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Study Design for Linkage, Association and TDT Studies

Study Design for Linkage, Association and TDT Studies. 林明薇 Ming-Wei Lin, PhD 陽明大學醫學系家庭醫學科 台北榮民總醫院教學研究部. Collins FS. (1992) Nature genetics 1:3-6. Collins FS. (1992) Nature genetics 1:3-6. Linkage Mapping for Disease Genes. Linkage analysis (Lod score method) Allele-sharing methods.

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Study Design for Linkage, Association and TDT Studies

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  1. Study Design for Linkage, Association and TDT Studies 林明薇 Ming-Wei Lin, PhD 陽明大學醫學系家庭醫學科 台北榮民總醫院教學研究部 M-W LIN

  2. Collins FS. (1992) Nature genetics 1:3-6 M-W LIN

  3. Collins FS. (1992) Nature genetics 1:3-6 M-W LIN

  4. Linkage Mapping for Disease Genes • Linkage analysis (Lod score method) • Allele-sharing methods M-W LIN

  5. Gregor Mendel • The principle of segregation of alleles. • The principle of independent assortment. M-W LIN

  6. Linkage Linkage describes the phenomenon whereby allele at neighbouring loci are close to one another on the same chromosome, they will be transmitted together more frequently than chance. M-W LIN

  7. Linkage Family M-W LIN

  8. Linkage Analysis Family M-W LIN

  9. Recombinant Gametes Crossing over between two neighbouring loci will produce recombinant gametes. M-W LIN

  10. Recombination Fraction Recombination fraction (θ) = number of recombinant gametes ---------------------------------------total gametes M-W LIN

  11. Estimation of Recombination Fraction • Direct Method: count recombinants. • Maximum Likelihood Method: Unknown phases Incomplete penetrance Heterogeneity M-W LIN

  12. M-W LIN

  13. M-W LIN

  14. Recombination Fraction • Recombination fraction is a measure of genetic distance. • 1cM= 1% chance of recombination between two loci. M-W LIN

  15. Likelihood Odds Likelihood of data if loci linked at θ Likelihood odds = Likelihood of data if loci unlinked L(θ< 0.5) = L(θ= 0.5) M-W LIN

  16. Lod Score L(θ< 0.5) Lod score (θ) = log10 L(θ = 0.5) M-W LIN

  17. Linkage Analysis Methods • Direct counting recombinants and non-recombinants • Maximum Likelihood Estimate M-W LIN

  18. Phase Known Family M-W LIN

  19. Phase Known L(θ) = (θ/2)r ((1-θ)/2) n-r r: No. of recombinants n: All meiosis M-W LIN

  20. Lod ScorePhase Known L(θ) LOD = log L(θ= 0.5) (θ/2) r [(1-θ) / 2] n-r = log { } (0.25) n = log 2nθr(1-θ)n-r M-W LIN

  21. Phase Unknown Family M-W LIN

  22. Phase Unknown L(θ) = 1/2 (θ/2)r [(1-θ)/2]n-r +1/2 (θ/2)n-r[(1-θ)/2]r r: No. of recombinants n: All meiosis M-W LIN

  23. Lod ScorePhase Unknown L(θ) LOD = log L(θ= 0.5) 1/2 [(θ/2) r[(1-θ)/2] n-r+(θ/2)n-r [(1-θ)/2]r ] =log { } (0.25) n = log {2n-1[θr(1-θ)n-r +θn-r(1-θ)r ]} M-W LIN

  24. Lod Score - Maximum Likelihood Estimate (Z) • Can be calculated at any values of  between 0 and 0.5, but are conventionally reported at  =0, 0.01, 0.05, 0.1, 0.2, 0.3, and 0.4. • Zmax is the maximum likelihood estimate (MLE) of . • Lod score can be converted to a chi-square statistic by 2(loge10)  4.6. M-W LIN

  25. Total Lod Score Lod score obtained from individual families can be added together to calculate the total lod score. M-W LIN

  26. Statistical Significance of the Lod Score lod score > 3: evidence of linkage 2 < lod score < 3: suggestive evidence of linkage -2 < lod score < 2: uninformative of linkage lod score < -2: exclusion of linkage M-W LIN

