2. Office hours 3-4pm Wednesdays 304A Stanley Hall

3. More realistic situation: in dad, phase of alleles unknown A1d d D A2d A1 A2 or A1d A2D

4. Dad phase unknown A1 A2 0.5 (total # meioses) Odds = 1/2[(1-r) n r k ]+ 1/2[(1-r) n r k ]odds ratio What single r value best explains the data? A1D A2d or A1d A2D

5. For this, you need to search r’s. maximum likelihood r = 0.13

6. Modern genetic scans What is the simplest explanation for so many tall black lines around Chr 13? A.Multiple markers in the region, which makes LOD higher B.Multiple markers are all linked to a single disease mutation C.Multiple mutations on Chr 13 cause the disease D.Higher LOD is counted by the number of linking markers (single family)

7. Modern genetic scans (single family)

8. Modern genetic scans What does the “max” in “max LOD score” refer to? A.The strongest-linking marker B.The most probable recombination fraction C.The most severe phenotype (single family)

9. Remember? maximum likelihood r = 0.13 Max LOD score is the one from the best r value

10. Modern genetic scans What is the simplest explanation for so many tall black lines around Chr 13? A.Multiple markers in the region, which makes LOD higher B.Multiple markers are all linked to a single disease mutation C.Multiple mutations on Chr 13 cause the disease D.Higher LOD is counted by the number of linking markers (single family)

11. Modern genetic scans What is the simplest explanation for so many tall black lines around Chr 13? A.Multiple markers in the region, which makes LOD higher B.Multiple markers are all linked to a single disease mutation C.Multiple mutations on Chr 13 cause the disease D.Higher LOD is counted by the number of linking markers (single family)

12. Modern genetic scans (22 families)

13. Modern genetic scans (Smooth curve = inferred genotype at positions between markers) (22 families)

14. Modern genetic scans Fit model twice (22 families)

15. But… (779 small families or sib pairs)

16. Why would an experiment fail to observe linkage?

17. Marker density matters ? Try to minimize genotyping cost. But if the only marker you test is >50 cM away, will get no linkage.

18. Number of families matters If low number of patients, no statistical significance. Tune in next lecture for more about this.

19. Improper statistics Can make noise look like a fabulously significant linkage peak.

20. Locus heterogeneity Fig. 3.16

21. Locus heterogeneity Fig. 3.16

22. Age of onset in breast cancer

23. age of onset

24. Age of onset in breast cancer age of onset

25. Age of onset in breast cancer age of onset Only early-onset families show linkage. Familial breast cancer is heterogeneous.

26. Locus heterogeneity Fig. 11.23

27. A landmark: BRCA1

28. More breast cancer FYI (see lecture 9/15)

29. Table 19.5 BRCA1 and 2 FYI

30. Only ~10% of breast cancers are hereditary p. 420

31. BRCA1 and 2 FYI Only ~10% of breast cancers are hereditary Different from sporadic: age, histology, sex p. 420

32. BRCA1 and 2 FYI Only ~10% of breast cancers are hereditary Different from sporadic: age, histology, sex BRCA1 and BRCA2 found from linkage analysis of families with multiple affecteds (1990, 1994) p. 420

33. BRCA1 and 2 FYI Only ~10% of breast cancers are hereditary Different from sporadic: age, histology, sex BRCA1 and BRCA2 found from linkage analysis of families with multiple affecteds (1990, 1994) BRCA1 or 2 mutation = ~80% likely to get disease p. 420

34. BRCA1 and 2 FYI Only ~10% of breast cancers are hereditary Different from sporadic: age, histology, sex BRCA1 and BRCA2 found from linkage analysis of families with multiple affecteds (1990, 1994) BRCA1 or 2 mutation = ~80% likely to get disease p. 420

35. Even familial form is more than just BRCA1 and 2

36. Multiple causes = hard to find any one cause In the limit of studying a single family with severe disease, more likely to find one strong locus. But hard to find such families, and segregating allele may not be relevant for chronic/common disease.

37. Statistics: first, a little more review from last class

38. Modern genetic scans What is the simplest explanation for so many tall black lines around Chr 13? A.Multiple markers in the region, which makes LOD higher B.Multiple markers are all linked to a single disease mutation C.Multiple mutations on Chr 13 cause the disease D.Higher LOD is counted by the number of linking markers (single family)

39. Rule of thumb: don’t believe linkage unless odds > 1000. Why?

40. LOD scores Odds = P(pedigree | r) P(pedigree | r = 0.5) r = genetic distance between marker and disease locus Odds = (1-r) n r k 0.5 (total # meioses)

41. LOD scores Odds = P(pedigree | r) P(pedigree | r = 0.5) r = genetic distance between marker and disease locus Odds = (1-r) n r k 0.5 (total # meioses) rodds 0.112.244 0.210.737 0.36.325 0.42.867 0.51

42. Coins Odds = P(your flips | r) P(your flips | r = 0.5) r = intrinsic probability of coming up heads (bias) Odds = (1-r) n r k 0.5 (total # flips)

43. Coins Odds = P(your flips | r) P(your flips | r = 0.5) r = intrinsic probability of coming up heads (bias) Odds = (1-r) n r k 0.5 (total # flips) Unknown we seek is “fairness” of a coin (analogous to recombination fraction)

44. Coins Odds = P(your flips | r) P(your flips | r = 0.5) r = intrinsic probability of coming up heads (bias) Odds = (1-r) n r k 0.5 (total # flips) Raw data are coin flips (analogous to a pedigree)

45. Coins Odds = P(your flips | r) P(your flips | r = 0.5) r = intrinsic probability of coming up heads (bias) Odds = (1-r) n r k 0.5 (total # flips) Odds ratio of model that coin is biased, relative to null

46. Coins Odds = P(your flips | r) P(your flips | r = 0.5) r = intrinsic probability of coming up heads (bias) Odds = (1-r) n r k 0.5 (total # flips) If you do 10,000 flips and 70,000 are heads, what do you expect for r? A. 0 B. 0.7 C. 0.5 D. 1

47. Coins Take out a coin and flip 4 times. How many heads?

48. Coins Want to find intrinsic prob of heads (analogous to recombination fraction). With only 4 data points, can’t use  2 (analogous to a small family).

