Does Black Birthweight Reach Genetic Potential?

Transcription

1 Does Black Birthweight Reach Genetic Potential? Genetic Epidemiology Model is Sensitive to Twin Sex-Composition and Mortality Muriel Zheng Fang October 7, 2012 I examine the relative importance of environmental and genetic variance components for birthweight, an indicator of health at birth. Using data from the National Longitudinal Study of Adolescent Health (Add Health) on genotyped twins who differ in their degree of genetic relatedness, I estimate the genetic and environmental components of variance in birthweights using two orthogonality conditions. First, since twins are in-utero at the same time and parents cannot invest differentially, the investment-endowment orthogonality implies that one twin serves as a counterfactual for the other. Second, the investment-zygosity orthogonality implies that MZ pairs serve as counterfactuals to DZ pairs. The source of variation in within-pair birthweight resemblance is the pairs genetic similarity, not selective investments as a function of whether twins are MZ or DZ, especially for this sample of twins born before the wider adoption of In Vitro Fertilization (IVF). Besides the two levels of Department of Economics, University of Akron, Akron, OH, 44325, United States. zfang1@uakron.edu

2 orthogonality, another source of identification strength is that the National Longitudinal Survey of Adolescent Health (Add Health) ascertains twin types with modern genetic methods, which reduces the incidences of reverse causality misclassification in which same sex DZ twins who look similar are more likely to be ported as MZ. The results suggest that the environmental contribution is relatively larger and the genetic contribution is relatively smaller for black children, than it is for whites. On the surface, this finding on blacks lower heritability is consistent with the literature that reports lower heritability estimates for subjects in poorer environments. I also document limitation to this research method: Add Health female same-sex twins birthweights are irregular compared to the Matched Multiple Birth from Natality records. I show in simulation that the estimates could be sensitive to slight perturbations in the twin-type composition (MZ-DZ, gender) and twin mortality risks. The sensitivity suggests that research on health outcome heritability could be improved by considering mortality selection. 1 Introduction: Why Study Racial Differences in Birthweight Variance Components? An association has also been established between low birth weight and adverse adult health and economic outcomes including greater likelihood for cardiovascular disease in adulthood (Barker, 1995), greater likelihood for disability and incarceration (Almond, 2006), lower education attainment (Behrman and Rosenzweig, 2004), and lower likelihood of economic self-sufficiency (Almond, 2006). Birthweight difference hence serves as a starting point to understand rich arrays of adulthood disparities. In the United States blacks on average have lower birthweight than non-hispanic whites. This is partially attributable to higher rates of preterm delivery among blacks (Kessel et al., 1984). However, even for infants born full term ( 38 weeks) the average black 2

3 birthweight is still lower than that of white by almost 200 grams (Oken et al., 2003). This paper investigates what factors contribute to the racial birthweight difference. Both environmental and genetic factors have been shown to be associated with birthweight at the individual level. Researchers have found that an increased risk for low birthweight is associated with environmental exposure to pollution, including sulfur dioxide and total suspended particulates (Rogers et al., 2000), carbon monoxide, nitrogen dioxide and sulfur dioxide (Ha et al., 2001), aromatic hydrocarbons in vehicle exhaust pollutant (Aguilera et al., 2009), exposure to phthalate from nonoccupational routes such as personal care products (Zhang et al., 2009), indoor air pollution from solid fuel use (Pope et al., 2010), and exposure to polybrominated biphenyls through accidental contamination (Givens et al., 2007). It has been shown that blacks have greater exposure to environmental pollutants than whites (Currie, 2011). There are also environmental influences specific to black in the United States: Fuller (2000) suggested that the mismatch between blacks heavy pigment and the inadequate UVB exposure of high latitudes could result in low levels of serum vitamin D, which contribute to low birthweight. Genetic factors also play a role in birthweight, although there is no evidence to suggest that the difference between birthweight in blacks and whites at the population level is associated with race-specific differences in specific genes. Birthweight have been associated with genetic mutations related to the regulation of insulin resistance, insulin secretion, and insulin-like growth factor (IGF). Common variant (Weedon et al., 2005, 2006) 1 and rare mutation (Hattersley et al., 1998) 2 of glucokinase (GCK) gene 3 have been found to 1 The presence of rs , a common GCK variant, is found to be associated with increased birthweight. The average difference is 64 g (Weedon et al., 2005) or 32 g (Weedon et al., 2006), depending on the sample. 2 Hattersley et al. (1998) found that children carrying rare GCK gene mutations have lower birthweights than their siblings who do not carry the mutation, with a mean birthweight difference of 521 g. A difference remains after correcting the birthweight for gestational age, gender and birth order. Hattersley et al. (1998) notes that the birthweight difference is largest when mother carries the GCK mutation but not the fetus. 3 GCK gene codes protein that impacts glucose metabolism. 3