  27. Is a Pedigree Useful for linkage Analysis? • Are critical individuals in the pedigrees doubly heterozygous at the loci? (Informative) • Can the offsprings be scored as recombinants or nonrecombinants? (Phase) M-W LIN

  28. Parameters Assumed in Lod Score Analysis • Transmission mode of disease • Recombination fraction • Trait allele frequencies • Penetrance values for each possible disease phenotypes • Marker allele frequencies. M-W LIN

  29. Advantages of Lod Score Analysis • Statistically, it is more powerful approach than any nonparametric method. • Utilizes every family member’s phenotypic and genotypic information. • Provides an estimate of the recombination fraction. • Provides a statistical test for linkage and for genetic (locus) heterogeneity. M-W LIN

  30. Limitations of Lod Score Method • assumes single locus inheritance • requires specification of disease gene frequency and penetrance • has reduced power when disease model is grossly misspecified M-W LIN

  31. Complex Diseases • No clear pattern of Mendelian inheritance • A mix of genetic and environmental factors • Incomplete penetrance • Phenocopies • Oligogenic or polygenic • Heterogeneity • High frequency of disease-causing allele M-W LIN

  32. Recurrence Risk (λ) Frequency in relatives of affected person λr = ------------------------------------------------------- Population frequency r denotes the degree of relationship M-W LIN

  33. Recurrence Risk Genetic mapping is much easier for traits with high λs (λs > 10) than for those with low λs (λs < 2). M-W LIN

  34. Recurrence Risk of Different Diseases M-W LIN

  35. Allele-sharing Methods • Identical by state (I.B.S.) Two alleles of the same form. • Identical by descent (I.B.D.) Two alleles are descended from the same ancestral allele. M-W LIN

  36. Allele-sharing Methods Testing whether affected relatives inherited a region IBD (or IBS) more often than expected under random Mendelian segregation. M-W LIN

  37. AC AB AC BC AB CD BC BC AC AB AD BC IBD = 0 IBD = 2 IBD = 1 M-W LIN

  38. BC BC AB AD BC AC IBS = 0 IBS = 2 IBS = 1 M-W LIN

  39. Affected Sib-pair Methods An affected sib-pair may share 0,1, 2 alleles identical by descent (IBD) with probabilities of 0.25, 0.5, 0.25, respectively, at any marker locus. M-W LIN

  40. AB AC IBD = 2 BC BC 25% BC AB IBD = 1 50% AC IBD = 0 25% BC AA M-W LIN

  41. Affected Sib-pair Methods If the marker locus is independent of the trait locus, the probabilities of the affected sib-pairs share 0,1, 2 alleles ibd will remain as 0.25, 0.50, 0.25. M-W LIN

  42. Affected Sib-pair Methods If the marker locus is linked to the trait locus, an excess of affected sib-pair sharing two alleles ibd will be expected. M-W LIN

  43. Allele-sharing Methods • Affected Sib-pairs • Affected Pedigree Member M-W LIN

  44. Pearson 2 statistics Comparing observed numbers of sib-pairs sharing 0, 1, 2 alleles IBD with their expectations under the null hypothesis. M-W LIN

  45. Pearson 2 statistics • Alternative hypothesis: IBD sharing 0 1 2 observed n0 n1 n2N = n0 + n1 + n2 • Null hypothesis:IBD sharing: 0 1 2 expected N/4 N/2 N/4 M-W LIN

  46. Comments on Allele-Sharing Method • There is no need to specify any genetic parameters of the transmission model. • Less powerful to detect linkage compared with the lod score method if the genetic transmission model can be specified correctly. • It is poor at providing a precise location of the disease gene. M-W LIN

  47. Thresholds for Mapping Complex Traits M-W LIN

  48. Association Study • Case-Control study • Transmission disequilibrium test (TDT) M-W LIN

  49. ○ □ □ ○ ○ ■ ● ■ ● ■ AD AC BC AC AB DD AC BD CD CD ○ □ ○ □ □ ● ● ■ ■ ● BC CD AA AD AC BC AB AD BD AD Case-Control study M-W LIN

  50. Linkage Disequilibrium Linkage disequilibrium is the non-random association in a population of alleles at closely linked loci. M-W LIN

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