Gene hunting from a Bayesian viewpoint

1. Gene hunting from a Bayesian viewpoint Tuan V. Nguyen Bone and Mineral Research Program Garvan Institute of Medical Research Sydney, Australia

2. Gene search is justified? • Exploration of disease pathway • Public health implications • Pharmacological applications • Treatment?

3. Complex traits

4. BMD: genetics and environments Variation in complex trait = G + E + GxE (G=genetics; E=environment, x=interaction) MZ twins; r=0.73 DZ twins; r=0.47

5. Genetics, BMD and fracture Fracture BMD

6. Does familial risk of BMD affect fracture risk? Intraclass correlation in BMD RR of BMD/Fx r = 0.8 r = 0.9 _________________________________________________ 5 1.14 1.16 6 1.17 1.20 7 1.21 1.24 8 1.24 1.28 _________________________________________________ Genes that affect BMD explain small variation in fx risk

7. Fracture risk: genetics and environments Twin study P Kannus et al, BMJ 1999; 319:1334-7

8. Current strategies • Linkage analysis • Association analysis • Genome-wide screen • “Candidate gene”

9. Linkage analysis – identical by descent (ibd) AB AC AB CD AB CD AB AC AC AD BC BC IBD = 0 IBD = 1 IBD = 2

10. Linkage analysis: basic model Squared difference in BMD among siblings o o o o o o o o o o o o o o o o o o o o o o o o o o o 0 1 2 Number of alleles shared IBD

11. Population-based association analysis Fracture AC AB AC BC AA AB BB AA AC AB Controls AC BB BC BC CC AB BB CC BC BB

12. Family-based association analysis AB AA AB AC BC AA AB BC AB

13. Genome-wide vs candidate gene approach Candidate gene analysis Genome-wide screen Complex No prior knowledge of mechanism Expensive No specific genes Simple Prior knowledge of mechanism Inexpensive Specific genes

14. Linkage vs association phenomena

15. Test statistic Test statistic = signal / noise = effect size / random error Result: significant (+ve) or not significant (-ve) Criteria: P-value P<0.05  +ve P>0.05  -ve

16. Consider an example OR = (0.1 / 0.9) / (0.05 / 0.95) = 2.11 LnOR = 0.74; SE(lnOR) = 0.18 P-value < 0.0001

17. Diagnostic analogy Diagnosis Genetic research

18. The meaning of P-value • P-value: probability of getting a significant statistical test given that there is no association (or no linkage) • P-value = P(significant stat | Ho is true)

19. The logic of P-value • If there was truly no association, the the observation is unlikely • The observation occurred • The no-association hypothesis is unlikely • If Tuan has hypertension, he is unlikely to have pheochromocytoma • Tuan has pheochromocytoma • Tuan is unlikley to have hypertension

20. P-value “Thinking about P values seems quite counter-intuitive at first, as you must use backwards, awkward logic. Unless you are a lawyer or a Talmudic scholar … you will probably find this sort of reasoning uncomfortable” (Intuitive Statistics)

21. What do we want to know? Clinical P(+ve | cancer), or P(cancer | +ve) ? Research P(Significant test | Association), or P(Association | Significant test) ?

22. Breast Cancer Screening Prevalence = 1%; Sensitivity = 90%; Specificity = 91% Population Cancer (n=10) No Cancer (n=990) +ve N=9 -ve N=900 -ve N=1 +ve N=90 P(Cancer| +ve result) = 9/(9+90) = 9%

23. Genetic association Prior prob. association = 0.05; Power = 90%; Pvalue = 5% 1000 SNPs True (n=50) False (n=950) +ve N=45 -ve N=902 -ve N=5 +ve N=48 P(True association| +ve result) = 45/(45+48) = 48%

24. Problem with p-value

25. P value is • NOT the likelihood that findings are due to chance • NOT the probability that the null hypothesis is true given the data • A p-value = 0.05 does not mean that there is a 95% chance that a real difference exists • The lower p-value, the stronger the evidence for an effect

26. Bayes factor P(data | H0) BF = _________________ P(data | H1)

27. Minimum Bayes factor Prob of null hypothesis Where P(H0) is the prior probability of the null hypothesis

28. Re-evaluation of some “positive” studies

29. Bayes Factor for genetic association study let p be the allelic frequency of genetic marker, then BF can be shown to be:

30. Bayes Factor and posterior probability of an association let p0 be the prior probability of a true association, the posterior probability of the association is:

31. Bayes factor vs p-value – t/z test

32. P-value and Bayes factor – LD test

33. Bayes factor and p-value Bayes factor P-value • Non-comparative • Observed + hypothetical data • Evidence only negative • Sensitive • No formal justification or interpretation • Comparative • Only observed data • Evidence +ve or –ve • Insensitive • Formal justification and interpretation

34. Summary • The criteria of p<0.05 is not an adequate measure of a genetic association • Bayes factor is potentially a relevant measure of association

35. Distribution of sample sizes Ioannidis et al, Trends Mol Med 2003

36. Distribution of effect sizes Ioannidis et al, Trends Mol Med 2003

37. Correlation between the odds ratio in the first studies and in subsequent studiesIoannidis et al, Nat Genet 2001

38. Evolution of the strength of an association as more information is accumulatedIoannidis et al, Nat Genet 2001

39. Predictors of statistically significant discrepancies between the first and subsequent studies of the same genetic association Ioannidis et al, Nat Genet 2001

40. Diagnosis and statistical reasoning

41. Risk factors for fracture • Drinking coffee • Drinking tea • Coca cola • High protein intake • Blonde hair • Being tall • Wear trouser (women) • High heel (women)

42. Cancer risk • Being a waiter • Owning a pet bird • Being short • Being tall • Hot dogs • Have a refrigerator! • Electric razors • Broken arms (women) • Fluorescent lights • Allergies • Breeding reindeer Altman and Simon, JNCI 1992

43. “Half of what doctors know is wrong. Unfortunately we don’t know which half.” Quoted from the Dean of Yale Medical School, in “Medicine and Its Myths”, New York Times Magazine, 16/3/2003