4 be associated with birthweight differences. Insulin-like growth factor (IGF) genes are also found to be associated with birthweight variations (Arends et al., 2002; Vaessen et al., 2002). 4 An association between variants of small heterodimer partner (SHP) gene and low birthweight has also been reported (Hung et al., 2003; Meyre et al., 2005). These studies illustrate the genetic factor for birthweight variation. This paper uses the techniques of Genetic Epidemiology to decompose the population variation in birthweight into genetic and environmental components, using a sample of monozygotic (MZ) and dizygotic (DZ) twins from the National Longitudinal Survey of Adolescent Health (Add Health). The analytic basis of Genetic Epidemiology rests on differences by degree of relatedness in levels of phenotypic resemblance within kinship pairs. If pairs who are more closely genetically related have higher levels of phenotypic resemblance than pairs who are less closely related, and if individuals within kinship pairs share environment to the same extent regardless of kinship types 5, then the difference in resemblance could be attributed to genetic factors. The Genetic Epidemiology model to parse the overall variance in birthweight into components associated with genetics and common environment is appropriate because the intrauterine environment is similar for a pair of twins and it is difficult for parents to make selective investments differentially by twin. Thus MZ and DZ twins are likely to share (intra-uterine) environment to the same degree. Because parental investments are 4 Arends et al. (2002) found that a minor variation (Allele 191) of insulin-like growth factor-i (IGF- I) gene were in transmission disequilibrium from parents to their Small for Gestational Age (SGA) children. [Transmission Disequilibrium is often tested on the alleles transmitted to children conditional on parental genotype. The knowledge of parental genotype makes the test robust to population substructure. Typically heterozygote (with regard to the location) parents would be informative, because homozygote parents always produce gametes carrying the same allele on the location and there is no variation in the alleles transmitted to children.] Arends et al. (2002) found allele 191 to be transmitted more, and allele 198 transmitted less from parents to Small for Gestational Age (SGA) children. Vaessen et al. (2002) also found an association between the IGF-I genotype and birthweight: absence of the wild-type (192 base-pair) allele was associated with a mean birthweight reduction of 215 g. 5 There are additional assumptions, for example, the assumption on the genetic model that influence the traits (whether it is additive or including other influences), the assumption that there is no assortative mating (of the parents) on the trait, and that the degrees of environment similarity for different kinship pairs are the same. The assumptions will be explained in details below. 4

5 orthogonal to the twins endowments, one twin thus serves as a counterfactual for another. Second, MZ pairs serve as counterfactual to DZ pairs because the major difference in the within-pair birthweight resemblance is the pairs genetic similarity. This similarity is arguably orthogonal to parental investment intentions for this sample of twins who are mostly born before the use of In Vitro Fertilization (IVF). 6 The plan of the paper is as follows. Section 2 describes the physiological reasons for expecting different levels of birthweight discordance between MZ and DZ twin pairs and highlights the importance of correct classification of twin type. Section 3 presents the Additive-genetic, Common environment, Unique environment decomposition model. Section 4 describes the data used in the analysis. Second 5 presents results for blacks and whites and explores a variety of explanations for the observed race difference. Section 6 concludes with a discussion. 2 Physiological Foundation for MZ, DZ Twins to Have Different Levels of Birthweight Discordance The basic units of analysis in Genetic Epidemiology are levels of phenotypic resemblance within kinship pairs. The idea is that if pairs who are more closely genetically related have higher levels of phenotypic resemblance than pairs who are less closely related, and if individuals within kinship pairs share environment to the same extent regardless of kinship types, 7 then the differences in levels of resemblance could be attributed to 6 The world s first IVF baby was born in 1978, and the first IVF baby in the United States is born on December 28, This first-in-u.s. fertility clinic reported only 29 babies, including one set of twins, to have been born by March 1983 (Garcia et al., 1984). The Add Health twins born between 1974 to 1983 should be considered as natural occurring twinning for practical purposes. 7 Note, the model is concerned with the environment shared by individuals within kinship pairs, as opposed to environment for individuals across different kinship pairs, or environment for all individuals in the sample. The basic unit of analysis is the pairs phenotypic resemblance, not the individual or the individual phenotype. Share environment to the same extent does not require all kinship pairs to have the same environment, instead it only requires that the level of environmental similarity for more closely related pairs is comparable to the level of environmental similarity for less closely related pairs. 5

