) approach for fine mapping, in the following ways: First, in contrast with the TDT approach, all markers contribute information, regardless of whether the parents are heterozygous at any one marker, and incomplete trio data can be utilized in our approach. Second, rather than performing the TDT at each marker separately, we propose a single test statistic that follows a chi(2) distribution with 1 df, under the null hypothesis of no linkage or linkage disequilibrium to the region. Third, in the presence of linkage evidence, we offer a means to estimate the location of the disease locus along with its sampling uncertainty. We illustrate the proposed method with data from a family study of asthma, conducted in Barbados.

Figure 1

Plots of E[Y(t)|Φ] versus t, for 0⩽t⩽80 cM, where τ=45 cM and Pr[h(t)|h(τ)] is assumed to be equal to 1.0-.01 × |t-τ|. a, N=10 with different values of C=E[Y(τ)|Φ]; b, C=.5 with different values of N.

Figure 2

Plots of E[Y(t)|Φ] versus t, for 0⩽t⩽80 cM, where τ=45 cM and Pr[h(t)|h(τ)] is generated from a uniform distribution over (.5, 1.0). a, N=10 with different values of C; b, C=.5 with different values of N.

Figure 3

TDT values for the 22 markers on chromosome 12 from the family study of asthma (Barnes et al. 1996). The solid line (—) denotes the conventional TDT; the dashed line (- - -) denotes the modified TDT.

Figure 4

Number of allele transmissions from heterozygous parents, for the 22 markers on chromosome 12 from the family study of asthma (Barnes et al. 1996).

Figure 5

Empirical and fitted values for the expected preferential-transmission statistics for the 22 markers on chromosome 12 from the family study of asthma (Barnes et al. 1996). The solid line (—) denotes the empirical E(Y(t)|Φ); the dashed line (- - -) denotes the empirical E[Y(t)|Φ]/Pr[h(t)|h(τ)]; the dotted line (⋅⋅⋅) denotes the fitted E[Y(t)|Φ]/Pr[h(t)|h(τ)].

Figure 6

Estimated Pr[h(t)|h(τ)] for the 22 markers on chromosome 12 from the family study of asthma (Barnes et al. 1996)