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Review
. 2005 Jun;2(2):90-112.
doi: 10.1186/1479-7364-2-2-90.

Sibship T2 association tests of complex diseases for tightly linked markers

Ruzong Fan  1 , Michael Knapp
Affiliations
Review

Sibship T2 association tests of complex diseases for tightly linked markers

Ruzong Fan et al. Hum Genomics. 2005 Jun.

Abstract

For population case-control association studies, the false-positive rates can be high due to inappropriate controls, which can occur if there is population admixture or stratification. Moreover, it is not always clear how to choose appropriate controls. Alternatively, the parents or normal sibs can be used as controls of affected sibs. For late-onset complex diseases, parental data are not usually available. One way to study late-onset disorders is to perform sib-pair or sibship analyses. This paper proposes sibship-based Hotelling's T2 test statistics for high-resolution linkage disequilibrium mapping of complex diseases. For a sample of sibships, suppose that each sibship consists of at least one affected sib and at least one normal sib. Assume that genotype data of multiple tightly linked markers/haplotypes are available for each individual in the sample. Paired Hotelling's T2 test statistics are proposed for high-resolution association studies using normal sibs as controls for affected sibs, based on two coding methods: 'haplotype/allele coding' and 'genotype coding'. The paired Hotelling's T2 tests take into account not only the correlation among the markers, but also take the correlation within each sib-pair. The validity of the proposed method is justified by rigorous mathematical and statistical proofs under the large sample theory. The non-centrality parameter approximations of the test statistics are calculated for power and sample size calculations. By carrying out power and simulation studies, it was found that the non-centrality parameter approximations of the test statistics were accurate. By power and type I error analysis, the test statistics based on the 'haplotype/allele coding' method were found to be advantageous in comparison to the test statistics based on the 'genotype coding' method. The test statistics based on multiple markers can have higher power than those based on a single marker. The test statistics can be applied not only for bi-allelic markers, but also for multi-allelic markers. In addition, the test statistics can be applied to analyse the genetic data of multiple markers which contain double heterozygotes--that is, unknown linkage phase data. An SAS macro, Hotel_sibs.sas, is written to implement the method for data analysis.

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Figures

Figure 1
Figure 1
Power curves of TH and TG at a significance level α = 0.05, using two bi-allelic markers H1 and H2, when P(Hi1) = P(Hi2) = 0.50, i = 1,2, PD = 0.15, and N = 200 sib-pairs for the first set of parameters of the four genetic models of Table 4. The power curves of TH1 and TG1 are calculated based on one marker H1. In the graphs, Delta_11 = Δ11 = P(H11D) - P(H11)PD is a measure of linkage disequilibrium (LD) between marker H1 and disease locus D; in addition, the other parameters are given by Δ21 = P(H21D) 2 P(H21)PD = Δ11, ΔH1H2 = P(H11H21) - P(H11)P(H21) = 0.05; and .
Figure 2
Figure 2
Power curves of TH and TG at a significance level α = 0.05, using two bi-allelic markers H1 and H2, when P(Hi1) = P(Hi2) = 0.50, i = 1,2, PD = 0.15 and N = 600 sib-pairs for the second set of parameters of the four genetic models of Table 5. The power curves of TH1 and TG1 are calculated based on one marker H1. In the graphs, Delta_11 = Δ11 = P(H11D) - P(H11)PD is a measure of linkage disequilibrium (LD) between marker H1 and disease locus D; in addition, the other parameters are given by Δ21 = P(H21D) - P(H21)PD = Δ11, ΔH1H2=PH11H21-PH11PH21=0.05, and Δ1D2=PH11DH21-PH11Δ21-PDΔH1H2-PH21Δ11-PH11PDPH21=Δ11/3.
Figure 3
Figure 3
Power curves of TH and TG at a significance level α = 0.05 using a quadric-allelic marker H1, when P(H11) = P(H12) = 0.35, P(H13) = P(H14) = 0.15 PD = 0.15 and N = 200 sib-pairs for the first set of parameters of the four genetic models of Table 4. Delta_11 = Δ11 = P(H11D) - P(H11)PD is a measure of linkage disequilibrium (LD) between marker H1 and disease locus D. In addition, Δ12 = -Δ11, Δ13 = -Δ14 = Δ11/2. The simulated power curves of STH and STG are calculated using combinations of both sib-pairs and sibships of size 3: the number of sib-pairs is equal to N/2 = 100; the number of sibships of size 3 is N/2 = 100; in each of N/4 = 50 sibships of size 3, one is affected and the other two are normal; in the remaining N/4 = 50 sibships of size 3, two are affected and the other one is normal.
Figure 4
Figure 4
Power curves of TH and TG at a significance level α = 0.05 using a quadric-allelic marker H1, when P(H11) = P(H12) = 0.35, P(H13) = P(H14) = 0.15, PD = 0.15 and N = 600 sib-pairs for the second set of parameters of the four genetic models of Table 5. Delta_11 = Δ11 = P(H11D) - P(H11)PD is a measure of linkage disequilibrium (LD) between marker H1 and disease locus D. In addition, Δ12 = -Δ11, Δ13 = - Δ14 = Δ11/2. The simulated power curves of STH and STG are calculated using combinations of both sib-pairs and sibships of size 3 and sibships of size 4; the number of sib-pairs is equal to N/2 = 300; the number of sibships of size 3 is N/2 = 120; and the number of sibships of size 4 is 3N/10 = 180; in each of N/10 = 60 sibships of size 3, one is affected and the other two are normal; in the remaining N/10 = 60 sibships of size 3, two are affected and the other one is normal; in each of N/10 = 60 sibships of size 4, one is affected and the other three are normal; in each of N/10 = 60 sibships of size 4, two are affected and the other two are normal; in the remaining N/10 = 60 sibships of size 4, three are affected and the other one is normal.
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