6 the pairs different levels of genetic relatedness. Consequently, the proportion of the phenotypic variation due to genetic contribution can be modeled by comparing the levels of phenotypic resemblance. A corollary is that if genetic closeness confers no difference in phenotypic resemblance, the model would estimate little contribution of genetic factors. Below I summarize research on the physiological foundation for MZ twins to be more similar in birthweight than DZ twins. MZ and DZ twin have fundamentally different formation mechanisms, hence they will have dissimilar levels of phenotypic similarity. Hall (2003) provides a general explanation for MZ twins: cells within the blastocyst develop discordance, recognize each other as foreign, and use cell-recognition mechanism to set up two separate cell masses. This suggests that MZ twins would have minor yet recognizable differences. Discordance in MZ twins are attributable to stochastic mechanisms 8. DZ twinning has a different mechanism: it requires more than one dominant ovarian follicle matured during the same menstrual cycle 9. There are rare cases of DZ twinning that the second fetus start later when the first fetus has already progressed one month, which leads to unbalanced development of the DZ twins. This exemplifies that different formation mechanisms allow DZ twins to be less similar than MZ twins. Twin pairs sex composition could lead to MZ twins to be more similar in birthweight than DZ twins in two different mechanisms. First, there is sex difference in birthweight with typical female newborns lighter than males. Other things equal, an different-sex pair consisting of a male and a female will be less similar than a male-male pair or a 8 Ante-partum physical and physiological reasons include initial differences in the number of cells at the time of split, differences in vascular flow, variation in attachment to the placenta, whether the twins share a placenta or have separate ones, i.e., whether they are monochorionic or dichorionic, and the total number of cell divisions when twinning occurs (Gringras and Chen, 2001; Hall, 2003). Genetic mechanisms include: chromosomal anomalies, single gene disorders, skewed X inactivation, genome imprinting defects, mitochondrial disturbances, minisatellites. 9 DZ twinning incidence rises with the following factors: an increased concentration of the folliclestimulating hormone, maternal age, increased parity, and genetic history. Taller and obese mothers are also at greater risk of DZ twinning (Hall, 2003; Hoekstra et al., 2008). Hoekstra et al. (2008) considers the associations between twinning and other factors such as folic acid, seasonality, and particular genetic mutation to be less convincing. 6

7 female-female one. Because different sex pairs are almost always DZ twins 10, MZ twins would be more similar in birthweight because of homogeneity within pairs. Second, even if we restrict the comparison to same-sex pairs, homogeneity across pairs also makes MZ birthweight more similar. Hall (2003) suggests that while the sex ratio in DZ twins is comparable to that of singletons, there is an excessive ratio of females in MZ twins 11. The higher across pairs homogeneity refers the fact that a larger proportion of the MZ twins are of the same composition (female-female) than that of the DZ same-sex pairs. Conley and Rauscher (2011) considers the reverse causality misclassification that twin pairs look more alike are more likely to be categorized as MZ pairs, and those who look less alike are more likely to be misclassified as DZ pairs. The misclassification in selfreported twin types leads to overestimate of genetic components because it exaggerates the MZ pairs similarity and diminishes DZ pairs similarity. Fortunately, the Add Health sample reduces misclassification by ascertain zygosity using genotyping on salivary buccal cell DNA 12. The improved accuracy in twin type is one source of strength for current study. 10 Hall (2003) documents the very rare cases in which MZ pairs could appear to be different-sex due to abnormalities in the expression of sex chromosome. 11 The speculated mechanism is that female embryos development are slower, their cells grow slowly until going through the X inactivation process. This leads to female same-sex twins having later separation, and hence female-female twins are more represented in the more closely related pairs. Twins can share a placenta in which case they are monochorionic. Most DZ twins and some MZ twins are dichorionic and have separate placentas. All monochorionic pregnancies involve MZ twins, whereas DZ twins and some MZ twins are dichorionic have separate placentas (Hall, 2003). Monochorionic twins generally have two amniotic sacs (diamniotic, DA), but in rare cases they share the same amniotic sac (monoamniotic, MA). Chorionicity differs by gender and may play role in birthweight discordance. Types of birth ranked in the order of increasing percentage of females are: singletons < DZ twins < MZ dichorionic (DC,MZ) twins<mz monochorionic diamniotic (DA,MC,MZ) twins < MZ monochorionic monoamniotic (MA,MC,MZ) twins < conjoined twins. 12 Twin type estimates based on observable phenotype similarities could be mistaken. Even DNA genotyping results could be misleading if the sample does not include somatic cells because stem cells are more likely to subject to transfusion. For MZ twins, monochorionic placentas of could have vascular connections which leads to sharing of stem cells. When the twins share the same vascular placental connection, or have bone marrow exchange with each other, twin type based on blood cell could be misleading. Even for DZ twins without vascular connection, they could still have microchimerism with fetal-mother-fetal exchange. DNA sequencing to identify twin types need to use somatic cells. 7

