Univariate Twin Analysis. OpenMx Tc Hermine Maes, Elizabeth Prom-Wormley, Nick Martin

Transcription

1 Univariate Twin Analysis OpenMx Tc Hermine Maes, Elizabeth Prom-Wormley, Nick Martin

2 Overall Questions to be Answered oes a trait of interest cluster among relate dividuals? an clustering be explained by genetic or nvironmental effects? hat is the best way to explain the degree t hich genetic and environmental effects aff trait?

3 Family & Twin Study Designs Family Studies Classical Twin Studies Adoption Studies

4 The Data ustralian Twin Register 8-30 years old, males and females ork from this session will focus on Body ass Index (weight/height 2 ) in females only ample size MZF = 534 complete pairs (zyg = 1) DZF = 328 complete pairs (zyg = 3)

5 Quick Look at the Data

6 Classical Twin Studies Basic Background The Classical Twin Study (CTS) uses MZ and DZ twins reared together MZ twins share 100% of their genes DZ twins share on average 50% of their genes Expectation- Genetic factors are assumed

7 Classical Twin Study Assumptions MZ twins are genetically identical Equal Environments of MZ and DZ pairs

8 Basic Data Assumptions Z and DZ twins are sampled from the sam opulation, therefore we expect :- Equal means/variances in Twin 1 and Tw Equal means/variances in MZ and DZ twi urther assumptions would need to be teste f we introduce male twins and opposite sex win pairs

9 Old Fashioned Data Checking MZ DZ T1 T2 T1 T2 an iance ariance(t1-t2) e, but how can we actually be sure that the

10 A Roadmap se the data to test basic assumptions (equ ans & variances for twin 1/twin 2 and MZ/D rs) aturated Model stimate contributions of genetic and ironmental effects on the total variance of notype CE or ADE Models est ACE (ADE) submodels to identify and

11 Saturated Twin Model

12 Deconstructed MZ1 mmz2 mdz1 mdz2

13 urated Code Deconstruc T1 T1 vmz1 T2 cmz21 covmz = 2 T1 T1 vdz1

14 Time to Play... with OpenMx Please Open the File twinsatcon.r

15 Estimated Values T1 T2 T1 T2 Saturated Model ean MZ DZ cov T1 T1 T2 0 Total Parameters mmz1, stimatedmmz2, vmz1,vmz2,cmz21 T2 mdz1, mdz2, vdz1,vdz2,cdz21 andardize covariance matrices for in pair correlations (covmz &

16 Estimated Values T1 T2 T1 T2 Saturated Model mean MZ DZ cov T T T T Total Parameters mmz1, stimatedmmz2, vmz1,vmz2,cmz21 mdz1, mdz2, vdz1,vdz2,cdz21 andardize covariance matrices for in pair correlations (covmz &

17 itting Nested Models Saturated Model likelihood of data without any constraints fitting as many means and (co)variances as possible Equality of means & variances by twin order test if mean of twin 1 = mean of twin 2 test if variance of twin 1 = variance of twin 2 Equality of means & variances by zygosity test if mean of MZ = mean of DZ test if variance of MZ = variance of DZ

18 Estimated Values quate Means Variances across Twin Order & Zygosity T1 T2 T1 T2 Equate Means & Variances across Twin Order mean MZ DZ cov T1 T1 T2 T2 mean MZ DZ cov T1 T1

19 Estimates quate Means Variances across Twin Order & Zygosity T1 T2 T1 T2 Equate Means & Variances across Twin Order mean MZ DZ cov T T T T mean MZ DZ cov T T1 0.78

20 Stats Model ep -2ll df AIC diff - aturated ll diff df T1=mT T1=mT2 & rt1=vart Zyg MZ=DZ gnificant differences between saturated mo odels where means/variances/covariance qual by zygosity and between twins

21 Questions? This is all great, but we still don t understand the genetic and environmental contributions to BMI

22 tterns of Twin Correlatio 2rDZ itive ins on rage 50% of itive cts rmz = rdz Shared Environmen t rmz > 2rDZ Additive & Dominance DZ twins on average share 25% of??? Additive Share Environ A = 2(rMZ C = 2rDZ E = 1- rmz

