Comparing heritability estimates for twin studies + : & Mary Ellen Koran. Tricia Thornton-Wells. Bennett Landman

Transcription

1 Comparing heritability estimates for twin studies + : & Mary Ellen Koran Tricia Thornton-Wells Bennett Landman January 20, 2014

2 Outline Motivation Software for performing heritability analysis Simulations Twin Study (SOLAR & OpenMX) Family Study (SOLAR) Live Demo Conclusion January 20, 2014 IIGC 2014 SOLAR Workshop 2

3 Outline Motivation Software for performing heritability analysis Simulations Twin Study (SOLAR & OpenMX) Family Study (SOLAR) Live Demo Conclusion January 20, 2014 IIGC 2014 SOLAR Workshop 3

4 Heritability (h 2 ) crash course A first question to ask before embarking on a genetic study: is a trait heritable? BEFORE GENOTYPING h 2 = degree of genetic association As h 2 -> 1, a trait increasingly heritable January 20, 2014 IIGC 2014 SOLAR Workshop 4

5 Cortical gray matter density is heritable January 20, 2014 IIGC 2014 SOLAR Workshop 5

6 Cortical area thickness is heritable January 20, 2014 IIGC 2014 SOLAR Workshop 6

7 Resting state fmri connectivity is heritable January 20, 2014 IIGC 2014 SOLAR Workshop 7

8 White matter microstructure is heritable January 20, 2014 IIGC 2014 SOLAR Workshop 8

9 We are just getting started Software for estimating heritability are freely available and functional on commodity hardware. Heritabilities can be estimated using diverse family structures (not just twins). We are just beginning to understand the role of brain phenotypes with substantial degrees of heritability. Missing heritability January 20, 2014 IIGC 2014 SOLAR Workshop 9

10 Choosing study designs Twin studies: h 2 = 2(r MZ r DZ ) Family studies: variance components method January 20, 2014 IIGC 2014 SOLAR Workshop 10

11 Estimating h 2 with variance components Family studies: σ T 2 = σ G 2 + σ E 2 σ G 2 = σ a 2 + σ d 2 Trait variation = genetic + environment Genetic variation = additive + dominant σ E 2 = σ c 2 + σ e 2 Environmental variation = familial/household + random/individual ACE model commonly used σ T 2 σ a 2 + σ c 2 + σ e 2 January 20, 2014 IIGC 2014 SOLAR Workshop 11

12 To wrap up. ACE model A σ a 2 σ a 2 + σ c 2 + σ e 2 C σ c 2 σ a 2 + σ c 2 + σ e 2 E σ e 2 σ a 2 + σ c 2 + σ e 2 Additive genetics Common environmental effects Individual environmental effects or Error h 2 = A = σ a 2 / σ T 2 January 20, 2014 IIGC 2014 SOLAR Workshop 12

13 Outline Motivation Software for performing heritability analysis Simulations Results Twin Study (SOLAR & OpenMX) Family Study (SOLAR) Live Demo Conclusion January 20, 2014 IIGC 2014 SOLAR Workshop 13

14 Estimating Heritability Sequential oligogenic linkage analysis routines Multipoint quantitative-trait linkage analysis in general pedigrees. Almasy, Blangero. Am J Hum Genet Tcl-based Structural equation modeling OpenMx: An Open Source Extended Structural Equation Modeling Framework. Boker, Neale, et.al. Psychometrika R-based January 20, 2014 IIGC 2014 SOLAR Workshop 14

15 SOLAR twins]$ solar SOLAR version (Experimental), last updated on December 31, 2013 Copyright (c) Texas Biomedical Research Institute Enter help for help, exit to exit, doc to browse documentation. solar> load pedigree ped2.ped solar> load phenotypes gen1.csv solar> model new solar> Unloading current pedigree data... solar> trait kindgen1 solar> covar age solar> outdir /data/solar_mek/ solar> polygenic Loading pedigree data from the file /data/solar_mek/10_18_2013_openmx_solar/twins/pair2/ped2.ped... solar> /data/solar_mek/10_18_2013_openmx_solar/twins/pair2/a_0/a_0_c_0/gen1.csv: ID age kindgen1 FAMID solar> solar> solar> solar> solar> ********************************************************************** * Maximize sporadic model * January 20, 2014 IIGC 2014 SOLAR Workshop 15