8 3 Additive- genetic, Common- environment, unique- Environment (ACE) Model: Regression and SEM Genetic Epidemiology models rest on the idea that if the correlation of outcomes within MZ twins is larger than that of DZ twins, the difference of correlation can be attributed to genetic influences. I choose the ACE model because preliminary analysis show support for it over alternative specification involving dominance effect 13. The ACE model posits that the outcome of one twin (proband) Y 1 as the sum of three independent parts: (1) Additivegenetic (A), corresponding to the narrow 14 heritability a 2 ; (2) Common-environment (C), corresponding to the between family component c 2 ; (3) non-shared-environmental (E), corresponding to the within family component e 2 components : Y 1 = A 1 + C 1 + E 1 (1) The outcome of the other twin (co-twin) is similarly Y 2 = A 2 + C 2 + E 2. With standardization, the correlation between the two twins outcomes equals the covariance ρ = ρ Y1,Y 2 = COV (Y 1, Y 2 ), and the three independent parts are described by the corresponding dimensionless proportions of the total variance: a 2, c 2, e 2. The ACE model makes following assumptions: 13 The ADE (Additive-genetic, Dominant-genetic, and non-shared Environmental contributions) model is another variant of the behavior genetics model that imply the genetic model is not additive but could have non-additive such as dominance effect. While both ACE and ADE models assume R MZ = 1, they differ in the value assigned to R DZ. The ACE model assumes that the contribution of alleles to outcomes is linearly additive, and assigns the Genetic component R DZ = 0.5. The ADE model accounts for nonlinear effect in the influence of Genetic component, and assigns other values to R DZ such as Both a 2 and c 2 components are identified, although their estimates change values in response to assumptions about R DZ. Researchers choose different plausible models to prevent the variance components becoming negative (Neale and Maes, 2004). For example, if ρ DZ < 0.5ρ MZ then there is evidence for dominance, and c 2 would be estimated negative in the ACE model with R DZ = 0.5. Because the birthweight data does not show evidence for genetic dominance and because ρ DZ is at least as large as 0.5ρ MZ, I use ACE model. In behavior genetic models h 2 and c 2 should be non-negative. In the ACE model this requires that R MZ R DZ 0.5R MZ. These conditions can be violated in a sample. 14 The broad heritability takes into account other mode of genetic influences such as the dominance, recessive or epistasis. The broad heritability is considered not additive. 8

9 1. the bivariate covariance between any two components of Additive-genetic (A), Commonenvironment (C), and the non-shared-environmental (E) is zero. 15 It implies: ρ = COV (Y 1, Y 2 ) = COV (A 1, A 2 ) + COV (C 1, C 2 ) + COV (E 1, E 2 ) (2) 2. the non-shared environment component is independent across twins within a pair, so COV (E 1, E 2 ) = 0. It implies: ρ = COV (A 1, A 2 ) + COV (C 1, C 2 ) (3) 3. MZ and DZ twins share environmental similarity of the same degree, the Commonenvironment components is the same across the two twin types COV (C 1, C 2 ) MZ = COV (C 1, C 2 ) DZ = c 2 ; and 4. the Genetic component can be expressed as a multiplicative function of the twin pair s biological relatedness R and the Additive-genetic variance component COV (A 1, A 2 ) MZ = R MZ a 2, and COV (A 1, A 2 ) DZ = R DZ a 2. The third and fourth assumptions together imply that the correlation in outcomes between MZ and DZ twins can be written as function of Additive-genetic and Commonenvironment variance component a 2, c 2 : ρ MZ = R MZ a 2 + c 2 (4) ρ DZ = R DZ a 2 + c 2 15 This implies an absence of Genetic - Environment covariance. An example of the Genetic - Environment covariance is that parents who transmit alleles that are associated with better outcomes also choose to live in a less polluted environment. 9

10 Solving yield the components a 2, c 2 : a 2 = ρ MZ ρ DZ R MZ R DZ (5) c 2 = ρ DZR MZ ρ MZ R DZ R MZ R DZ The equations above describe the correspondence between the sample properties ρ MZ and ρ DZ and estimated variance components of a 2, c 2. The estimates require assumption on the parameters R MZ, R DZ. With the additional assumption of no assortative mating that the alleles from parents are no more similar than that of a random pair from the population, ACE model assumes R MZ = 1 implying MZ twins share the same genetic inheritance, and R DZ = 0.5 implying DZ twins share half the genetic inheritance. The DeFries-Fulker regression (DeFries and Fulker, 1985; Waller, 1994) implements the ACE (Additive-genetic, Common-environment, and non-shared Environmental contributions) model by setting up the birthweight of one twin (Y 1 ) as the dependent variable, regressing on the birthweight of the other twin Y 2, a measurement of the pairs genetic relatedness R, and an R and Y 2 interaction term R Y 2 : Y 1 = α 0 + α 1 R + α 2 Y 2 + α 3 R Y 2 + ε (6) The regression uses a double-entry set up that a particular twin is first used as Y 1 in one observation and then as Y 2 in another, to make Y 1 and Y 2 twin symmetric, and prevent the Y 2 coefficient ( Y 2 Y 1 Y 2 Y 2 ) from changing with respect to the choice of Y 1 twin. This leads to the same univariate variance V AR(Y 1 ) = V AR(Y 2 ), and the Y 2 coefficient is Y Y 2Y 1 = COV (Y 2, Y 1 ) 2Y 2 V AR(Y 2 ) = COV (Y 2, Y 1 ) V AR(Y1 )V AR(Y 2 ) = ρ Y 1,Y 2 (7) 10