49. Coins r = intrinsic probability of coming up heads (bias) 2 heads Odds = (1-r) n r k 0.5 (total # flips) rodds 00 0.10.1296 0.20.4096 0.30.7056 0.40.9216 0.51 0.60.9216 0.70.7056 0.80.4096 0.90.1296 10 Odds ratio of model that coin is biased, relative to null

50. Coins 2 heads Odds = (1-r) n r k 0.5 (total # flips) rodds 00 0.10.1296 0.20.4096 0.30.7056 0.40.9216 0.51 0.60.9216 0.70.7056 0.80.4096 0.90.1296 10 r = intrinsic probability of coming up heads (bias) Odds ratio of model that coin is biased, relative to null

51. Coins 2 heads Odds = (1-r) n r k 0.5 (total # flips) rodds 00 0.10.1296 0.20.4096 0.30.7056 0.40.9216 0.51 0.60.9216 0.70.7056 0.80.4096 0.90.1296 10 r = intrinsic probability of coming up heads (bias) observed rate is best numerical solution

52. Coins 3 heads rodds 00 0.10.0144 0.20.1024 0.30.3024 0.40.6144 0.51 0.61.3824 0.71.6464 0.81.6384 0.91.1664 10 r = intrinsic probability of coming up heads (bias)

53. Coins 3 heads2 heads1 heads rodds 00 0.11.1664 0.21.6384 0.31.6464 0.41.3824 0.51 0.60.6144 0.70.3024 0.80.1024 0.90.0144 10 0 heads rodds 016 0.110.498 0.26.5536 0.33.8416 0.42.0736 0.51 0.60.4096 0.70.1296 0.80.0256 0.90.0016 10 4 heads rodds 00 0.10.0016 0.20.0256 0.30.1296 0.40.4096 0.51 0.62.0736 0.73.8416 0.86.5536 0.910.498 116 rodds 00 0.10.1296 0.20.4096 0.30.7056 0.40.9216 0.51 0.60.9216 0.70.7056 0.80.4096 0.90.1296 10 rodds 00 0.10.0144 0.20.1024 0.30.3024 0.40.6144 0.51 0.61.3824 0.71.6464 0.81.6384 0.91.1664 10 r = intrinsic probability of coming up heads (bias)

54. Coins 3 heads2 heads1 heads rodds 00 0.11.1664 0.21.6384 0.31.6464 0.41.3824 0.51 0.60.6144 0.70.3024 0.80.1024 0.90.0144 10 0 heads rodds 016 0.110.498 0.26.5536 0.33.8416 0.42.0736 0.51 0.60.4096 0.70.1296 0.80.0256 0.90.0016 10 4 heads rodds 00 0.10.0016 0.20.0256 0.30.1296 0.40.4096 0.51 0.62.0736 0.73.8416 0.86.5536 0.910.498 116 rodds 00 0.10.1296 0.20.4096 0.30.7056 0.40.9216 0.51 0.60.9216 0.70.7056 0.80.4096 0.90.1296 10 rodds 00 0.10.0144 0.20.1024 0.30.3024 0.40.6144 0.51 0.61.3824 0.71.6464 0.81.6384 0.91.1664 10 r = intrinsic probability of coming up heads (bias)

55. Coins 3 heads2 heads1 heads rodds 00 0.11.1664 0.21.6384 0.31.6464 0.41.3824 0.51 0.60.6144 0.70.3024 0.80.1024 0.90.0144 10 0 heads rodds 016 0.110.498 0.26.5536 0.33.8416 0.42.0736 0.51 0.60.4096 0.70.1296 0.80.0256 0.90.0016 10 4 heads rodds 00 0.10.0016 0.20.0256 0.30.1296 0.40.4096 0.51 0.62.0736 0.73.8416 0.86.5536 0.910.498 116 rodds 00 0.10.1296 0.20.4096 0.30.7056 0.40.9216 0.51 0.60.9216 0.70.7056 0.80.4096 0.90.1296 10 rodds 00 0.10.0144 0.20.1024 0.30.3024 0.40.6144 0.51 0.61.3824 0.71.6464 0.81.6384 0.91.1664 10 r = intrinsic probability of coming up heads (bias)

56. Coins Is this person’s coin really biased?

57. Coins By chance, can get good LOD score for just about anything.

58. Coins By chance, can get good LOD score for just about anything. The more students you have flipping coins, the more likely you are to see this “unlikely” combination. The multiple testing problem

59. Multiple testing in genetics Testing lots of markers for linkage to a trait is analogous to having lots of students, each flipping a coin.

60. Multiple testing in genetics Testing lots of markers for linkage to a trait is analogous to having lots of students, each flipping a coin. Can get spurious high LOD to an unlinked marker, just by chance.

61. Don’t let this happen to you!