16 Inputs to SOLAR Pedigree File Phenotype File January 20, 2014 IIGC 2014 SOLAR Workshop 16

17 Output of SOLAR Pedigree: /data/solar_mek/livedemo/twins4/pair20/ped20.ped Phenotypes: /data/solar_mek/livedemo/twins4/pair20/a_50/a_50_c_0/gen10.csv Trait: kindgen10 Individuals: 80 H2r is p = (Significant) H2r Std. Error: Proportion of Variance Due to All Final Covariates Is Loglikelihoods and chi's are in /data/solar_mek/livedemo/twins4/pair20/a_50/a_50_c_0/gen10out//polyg enic.logs.out Best model is named poly and null0 Final models are named poly, spor, nocovar Residual Kurtosis is , within normal range January 20, 2014 IIGC 2014 SOLAR Workshop 17

18 OpenMX January 20, 2014 IIGC 2014 SOLAR Workshop 18

19 Inputs to OpenMX Pedigree Coded in SEM Phenotype Variables January 20, 2014 IIGC 2014 SOLAR Workshop 19

20 Outputs of OpenMX Results stored into R variables January 20, 2014 IIGC 2014 SOLAR Workshop 20

21 Cross Platform Comparison Closed source/black box Easily extendible to complex families Easier to specify complicated pedigrees Single threaded execution Complete list of command descriptions Multi-platform (tcl-based) Open source Difficult to extend to complex families Requires user input for starting values of A, C, E Tends to not converge more often than SOLAR Integrates with R s cluster processing Well managed, active forum, lots of help documents on a wiki January 20, 2014 IIGC 2014 SOLAR Workshop 21

22 Outline Motivation Software for performing heritability analysis Simulations Twin Study (SOLAR & OpenMX) Family Study (SOLAR) Live Demo Conclusion January 20, 2014 IIGC 2014 SOLAR Workshop 22

23 Why use simulation? Debug Performance assessment Method comparison January 20, 2014 IIGC 2014 SOLAR Workshop 23

24 Why simulate? : Debug How do we know if the software is properly Installed (documentation), Configured (system / platform), Used (user error) Isolate errors, crashes, convergence issues Freely sharable design Reproducible results without large data exchange Commoditize heritability analysis January 20, 2014 IIGC 2014 SOLAR Workshop 24

25 Why simulate? : Performance New studies operate on edge cases that may have not been expected by the designers. Are there coding bugs? Are there theoretical bugs? Are crashes due to poorly formatted data? Confirm that a generative model for the study is well understood. Produce empirical power curves for study planning. Assess estimator performance January 20, 2014 IIGC 2014 SOLAR Workshop 25

26 Alternative for Power Estimation I h2power Purpose: Perform heritability power calculations This command performs a power calculation for the currently loaded pedigree, with the following default assumptions: (1) the trait to be studied is either quantitative or dichotomous (e.g. affected/unaffected) (2) the trait to be studied is influenced by additive genetics (3) all pedigree members will be phenotyped for the trait to be studied (unless the -data option is used to exclude those individuals who will not have phenotypic data; see the description of this option below) Also see power. January 20, 2014 IIGC 2014 SOLAR Workshop 26

27 Alternative for Power Estimation II Theoretical power models are available using spectral properties of the pedigree structure. John Blangero, et al. Chapter One - A Kernel of Truth : Statistical Advances in Polygenic Variance Component Models for Complex Human Pedigrees. Advances in Genetics Volume January 20, 2014 IIGC 2014 SOLAR Workshop 27

28 Why simulate? : Comparison Simulations provide scalable access to many (virtual) subjects with known genetic association structure Measure accuracy (bias) of heritability estimators with ground truth Measure precision (variance) of heritability estimators Mean Squared Error = Bias 2 + Variance. Quantify absolute and relative accuracy January 20, 2014 IIGC 2014 SOLAR Workshop 28

29 Modeling family structures MZ and DZ Twins Nuclear Families (Quartets) Grand- Nuclear Families (Octets) January 20, 2014 IIGC 2014 SOLAR Workshop 29