11 Since the coefficient Y 2 Y 1 Y 2 Y 2 is estimated α 2 + α 3 R this establish a correspondence between the regression coefficients and the correlation coefficients that reflect phenotypic resemblance for different kinship pairs: (α 2 + R MZ α 3 ) = ρ MZ MZtwins (α 2 + R DZ α 3 ) = ρ DZ DZtwins (8) Solving yields: α 3 = ρ MZ ρ DZ R MZ R DZ (9) α 2 = ρ DZR MZ ρ MZ R DZ R MZ R DZ This parallels the earlier results in equation 5, and implies a correspondence between the regression coefficients and the variance component estimates: α 3 = a 2 (10) α 2 = c 2 Thus E(α 2 ) = c 2 is an estimate of the Common-environment component, and E(α 3 ) = a 2 is an estimate of Additive-genetic variance component for the phenotype Y. Since each unique sibling pair enters in the data set twice, standard errors are adjusted for the fact that the records are not independent. Figure 1 illustrates the correspondence between (ρ DZ, ρ MZ ) and the estimated variance components (a 2, c 2 ) in ACE models. The cross-hatched region represents the set of (ρ DZ, ρ MZ ) that are consistent with the ACE model and satisfy 0 a 2 1 and 0 c 2 1. As long as ρ DZ is larger than 0.5ρ MZ, to the right of the c 2 = 0 line, the Common-environment component will be non-negative. The closer ρ DZ is to 0.5ρ MZ, the (ρ DZ, ρ MZ ) point is close to the c 2 = 0 line, and the smaller is the Common-environment 11

12 component. If ρ DZ is smaller than ρ MZ, to the left of the a 2 = 0 line, the Additive-genetic component will be non-negative. The closer ρ DZ is to ρ MZ, the (ρ DZ, ρ MZ ) point is close to the a 2 = 0 line, then the smaller is the Additive-genetic variance component a 2. ρ MZ ACE Model R DZ = 1 2, R MZ = 1 1 a 2 = 1 line a 2 = 2(ρ MZ ρ DZ ) series a 2 = 0 line c 2 = 2ρ DZ ρ MZ series 1 ρ DZ c 2 = 0 line c 2 = 1 line Figure 1: Additive-genetic and Common-environment variance components as functions of MZ, DZ intrapair correlations, in ACE model with R MZ = 1, R DZ = 0.5, a 2 = ρ MZ ρ DZ R MZ R DZ = 2(ρ MZ ρ DZ ) and c 2 = ρ DZR MZ ρ MZ R DZ R MZ R DZ = R MZ 2R DZ. I also estimate a variant of the model that includes a gender-difference regressor to account for sexual difference in birthweight at the individual level within DZ twins (Oken et al., 2003). The model is: Y 1 = α 0 + α 1 R + α 2 Y 2 + α 3 R Y 2 + β(male 1 Male 2 ) + ε (11) where the term (Male 1 Male 2 ) equals 0 for same-sex twin pairs, 1 if Y 1 is male and Y 2 is female, and 1 if Y 1 is female and Y 2 is male. β is thus expected to be positive to 12

13 account for slightly higher birthweights of males. 3.1 Structural Equation Model (SEM) Variance decomposition was historically developed in the Structural Equation Model (SEM) framework (Wright, 1920). By using a Cholesky decomposition to represent covariance matrix (Neale and Maes, 2004), SEM estimates of the variance components are non-negative. This avoids potential problems in the DeFries-Fulker regression framework when variance component estimates are negative. Figure 1 shows that for (ρ MZ, ρ DZ ) combinations outside the hatched region, for example, points to the right of a 2 = 0, Additive-genetic variance component estimate would be negative. Figure 2 illustrates the SEM model. The boxes represent birthweight for twins, the ovals represent the latent components for Additive-genetic, Common-environment, and the unique-environment. The lower letter a, c, e represents the relationship between the latent components to the observed birthweight. The part of twin birthweight covariance that is attributable to the twins genetic similarity is represented by the arched line connecting the latent genetic factors for the two twins A 1 and A 2. The coefficient 1 on the line represents that for MZ twins who share the same genetic inheritance, their latent genetic factors are related with a coefficient of 1. The coefficient 0.5 represents the genetic relatedness for DZ twins, which is 0.5. Because of the previously stated third assumption on MZ and DZ twins sharing the same environment, both twin types have the coefficient of 1 between their Common-environment components. The absence of relatedness between the unique-environment components between two twins stems from the stated second assumption that the unique-environment are not related within the twin pairs. The covariance matrix for MZ twins in the ACE model is : COV (Y 1, Y 2 ) MZ,ACE = a2 + c 2 + e 2 a 2 + c 2 (12) a 2 + c 2 a 2 + c 2 + e 2 13

