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ACE Problems

ACE Problems. Greg Carey BGA, 2009 Minneapolis, MN. Thought Experiment 1:. Future technology identifies all loci and alleles that contribute to a phenotype. Genotype a very large sample for all these loci. Code the alleles for additive effects.

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ACE Problems

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  1. ACEProblems Greg Carey BGA, 2009 Minneapolis, MN

  2. Thought Experiment 1: • Future technology identifies all loci and alleles that contribute to a phenotype. • Genotype a very large sample for all these loci. • Code the alleles for additive effects. • Regress the phenotypes on the additive codes. • Predicted values of the phenotypes are the additive genetic values = numerical estimates of latent variable A.

  3. A21 A2j A11 A1i An1 Ank Locus 2 Locus 1 Locus n  a11 a1i a21 a2j an1 ank ^ P   

  4. Assumption 1: • Phenotypes are influenced by concrete environmental events or Xs.

  5. Thought Experiment 2: • Measure all the Xs for a large sample of individuals. • Regress the phenotype on all the Xs. • Predicted values equal the total environmental values = numerical estimates of the sum of latent variables C + E.

  6. X1 X2 Xn b1 b2 bn ^ P

  7. Problem at Hand: • If (C + E) = SbiXi, we should be able to find weights for C and weights for E so that:(1) C and E are uncorrelated in an individual;(2) the Es for siblings are uncorrelated.

  8. X11 X12 E1 C1 P1

  9. Necessary Condition 1: • Every X variable can be placed into one of two mutually exclusive classes—those predicting E and those predicting C. • (X variables can be either green or red).

  10. X1e X1c E1 C1 P1

  11. Necessary Condition 2: • X variables predicting the unique environment cannot be correlated with X variables predicting the common environment within an individual. • (No magenta correlations).

  12. X1e X2c X2e X1c E2 E1 C1 C2 P1 P2

  13. Necessary Condition 3: • No sibling correlations among the Xs for the unique environment. • (Green Xs cannot correlate across siblings or no green correlational paths).

  14. X1e X2c X2e X1c E2 E1 C1 C2 P1 P2

  15. Necessary Condition 4: • No X for sib 1’s unique environment can correlate with any X for sib 2’s common environment. • (No magenta correlational paths)

  16. X1e X2c X2e X1c E2 E1 C1 C2 P1 P2

  17. Necessary Condition 5: • When C1 = C2,

  18. Necessary Condition 5: • When C1 = C2, • (With some algebra), a red X for sib 1 and itscounterpart for sib 2 must correlate 1.0.

  19. Xjc X12 X1ke X11e X21e X1c X2ke E1 C E2 P1 P2

  20. ACE Model Assumption: • Select any X variable.

  21. ACE Model Assumption: • Select any X variable. • That X must correlate either 0.0 or 1.0 for the relatives.

  22. ACE Model Assumption: • Select any X variable. • That X must correlate either 0.0 or 1.0 for the relatives. • It is not possible to have an X that correlates,say, .43 between sibs.

  23. ACE Model Assumption: • Conversely, if peer substance abuse correlates .38 among sibs, then

  24. ACE Model Assumption: • Conversely, if peer substance abuse correlates .38 among sibs, then • Peer substance abuse can NOT be an environmental influence on substance abuse.

  25. What Happened? • In the beginning,

  26. What Happened? • In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970).

  27. What Happened? • In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970). • E2variance component morphed into variableC in path analysis.

  28. What Happened? • In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970). • E2variance component morphed into variableC in path analysis. • E1variance component morphed into variableE in path analysis.

  29. What Happened? • In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970). • E2variance component morphed into variableC in path analysis. • E1variance component morphed into variableE in path analysis. • Variance components G1 and G2 were eliminated and replaced with variable A.

  30. What Happened? • In the process, we overlooked the fact that correlation (variance components) does notnecessarily imply causality.

  31. School Res1 Res2 Pupil1 Pupil2

  32. Can legitimately calculate: • Variance component for School.

  33. Can legitimately calculate: • Variance component for School. • Orthogonal variance component for Error.

  34. Can legitimately calculate: • Variance component for School. • Orthogonal variance component for Error. • Test of significance of the variance component for School.

  35. Can legitimately calculate: • Variance component for School. • Orthogonal variance component for Error. • Test of significance of the variance component for School. • Intraclass correlation for School.

  36. But is this causal?

  37. But is this causal? • Not necessarily!

  38. Family1 Family2 School Res1 Res2 Pupil1 Pupil2

  39. How Important Is This? • For the simple analysis of a single phenotype, no problem. • For some models of GE correlation, how does a variable (G) correlate with a variance component? • What about multivariate models?

  40. Solution?

  41. Solution? Common andUniqueEnvironment

  42. Solution? Shared andNonsharedEnvironment

  43. Solution? Use Total Environment = C + E

  44. a h A1 E2 E1 A2 b b b b e a a e P1 P2

  45. $5,000 prize

  46. $5,000 prize Bouchard Prize

  47. $5,000 prize Bouchard Prize Prove me wrong or irrelevant

  48. $5,000 prize Bouchard Prize Prove me wrong or irrelevant Equations, not words

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