30 Quantitative Trait Simulation Pedigrees Created subjects A simulated C simulated Phenotype files created y = X β + N(0, 2ΦA + γc + 1 E) y = simulated phenotype X = simulated covariate ( age ) β= arbitrary coefficient (.005) N= noise dependent on: A, C, E = specified by user Φ = expected fraction of genome shared between subjects (MZ =.5, DZ =.25, parent-child=.25) γ = assumed common environment between relationship pairs (DZ, MZ, siblings = 1) January 20, 2014 IIGC 2014 SOLAR Workshop 30

31 Example Pedigree Simulation Simulating family structures and phenotypes Twin 1 Twin 2 MZ twins Twin 1 A + C + E A + C Twin 2 A + C A + C + E January 20, 2014 IIGC 2014 SOLAR Workshop 31

32 Example Pedigree Simulation Simulating family structures and phenotypes Twin 1 Twin 2 MZ twins Twin 1 A + C + E A + C Twin 2 A + C A + C + E Twin 1 Twin 2 DZ twins Twin 1 A + C + E.5*A + C Twin 2.5*A + C A + C + E January 20, 2014 IIGC 2014 SOLAR Workshop 32

33 Outline Motivation Software for performing heritability analysis Simulations Twin Study (SOLAR & OpenMX) Family Study (SOLAR) Live Demo Conclusion January 20, 2014 IIGC 2014 SOLAR Workshop 33

34 Twin Study: Cross Platform Comparison January 20, 2014 IIGC 2014 SOLAR Workshop 34

35 Cross Platform Comparison Simulated quantitative phenotype with the ACE Model and covariate of simulated age in twins Pedigrees Created subjects MZ : DZ = 1:1 A simulated C simulated Phenotype files created January 20, 2014 IIGC 2014 SOLAR Workshop 35

36 Family Study of Heritability Estimates with SOLAR Heritability (A) Estimates Simulated Heritability (A) % Number of Subjects Pedigrees Created subjects A simulated C simulated Phenotype files created January 20, 2014 IIGC 2014 SOLAR Workshop 36

37 Cross Platform Comparison-Twin Study C = 0 Simulated Heritability (A) % Bias in Heritability Estimates (A) January 20, 2014 IIGC 2014 SOLAR Workshop 37

38 Cross Platform Comparison-Twin Study C = 0 Simulated Heritability (A) % Bias in Heritability Estimates (A) January 20, 2014 IIGC 2014 SOLAR Workshop 38

39 Cross Platform Comparison-Twin Study C = 0 Heritability (A) % = abs Bias OpenMX abs Bias SOLAR Blue = OpenMX more biased Red = SOLAR more biased January 20, 2014 IIGC 2014 SOLAR Workshop 39

40 Cross Platform Comparison-Twin Study Heritability (A) Estimates C = 0 Bias in A Simulated Heritability (A) % Variance in A January 20, 2014 IIGC 2014 SOLAR Workshop 40

41 Cross Platform Comparison-Twin Study Heritability (A) Estimates C = 0.30 Bias in A Simulated Heritability (A) % Variance in A January 20, 2014 IIGC 2014 SOLAR Workshop 41

42 Cross Platform Comparison-Twin Study Heritability (A) Estimates C = 0.50 Bias in A Simulated Heritability (A) % Variance in A January 20, 2014 IIGC 2014 SOLAR Workshop 42

43 Cross Platform Comparison-Twin Study Heritability (A) Estimates C = 0.70 Bias in A Simulated Heritability (A) % Variance in A January 20, 2014 IIGC 2014 SOLAR Workshop 43

44 Cross Platform Comparison-Twin Study C = 0 C = 0.30 C = 0.50 C = 0.70 Simulated Heritability (A) % = abs Bias OpenMX abs Bias SOLAR Blue = OpenMX more biased Red = SOLAR more biased January 20, 2014 IIGC 2014 SOLAR Workshop 44

45 Outline Motivation Software for performing heritability analysis Simulations Twin Study (SOLAR & OpenMX) Family Study (SOLAR) Live Demo Conclusion January 20, 2014 IIGC 2014 SOLAR Workshop 45

46 Family Study of Heritability Estimates with SOLAR January 20, 2014 IIGC 2014 SOLAR Workshop 46

47 Family Study of Heritability Estimates with SOLAR Heritability (A) Estimates C = 0 Bias in A Simulated Heritability (A) % Variance in A January 20, 2014 IIGC 2014 SOLAR Workshop 47