14 1/0.5 1/1 A 1 C 1 E 1 A 2 C 2 E 2 a c e a c e Twin 1 birth weight Twin 2 birth weight Figure 2: ACE (Additive-genetic, Common-environment, unique Environment) model for birthweight variance decomposition. The genetic relatedness for MZ twins is 1 and for DZ twins is 0.5. The equal-environment assumption is reflected in the specification that both types have the 1 coefficients between their Commonenvironment components. and the covariance matrix for DZ twins in the ACE model is: COV (Y 1, Y 2 ) DZ,ACE = a2 + c 2 + e a 2 + c 2 (13) 0.5 a 2 + c 2 a 2 + c 2 + e 2 I estimate the a 2, c 2, e 2 components using the openmx package (Boker et al., 2011). I also test the hypothesis that a specific variance component is zero, using restricted models that are nested within the ACE framework. For example, I test if Additivegenetic variance component a 2 is zero, by comparing the ACE model to the nested CE model with a fixed to zero. For example, the MZ variance matrix under CE model reduces to a2 + e 2 a 2. I use likelihood ratio tests between the restricted models to test if a 2 a 2 + e 2 a 2 = 0. Similarly I test if the Common-environment variance component c 2 is zero. 14

15 4 Data: Add Health and Matched Multiple Birth 4.1 Add Health Add Health is a nationally representative sample of adolescents in grades 7-12 selected from 134 schools in the United States. The respondents are born in 1974 to The first Wave interview was conducted in with respondents ages ranged from 11 to 21 years. It was followed up with 3 subsequent waves: Wave II was conducted in 1996, Wave III in , and Wave IV in Genetic markers results are provided for respondents in Wave III, a subset of which are twins whose twin types uncertainty are resolved. A few Respondents report conflicted values on key demographic variables such as sex, date of birth, race-ethnicity across the interview waves. Some conflicts could be resolved by a simple majority rule 16. Respondents with remaining conflicts or missing information on important demographic variables such as sex or race-ethnicity are excluded from analysis. Multiple births of higher orders, for example, three respondents reported from the same triplet are excluded from the analysis. Respondents birthweights are reported by their parents in Wave I interview. I exclude individuals with birthweight missing (n=129). I also restrict the sample to twins with birthweight between [260, 4734] grams, using the 1% and 99% percentile growth reference for United States singletons in 1999 and 2000 reported by Oken et al. (2003). Birthweights outside this range are excluded (n=60). I exclude birth date discordance (n=9) because twins with birth date discordance might be affected by pregnancy complications that make birthweights different from the general twin. I compare the Additive-genetic and Common-environment variance component estimates across white and black subsamples. The two groups collectively accounted for 16 For example, a respondent would be assigned female if she self-reports female two times, and male one time. 15

16 about 81% (1016/1254) of eligible twin respondents. I omitted many risk factors that are usually found to affect the birthweight of singletons such as in-utero exposure to smoking, because these factors are pregnancy-specific, twins from the same pregnancy would share the same exposure, there is no within-pair variation and these factors not affect within-pair birthweight resemblance. 4.2 Matched Multiple Birth (MMB) Data from Natality Records The Matched Multiple Birth (MMB) published by National Center for Health Statistics (NCHS) is a publicly available dataset that is closest to the study need in terms of time frame, match yield rate, and sample size. 17 The comparison between MMB to Add Health also focuses on patterns that are supposedly stable and documented in neonatology, such as that MZ twins are expected to have lower birthweight than DZ twins, different-sex DZ pairs would have relatively lower resemblance. I also use MMB data to simulate the effect of sample composition changes on variance component estimates. 17 Twins born at the same time as Add Health twins (1974 to 1983) would be a good data source to assess Add Health twins birthweight representativeness, or the departures from the norm. Although the Center for Disease Control and Prevention (CDC) has long established a system for Natality records, there is no publicly available multiple-birth dataset that overlap with the Add Health cohort. The traditional Live Birth and Fetal Death file (LBFD) is not suitable for the task of studying multiple pregnancies: the LBFD file contains records for individuals who are part of multiple pregnancies but does not publish variables that could identify the correct sets of individuals that belong to the same pregnancy. I also attempted to match individual records in the year 1983 Cohort Linked Birth and Death (CLBD) data, the earliest CLBD that is publicly accessible from NBER, using only the limited CLBD public data such as county of occurence, mother s age, birth order, et cetera. The preferred method that balances between match accuracy and yield rate has more than 25 % records unmatched. (Of the 53,665 reported twin pregnancies in 1983 there are 13,562 cases that I could not match.) Given that the 1. unmatched cases likely involves more cases of fetal and neonatal death than cases that survive (Martin et al., 2002); and 2. twin studies variance decomposition estimates are sensitive to a small amount of mismatch (Conley and Rauscher, 2011), a sample with 25% mismatch would be not be usable because it introduce more questions than it could help to answer. In the decade from the last Add Health twin pairs was born to the first year in MMB data, there are increasing uses of Assisted Reproductive Technology (ART) (Centers for Disease Control and Prevention (CDC), 2002), changes to population who are giving birth to twins (Kiely and Kiely, 2001), changes in twinning rate in this population (Blondel and Kaminski, 2002), and changes in twin fetal and neonatal mortality rate (Blickstein and Keith, 2004). These changes could potentially makes the MMB less comparable to the Add Health, but MMB has higher yield in matching individuals than the less-informed match using 1983 LBFD. 16

