Heterogeneity Boulder 2004 Heterogeneity Questions Are the contributions

Heterogeneity Boulder, 2004

Heterogeneity Questions Are the contributions of genetic and environmental factors equal for different groups, such as sex, age, race, ethnicity, SES, environmental exposure, etc. ? n Gene x Sex/ Age/ Race / Environment Interaction n

Heterogeneity Questions n Is heterogeneity due to differences in the magnitude of the effects (quantitative)? e. g. Are genetic/ environmental contribution of factors greater/smaller in males than in females? n Is heterogeneity due to differences in the nature of the effects (qualitative)? e. g. Are there different genetic/environmental factors influencing the trait in males and females?

Heterogeneity across groups differences in variance components n NOT mean differences n group membership n continuous heterogeneity n

Group Comparisons Comparison Concordant for group membership Discordant for group membership gender MZ & DZ: MM & FF DZ: opposite sex age MZ & DZ: young & old nationality MZ & DZ: OZ & US environment MZ & DZ: urban & rural

Models for Concordant Pairs Model Group 1 Full / Constrained / Heterogeneity Homogeneity a 1 c 1 e 1 Group 2 a 2 c 2 e 2 a 1 c 1 e 1 Statistics 12 12 Parameters 6 3 Degrees of Freedom 6 9

Models for Concordant and Discordant Pairs Model Group 1 Full / Constrained / Heterogeneity Homogeneity a 1 c 1 e 1 Group 2 a 2 c 2 e 2 a 1 c 1 e 1 Statistics 15/18 Parameters 6 3 Degrees of Freedom 9/12 12/15

Models for Concordant and Discordant Pairs Model Scalar General Group 1 a 1 c 1 e 1 Group 2 a 1 c 1 e 1 k a 2 c 2 e 2 h Statistics 15/18 Parameters 4 7 Degrees of Freedom 9/12 12/15

Summary of Models n n Homogeneity Model: no quantitative, no qualitative differences Heterogeneity Model: quantitative but no qualitative differences Scalar Model: special case of heterogeneity model with proportional quantitative differences General Model: quantitative and qualitative differences

Homogeneity Model

Example Homogeneity Model

Homogeneity Model Variance Covariance Correlation MZM 0. 98 0. 89 0. 91 MZF 0. 98 0. 89 0. 91 DZM 0. 98 0. 57 0. 58 DZF 0. 98 0. 57 0. 58 DZMF 0. 98 0. 57 0. 58

Heterogeneity Model

Example Heterogeneity Model

Heterogeneity Model Variance Covariance Correlation MZM 0. 59 0. 50 0. 85 MZF 0. 98 0. 89 0. 91 DZM 0. 59 0. 38 0. 64 DZF 0. 98 0. 57 0. 58 DZMF 0. 59 / 0. 98 0. 45 0. 59

Scalar Model

Example Scalar Model

Scalar Model Variance Covariance Correlation MZM 0. 98 0. 89 0. 91 MZF 2. 20 2. 00 0. 91 DZM 0. 98 0. 57 0. 58 DZF 2. 20 1. 28 0. 58 DZMF 0. 98 / 2. 20 0. 85 0. 58

General Model

Example General Model

General Model Variance Covariance Correlation MZM 0. 98 0. 89 0. 91 MZF 0. 98 0. 89 0. 91 DZM 0. 98 0. 57 0. 58 DZF 0. 98 0. 57 0. 58 DZMF 0. 98 0. 25 0. 26

Alternative General Model

Example 2 General Model

Summary of Models