48 Family Study of Heritability Estimates with SOLAR Heritability (A) Estimates C = 0.30 Bias in A Simulated Heritability (A) % Variance in A January 20, 2014 IIGC 2014 SOLAR Workshop 48

49 Family Study of Heritability Estimates with SOLAR Heritability (A) Estimates C = 0.50 Bias in A Simulated Heritability (A) % Variance in A January 20, 2014 IIGC 2014 SOLAR Workshop 49

50 Family Study of Heritability Estimates with SOLAR Heritability (A) Estimates C = 0.70 Bias in A Simulated Heritability (A) % Variance in A January 20, 2014 IIGC 2014 SOLAR Workshop 50

51 Heritability Estimates with Family Data If you don t know common environment contribution (C) nuclear, grand-nuclear family study in SOLAR twin study in OpenMX If you know C = 0 twin family study in SOLAR If you know C > 0 nuclear, grand-nuclear family study in SOLAR twin family study in OpenMX January 20, 2014 IIGC 2014 SOLAR Workshop 51

52 Outline Motivation Software for performing heritability analysis Simulations Twin Study (SOLAR & OpenMX) Family Study (SOLAR) Live Demo Conclusion January 20, 2014 IIGC 2014 SOLAR Workshop 52

53 Platform Scientific Linux bit OS SOLAR (Experimental), last updated on December 31, 2013 R **NOT 3.X.X** OpenMX January 20, 2014 IIGC 2014 SOLAR Workshop 53

54 Simulation Run Times Simulation Single Core 1.6 GHz OpenMX (including simulations) Scientific Linux 6.4 with Kernel MacBook Pro with VMWare Fusion 7 SOLAR AE Twins 155 min 266 min ACE Twins 242 min 382 min Nuclear Families Grand Nuclear Families min 1803 min January 20, 2014 IIGC 2014 SOLAR Workshop 54

55 January 20, 2014 IIGC 2014 SOLAR Workshop 55

56 Outline Motivation Software for performing heritability analysis Simulations Twin Study (SOLAR & OpenMX) Family Study (SOLAR) Live Demo Conclusion January 20, 2014 IIGC 2014 SOLAR Workshop 56

57 Does any of this matter? h ±0.11 January 20, 2014 IIGC 2014 SOLAR Workshop 57

58 Cross Platform Comparison-Twin Study C = 0 Simulated Heritability (A) % Bias in Heritability Estimates (A) January 20, 2014 IIGC 2014 SOLAR Workshop 58

59 Cross Platform Comparison-Twin Study C = 0 Heritability (A) % = abs Bias OpenMX abs Bias SOLAR Blue = OpenMX more biased Red = SOLAR more biased January 20, 2014 IIGC 2014 SOLAR Workshop 59

60 Side by Side Comparison SOLAR OpenMX January 20, 2014 IIGC 2014 SOLAR Workshop 60

61 Side by Side Comparison SOLAR OpenMX January 20, 2014 IIGC 2014 SOLAR Workshop 61

62 Commonality of the common effect Phenotype A C White matter tracts (Whole brain FA) White Matter (neonatal regional metrics) ~0.5 Low Kochunov, et.al., Neuroimage,2010 Cortical Thickness ~0.7 <0.10 Kremen, et.al. Neuroimage, 2010 Brain Volume ~0.7 <0.05 Kremen, et.al. Neuroimage, 2010 ~0-0.8 ~ Geng, et al., Twin Res Hum Genet. 2012

63 e-science Objectives Provide a freely available platform for learning Virtual Machine available on NITRC Quantify differences between OpenMX and SOLAR Studies both AE and ACE models Illustrate integration with other analysis environments Currently, we are using R. In continuing work, integrate SOLAR s nifti support with pipeline platforms January 20, 2014 IIGC 2014 SOLAR Workshop 63

64 Thank you. Neda Jahanshad Peter Kochunov Tom Nichols Paul Thompson John Blangero David C. Glahn And the ENIGMA DTI working group. MASI Lab Fall 2013 NIH/NIBIB R01 EB January 20, 2014 IIGC 2014 SOLAR Workshop 64