17 I restrict the MMB data to records that are reported to be from a twin pregnancy (N=418,354), and exclude the records that have their identification number missing (n=4,731), all records from the sets which have more than two individuals or have only one individual despite reporting twin pregnancies (n=13), both twins if either one has birthweight missing (n=3,458), both twins if either one has birthweight outside the empirical 1-99 percentile range gram (n=11,386), both twins if the reported mother s races conflict within the pair (n=1,766), both twins if either one has fetal death earler than 20 weeks 18 (n=16), both twins if either one has gestational age missing (n=2,144), both twins if the reported gestational age conflicts with each other (n=13,492). The resulting data has 309,844 individuals from 154,922 twin pairs, or 74% of the eligible set from MMB data. 5 Results: Diverging Black and White Birthweight Variance Components, Sensitivity to Sex-Composition and Mortality Table 1 shows the detailed sample characteristics for Add Health, breaking down into smaller categories by race, twin pair sex composition, and zygosity. Examining the within-pair birthweight correlations, the basic units of analysis, finds evidence in support of Additive-genetic components of birthweight: the MZ twin pairs have higher phenotypic resemblance than the closely related DZ pairs for white. However, this table raises question on the phenotypic resemblance for black: the black female MZ twins birthweight resemblance is less than those of female same-sex and male same-sex and also different-sex DZ twins. Examination of sample correlation suggest black female may be driving results because it violates the requirements that ρ MZ > ρ DZ. Next I show that the variance 18 This follows the fetal death definition of having survived at least 20 weeks of gestation 17

18 component estimates are sensitive to the sample properties. This exercise is conducted to shed additional light on the behavior of these models. Table 1: Detailed sample characteristics for Add Health sample, by race, twin pair sex composition, and zygosity. white twins, within-pair birthweight correlation female same-sex male same-sex different-sex MZ DZ MZ DZ DZ ρ no. pairs white twins, individuals birthweight summary statistics female male mean std no. individuals % of total black twins, within-pair birthweight correlation female same-sex male same-sex different-sex MZ DZ MZ DZ DZ ρ no. pairs black twins, individuals birthweight summary statistics female male mean std no. individuals % of total DeFries-Fulker Regression Results Table 2 shows the ACE model regression results and the estimates for Additive-genetic, Common-environment contributions. The first set of columns is based on the full sample and does not include a variable for gender-difference birthweight regressor. The second set of columns, based on the same sample, include the gender-difference regressor. 18

19 The estimates of Additive-genetic and Common-environment variance components are similar within a race. Adding the gender-difference birthweight regressor does not change the estimates. Black Additive-genetic variance component is lower and its Commonenvironment variance component is higher than those for white, respectively, in both sets of models. The Additive-genetic and Common-environment variance components for white are positive and statistically significant different from zero. The Additive-genetic component (a 2 correspond to α 3 ) is estimated to account for 38 or 39 % of total birthweight phenotype variance for whites. The point estimates of Additive-genetic components for black is not statistically different from zero, is very small in absolute value, and it slightly dips to negative. On the other hand, the point estimates of Common-environment for blacks (c 2 correspond to α 2 ) is positive and statistically different from zero, accounting for 81 or 83 % of total birthweight phenotype variance for blacks. It is larger than the Common-environment estimates for whites, estimated to account for 47 or 49 % total phenotype variance. Table 2: ACE model, DeFries-Fulker Regression Results gender-difference white black white black α 3 Additive-genetic 0.39*** *** (0.09) (0.20) (0.09) (0.20) α 2 Common-environment 0.47*** 0.81*** 0.49*** 0.83*** (0.08) (0.12) (0.08) (0.12) β gender-difference ** (42.25) (62.52) Sample size Note: standard error in parentheses. p < 0.05, p < 0.01, p < Test of coefficients equality across white and black. α 3 Additive-genetic χ 2 1 = 3.47 χ 2 1 = 3.50 α 2 Common-environment χ 2 1 = 5.75 χ 2 1 = 5.94 Jointly test α 2, α 3 χ 2 2 = 7.29 χ 2 2 = 7.76 Note: p < 0.05 before adjusting for multiple testing, p < 0.05 after adjusting for multiple testing. 19

