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The Generalized Relative Pairs IBD Distribution: Its Use in the Detection of Linkage

View Article: PubMed Central - PubMed

ABSTRACT

I introduce a novel approach to derive the distribution of disease affectional status given alleles identical by descent (IBD) sharing through ITO method. My approach tremendously simplifies the calculation of the affectional status distribution compared to the conventional method, which requires the parental mating information, and could be applied to disease with both dichotomous trait and quantitative trait locus (QTL). This distribution is shown to be independent of relative relationship and be employed to develop the marker IBD distributions for relative relationship. In addition, three linkage tests: the proportion, the mean test, and the LOD score test are proposed for different relative pairs based on their marker IBD distributions. Among all three tests, the mean test for sib pair requires the least sample size, thus, has the highest power. Finally, I evaluate the significance of different relative relationships by a Monte-Carlo simulation approach.

No MeSH data available.


The LOD test power for doubly affected relative pairs with the dichotomous trait and extreme discordant relative pairs with QTL. Required sample size N of level α = 0.001 LOD score test with 90% power to detect linkage θ for doubly affected relative pairs (A) and extreme discordant relative pairs with QTL(C). Power to detect linkage θ of level α = 0.001 LOD score test by using N = 300 doubly affected relative pairs (B) and N = 300 extreme discordant relative pairs with QTL(D).
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Figure 2: The LOD test power for doubly affected relative pairs with the dichotomous trait and extreme discordant relative pairs with QTL. Required sample size N of level α = 0.001 LOD score test with 90% power to detect linkage θ for doubly affected relative pairs (A) and extreme discordant relative pairs with QTL(C). Power to detect linkage θ of level α = 0.001 LOD score test by using N = 300 doubly affected relative pairs (B) and N = 300 extreme discordant relative pairs with QTL(D).

Mentions: Note that the parameter of interest is not the recombination fraction θ any more, but Nj, the count of relative pairs sharing j allele(s) IBD. With denoting the ML estimates for ϵ as it varies in the parameter space, then the LOD score T for the likelihood ratio test based on equation (10) is given by(11)T=2lgϵ^Nϵ^(1−ϵ^)N(1−ϵ^)ϵ0Nϵ^(1−ϵ0)N(1−ϵ^),where is the conditional marker IBD probabilities under hypothesis. Thus, the likelihood ratio test statistic T asymptotically distributed as χ2 with 1 d.f. Defining equation (11) as T(Nj, N), and assuming level-α test with 1 −β power, I obtain {Nj, N} for each relative relationship as the critical size of relative pairs sharing allele IBD and total required sample size, respectively. One can check easily that T is an increasing function of Nj when Ns are fixed. In other words, for an each N, I reject the hypothesis if the counts of allele IBD are greater than Nj. Usually, the LOD score test use more strict criterion than the proportion test does. Here, the total required sample size N of the 90% power, level α = 0.001 LOD score test power is plotted as a function of the recombination fraction θ for both doubly affected relative pairs with the dichotomous trait and extreme discordant relative pairs with QTL (Figures 2A,C). In many respects, they behave similarly such that sib pairs have larger power for low θ, while grandparent–grandchild pairs have the best power for high θ (Figures 2B,D). In general, both critical allele IBD sharing size Nj and total relative pair size N are increasing as θ gets closer to 0.5 or as the power of the test increases.


The Generalized Relative Pairs IBD Distribution: Its Use in the Detection of Linkage
The LOD test power for doubly affected relative pairs with the dichotomous trait and extreme discordant relative pairs with QTL. Required sample size N of level α = 0.001 LOD score test with 90% power to detect linkage θ for doubly affected relative pairs (A) and extreme discordant relative pairs with QTL(C). Power to detect linkage θ of level α = 0.001 LOD score test by using N = 300 doubly affected relative pairs (B) and N = 300 extreme discordant relative pairs with QTL(D).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5120125&req=5

Figure 2: The LOD test power for doubly affected relative pairs with the dichotomous trait and extreme discordant relative pairs with QTL. Required sample size N of level α = 0.001 LOD score test with 90% power to detect linkage θ for doubly affected relative pairs (A) and extreme discordant relative pairs with QTL(C). Power to detect linkage θ of level α = 0.001 LOD score test by using N = 300 doubly affected relative pairs (B) and N = 300 extreme discordant relative pairs with QTL(D).
Mentions: Note that the parameter of interest is not the recombination fraction θ any more, but Nj, the count of relative pairs sharing j allele(s) IBD. With denoting the ML estimates for ϵ as it varies in the parameter space, then the LOD score T for the likelihood ratio test based on equation (10) is given by(11)T=2lgϵ^Nϵ^(1−ϵ^)N(1−ϵ^)ϵ0Nϵ^(1−ϵ0)N(1−ϵ^),where is the conditional marker IBD probabilities under hypothesis. Thus, the likelihood ratio test statistic T asymptotically distributed as χ2 with 1 d.f. Defining equation (11) as T(Nj, N), and assuming level-α test with 1 −β power, I obtain {Nj, N} for each relative relationship as the critical size of relative pairs sharing allele IBD and total required sample size, respectively. One can check easily that T is an increasing function of Nj when Ns are fixed. In other words, for an each N, I reject the hypothesis if the counts of allele IBD are greater than Nj. Usually, the LOD score test use more strict criterion than the proportion test does. Here, the total required sample size N of the 90% power, level α = 0.001 LOD score test power is plotted as a function of the recombination fraction θ for both doubly affected relative pairs with the dichotomous trait and extreme discordant relative pairs with QTL (Figures 2A,C). In many respects, they behave similarly such that sib pairs have larger power for low θ, while grandparent–grandchild pairs have the best power for high θ (Figures 2B,D). In general, both critical allele IBD sharing size Nj and total relative pair size N are increasing as θ gets closer to 0.5 or as the power of the test increases.

View Article: PubMed Central - PubMed

ABSTRACT

I introduce a novel approach to derive the distribution of disease affectional status given alleles identical by descent (IBD) sharing through ITO method. My approach tremendously simplifies the calculation of the affectional status distribution compared to the conventional method, which requires the parental mating information, and could be applied to disease with both dichotomous trait and quantitative trait locus (QTL). This distribution is shown to be independent of relative relationship and be employed to develop the marker IBD distributions for relative relationship. In addition, three linkage tests: the proportion, the mean test, and the LOD score test are proposed for different relative pairs based on their marker IBD distributions. Among all three tests, the mean test for sib pair requires the least sample size, thus, has the highest power. Finally, I evaluate the significance of different relative relationships by a Monte-Carlo simulation approach.

No MeSH data available.