23 BMI Twin Correlations A = 2(rMZ-rD C = 2rDZ - rm E = 1- rmz A = 0.96 C = E = 0.22

24 A Roadmap se the data to test basic assumptions inhe tandard ACE (ADE) models aturated Model stimate contributions of genetic and ironmental effects on the total variance of notype DE or ACE Models est ADE (ACE) submodels to identify and ort significant genetic and environmental

25 ADE Model A Few Considerations Dominance refers to non-additive genetic effects resulting from interactions between alleles at the same locus ADE models also include effects of interact between different loci (epistasis) In addition to sharing on average 50% of th DNA, DZ twins also share about 25% of eff

26 Path Coefficients <- mxalgebra( expression=a %*% t(a), e="a" ) <- mxalgebra( expression=d %*% t(d), e= D" ) a 1 x 1 m d 1 x 1 m

27 Variance Components a 1 x 1 m d * * 1 x 1 m

28 Means & Covariances expmea n expmea n expmean= 1 x 2 ma T1 T1 A+D+E T2

29 Means & Covariances T1 T2 T1 A+D+E A T2 A+D T1 T1 A+D+E T2

30 Means & Covariances T1 T2 T1 T2 A+D+E A+ A+D A+D T1 T1 A+D+E T2 0.5A+

31 DE Model Deconstructed 4 Parameters Estimated ExpMean Variance due to A

32 A Roadmap se the data to test basic assumptions inhe tandard ACE (ADE) models aturated Model stimate contributions of genetic and ironmental effects on the total variance of notype DE or ACE Models est ADE (ACE) submodels to identify and ort significant genetic and environmental

33 Please Open twinadecon.r Full ADE Model Comparison against Saturated Nested Models AE Model test significance of D E Model vs AE Model test significance of A E Model vs ADE Model test combined significance of A & D

34 Fixing the v ject ing el Object containing Full Model del <- mxmodel( AdeFit, name="ae" ) el <- omxsetparameters( AeModel, s= d11", free=false, values=0) The d path will estimate

35 Goodness of Fit Stats ep -2ll df AIC diff - diff 2ll df p turated ADE AE DE no! no! no! no! no! no! no! E

36 Goodness-of-Fit Statistics ep -2ll df AIC diff - 2ll diff df turated ADE AE E p

37 hat about the magnitudes of genetic and environmental contributions to BMI?

38 A Roadmap se the data to test basic assumptions inhe tandard ACE (ADE) models aturated Model stimate contributions of genetic and ironmental effects on the total variance of notype DE or ACE Models est ADE (ACE) submodels to identify and ort significant genetic and environmental

39 Estimated Values a d e c a 2 d 2 e 2 c 2 DE - AE - E -

40 Estimated Values a d e c a 2 d 2 e 2 ADE AE E

41 Okay, so we have a sense of which model best explains the data...or do we?

42 BMI Twin Correlations A = 2(rMZ-rD C = 2rDZ - rm E = 1- rmz ADE or ACE

43 iving the ACE Model Try (if there is time)

44 Goodness-of-Fit Statistics odel ep -2ll df AIC diff - 2ll diff df turated DE CE

45 Goodness-of-Fit Statistics odel ep -2ll df AIC diff - 2ll diff df turated DE CE

46 Estimated Values a d e c a 2 d 2 e 2 c 2 DE AE CE AE E

47 Estimated Values a d e c a 2 d 2 e 2 c 2 DE AE CE AE E

48 Conclusions BMI in young OZ females (age 18-30) additive genetic factors: highly significant dominance: borderline significant specific environmental factors: significant shared environmental factors: not

49 Potential Complications Assortative Mating Gene-Environment Correlation Gene-Environment Interaction Sex Limitation Gene-Age Interaction

50 Processes Built the ADE Model as Coded in twinadecon.r Generate Parameter Estim Make matrices patha, pathd, pathe Do Matrix Algebra w Matric cova, covd, cove, covmz,co Call Data for Use in the Mo datamz, datadz Call Data for Use in the Mo datamz, datadz Build Model from Matrices modelmz, modeldz Build/Complie Overall Mod from Matrices/Algebras AdeModel Run Overall Model AdeModel Get Summary Information Overall Model AdeSumm

51 Thank You!