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Heterogeneity II

Heterogeneity II. Danielle Dick, Tim York, Marleen de Moor, Dorret Boomsma Boulder Twin Workshop March 2010. Heterogeneity Questions I.

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Heterogeneity II

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  1. Heterogeneity II Danielle Dick, Tim York, Marleen de Moor, Dorret Boomsma Boulder Twin Workshop March 2010

  2. Heterogeneity Questions I • Standard Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance? • Heterogeneity: Are the contributions of genetic and environmental factors equal for different groups, such as sex, race, ethnicity, SES, environmental exposure, etc.?

  3. Ways to Model Heterogeneity in Twin Data • Multiple Group Models • Sex Effects • Divorced/Not Divorced • Young/Old cohorts • Urban/Rural residency • Etc…

  4. Sex Effects Females Males

  5. Sex Effects Females Males aF = aM ? cF = cM ? eF = eM ?

  6. Divorce Effects Divorced Not Divorced aD = aND ? cD = cND ? eD = eND ?

  7. Problem: • Many variables of interest do not fall into groups • Age • Socioeconomic status • Regional alcohol sales • Parental warmth • Parental monitoring • Grouping these variables into high/low categories may lose information

  8. ‘Definition variables’ in Mx • General definition: Definition variables are variables that may vary per subject and that are not dependent variables • In Mx:The specific value of the def var for a specific individual is read into a matrix in Mx when analyzing the data of that particular individual

  9. ‘Definition variables’ in Mx create dynamic var/cov structure • Common uses: • To model changes in variance components as function of some variable (e.g., age, SES, etc) • As covariates/effects on the means (e.g. age and sex)

  10. Standard model • Means vector • Covariance matrix

  11. Model-fitting approach to GxE A C E A C E c a e a c e m m Twin 1 Twin 2 M M

  12. Model-fitting approach to GxE A C E A C E c a+XM e a+XM c e m m Twin 1 Twin 1 Twin 2 Twin 2 M M

  13. Individual specific moderators A C E A C E c a+XM1 e a+XM2 c e m m Twin 1 Twin 1 Twin 2 Twin 2 M M

  14. E x E interactions A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 e+ZM1 e+ZM2 m m Twin 1 Twin 1 Twin 2 Twin 2 M M

  15. Definition Variables in Mx X a M1 Total genetic variance = a+XM1

  16. Classic Twin Model: Var (P) = a2 + c2 + e2 • Moderation Model: Var (P) = (a + βXM)2 + (c + βYM)2 + (e + βZM)2 Purcell 2002, Twin Research

  17. Var (T) = (a + βXM)2 + (c + βYM)2 (e + βZM)2 Where M is the value of the moderator and Significance of βX indicates genetic moderation Significance of βY indicates common environmental moderation Significance of βZ indicates unique environmental moderation

  18. Unstandardized versus standardized effects

  19. Matrix Letters as Specified in Mx Script A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 c+cM*D1 c+cM*D2 e+ZM1 e+ZM2 a +aM*D1 a+aM*D2 e+eM*D2 e+eM*D1 Twin 1 Twin 2 M M m m mu mu

  20. ‘Definition variables’ in Mx create dynamic var/cov structure • Common uses: • To model changes in variance components as function of some variable (e.g., age, SES, etc) • As covariates/effects on the means (e.g. age and sex)

  21. Definition variables used as covariates General model with age and sex as covariates: yi =  + 1(agei) + 2 (sexi) +  Where yi is the observed score of individual i, is theintercept or grand mean, 1is the regression weight of age, ageiis the age of individual i, 2 is the deviation of males (if sex is coded 0= female; 1=male), sexiis the sex ofindividual i, and is the residual that is not explained by the covariates (and can be decomposed further into ACE etc).

  22. Allowing for a main effect of X • Means vector • Covariance matrix

  23. Common uses of definition variables in the means model • Incorporating covariates (sex, age, etc) • Testing the effect of SNPs (association) • In the context of GxE, controlling for rGE

  24. Adding Covariates to Means Model A C E A C E c a e a c e m+MM1 m+MM2 Twin 1 Twin 2 M M

  25. Matrix Letters as Specified in Mx Script A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 c+cM*D1 c+cM*D2 e+ZM1 e+ZM2 a +aM*D1 a+aM*D2 e+eM*D2 e+eM*D1 Twin 1 Twin 2 M M m+MM2 m+MM1 mu+b*D2 mu+b*D1 Main effects and moderating effects

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