Heterogeneity And SubjectSpecific Heritabilities Peter Molenaar The Pennsylvania

Heterogeneity And Subject-Specific Heritabilities Peter Molenaar The Pennsylvania State University Chicago, September 16, 2011

Epigenetic Origins of Heterogeneity across subjects Molenaar, P. C. M. , Boomsma, D. I. , & Dolan, C. V. (1993). A third source of developmental differences. Behavior Genetics, 23, 519 -524. Molenaar (2007). On the implications of the classical ergodic theorems: Analysis of developmental processes has to focus on intra -individual variation. Developmental Psychobiology, 50, 60 -69.

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Subject-Specific Heritabilities Molenaar, P. C. M. (2010) On the limits of standard quantitative genetic modeling of inter-individual variation: Extensions, ergodic conditions and a new genetic factor model of intra-individual variation. In: K. E. Hood, C. T. Halpern, G. Greenberg, & R. M. Lerner (Eds. ), Handbook of developmental science, behavior, and genetics. Malden, MA: Blackwell. Nesselroade, J. R. , & Molenaar, P. C. M. (2010). Analyzing intra-person variation: Hybridizing the ACE model with P-technique factor analysis and the idiographic filter. Behavior Genetics, 40, 776 -783.

Longitudinal Genetic Factor Model (Inter-Individual Variation) Let yijkmt denote the observed phenotypic score at the mth observed variable (m = 1, 2, …, M) for the jth member (j = 1, 2) of the ith twin pair (i = 1, 2, …, N) of type k (k = 1 for MZ and k = 2 for DZ) at the tth measurement occasion t (t = 1, 2, …, T)

yijkmt = mt ijkt + mt. Cijkt + mt. Eijkt + ijkmt ijkt is the additive genetic factor score of the jth member of the ith twin pair of type k at measurement occasion t Cijkt is the common environmental factor score of the jth member of the ith twin pair of type k at measurement occasion t Eijkt is the specific environmental factor score of the jth member of the ith twin pair of type k at measurement occasion t

Longitudinal Evolution of Factor Scores ijkt = t, t-1 ijkt-1 + ijkt Cijkt = t, t-1 Cijkt-1 + ijkt Eijkt = t, t-1 Eijkt-1 + ijkt

Y 111 … Yp 11 Generic Longitudinal Factor Model Y 112 … A 1 (t) (t+1) C 1 (t) (t+1) 0. 5 E 1 (t) (t+1) 1. 0 Y 121 Yp 12 Time 1 1. 0 Time 2 A 2 (t) (t+1) C 2 (t) (t+1) E 2 (t) (t+1) … Yp 21 Y 122 … Yp 22

The general Longitudinal Genetic Factor Model is based on the strong assumption that all parameters (genetic, common and specific environmental factor loadings and lagged regression coefficients) are invariant across subjects.

Genetic Factor Model for Intra-Individual Variation (i. FACE). Application to single DZ twin pair (i and k subscripts fixed). yjmt = jm jt + jm. Cjt + jm. Ejt + jmt jt = j jt-1 + jt Cjt = j. Cjt-1 + jt Ejt = j. Ejt-1 + jt All parameters in i. FACE are subject-specific.

Y 11(t) … Yp 1(t) i. FACE Y 11(t+1) … A 1 (t) (t+1) C 1 (t) (t+1) 0. 5 E 1 (t) (t+1) 1. 0 Y 12(t) Yp 1(t+1) Time t 1. 0 Time t+1 A 2 (t) (t+1) C 2 (t) (t+1) E 2 (t) (t+1) … Yp 2(t) Y 12(t+1) … Yp 2(t+1)

Application i. FACE to Multi-Lead EEG Data Obtained in Oddball Task

DZ Twin Pair (cor[A 1, A 2] =. 40) Twin 1 a 2 Cz. 000 Pz. 736 T 5. 285 T 6. 022 c 2. 016. 039. 005. 000 e 2. 980. 226. 710. 977 res. 703. 063. 052. 000

DZ Twin Pair (cor[A 1, A 2] =. 40) Twin 2 a 2 Cz. 045 Pz. 048 T 5. 002 T 6. 109 c 2. 492. 400. 018. 138 e 2. 463. 551. 981. 753 res. 779. 471. 041. 062

DZ Twin Pair (cor[A 1, A 2] =. 37) Twin 1 a 2 C 3. 019 P 3. 187 C 4. 186 P 4. 151 c 2. 532. 749. 508. 828 e 2. 449. 063. 305. 021 res. 743. 013. 009. 321

DZ Twin Pair (cor[A 1, A 2] =. 37) Twin 2 a 2 C 3. 159 P 3. 450 C 4. 842 P 4. 456 c 2. 007. 008. 094. 007 e 2. 834. 543. 065. 538 res. 092. 173. 846. 262

Heritability is high for a few leads which differ across subjects (Pz for twin 1; P 3 and P 4 for twin 2) The effects of common environment are high for leads neighboring the ones with high heritability (P 3 and P 4 for twin 1; Pz for twin 2), possibly due to A x C interaction (Molenaar et al. , Genetic Epidemiology, 1990) Analogous results are obtained for other DZ twin pairs

Twin 1 Additive Genetic Common Environment Pz P 3 C 4 P 4

Twin 2 Additive Genetic Common Environment Pz P 3 P 4

Application of i. FACE to multi-lead EEG preliminary and can be generalized in several respects, including: - Alternative estimation techniques Alternative model variants Application to complete set of leads (19) Application to separate ERP components Frequency domain analysis

Conclusions - i. FACE (combination of IF and the ACE model) provides a principled new methodology to assess heterogeneity (subject-specificity). - It is expected that i. FACE will help better understand the relationships between genetic influences and phenotypes mediated by subjectspecific physiological and brain systems.

I thank: In the USA: John Nesselroade Mike Rovine Nilam Ram Eric Loken Katie Gates In Europe: Dorret Boomsma Dirk Smit NSF grant 0852147

Simulation Study Twin 1 true (h 1)2 =. 34 true (h 2)2 =. 86 true (h 3)2 =. 35 true (h 4)2 =. 57 est (h 1)2 =. 36 est (h 2)2 =. 86 est (h 3)2 =. 36 est (h 4)2 =. 60 Twin 2 true (h 1)2 =. 73 true (h 2)2 =. 20 true (h 3)2 =. 54 true (h 4)2 =. 49 est (h 1)2 =. 62 est (h 2)2 =. 15 est (h 3)2 =. 45 est (h 4)2 =. 40

Idiographic Filter is: - Based on analysis of intra-individual variation - Involves a new definition of measurement equivalence at the level of latent variables - Allows for subject-specific factor loadings Nesselroade, J. R. , Gerstorf, D. , Hardy, S. A. , & Ram, N. (2007). Idiographic filters for psychological constructs. Measurement, 5, 217 -235.