20 Testing for coefficient differences between the white and black groups are displayed in the lower panel of Table 2. When two testings on α 2, α 3 are conducted between white and black groups, the critical value adjusted for multiple testing using Bonferroni methods 19. The Common-environmental variance component estimate is different between the white and black groups in regression models, with or without the gender-difference regressor, and with or without the adjustments on multiple testing. The Additive-genetic variance component estimate is not statistically different, regardless of the gender-difference regressor or the adjustments for multiple testing. The χ 2 test rejects the equality of Commonenvironmental and Additive-genetic variance components estimates between white and black, both with or without the gender-difference regressor SEM Results by Race, Sex Composition Table 3 shows the SEM estimates on ACE, AE, and CE models using each of the sex composition: female same-sex and male same-sex. The upper panel displays results for white sample, and the lower panel displays results for blacks. Within each panel, the first set of columns describe the findings based on female same-sex pairs, and the second set of columns describe the findings based on male same-sex pairs. Within each set of the columns, I test two nested sub-models, AE and CE models, against the general ACE model on whether a particular variance component is zero. The test statistics are on the bottom line of each panel. The variance component estimates pattern across black and white groups show large divergence in the female same-sex group. While the black female same-sex group shows an almost negligible Additive-genetic component a 2, and fails to reject the nested CE 19 The two separate tests α 2, α 3 within Reference Model are adjusted for multiple testing. So the number of multiple testing is two, and the critical values are adjusted corresponding. For example, α = α 2 the critical value for α = 0.05 and α = is Because the joint test is not independent from the separate tests on α 2, α 3, no adjustment is made on critical values. 20

21 Table 3: ACE, AE, CE models fitted separately, by race, and twin pair sex compositions White, by sex compositions (number of observations) female same-sex (250) male same-sex(298) Variance components ACE AE CE ACE AE CE a 2 Additive-genetic c 2 Common-environment e 2 unique Environment Likelihood ratio test (χ 2 1) between the nested and the ACE model Black, by sex compositions (number of observations) female same-sex (104) male same-sex (100) Variance components ACE AE CE ACE AE CE a 2 Additive-genetic c 2 Common-environment e 2 unique Environment Likelihood ratio test (χ 2 1) between the nested and the ACE model Note: is significant at 5%, is significant at 1%, is significant at 0.1%, without multiple testing adjustment. p < 0.05, p < 0.01 after adjusting for multiple testing. 21

22 model and the hypothesis that the Additive-genetic component a 2 is zero. The white female same-sex group strongly reject the nested CE model and the hypothesis that the Additive-genetic component a 2 is zero. 21 The pattern is reversed when it comes to test whether the Common-environment component c 2 is zero. The black female same-sex group strongly rejects the nested AE model and the hypothesis that the Common-environment component c 2 is zero, while the white female same-sex group could not reject the nested AE model and the hypothesis that the Common-environment component c 2 is zero. The differences within the female same-sex seems to difficult to reconcile. On the other hand, the estimates pattern for male same-sex sample are less diverging across black and white groups. The black male same-sex and white male same-sex groups have the same point estimates on the Additive-genetic component a 2 at Both strongly reject the nested AE model and the hypothesis that the Common-environment component c 2 is zero, and give marginal support to the Additive-genetic component a 2. Although a separate test comparing the model that restricts white male same-sex and black male same-sex to have the same variance components to the unrestricted models are rejected (not shown), this set of results highlights the role of the Common-environment component c 2, and also the similarity across racial groups, which Visscher et al. (2008) argues is often the case for heritability of similar traits to be similar within or even across species. The results from SEM framework raise a question, namely that the different patterns of variance component estimates across racial groups observed in this sample might be driven by racially diverging patterns, or irregularities, in female same-sex twins. Figure 3 illustrates the problem and variance component estimates for white and black, in the aggregate as well as the two same-sex samples. The correlation coefficients for DZ and MZ twins are plotted on the x- and y- axes respectively. The relative difference in 21 The critical value are adjusted for multiple testing, and most model differences are still statistically significant with the Bonferroni adjustment. 22

23 ρ MZ 1 White male-male White female-female White Black Black male-male Black female-female a 2 = 1 line a 2 = 0 line ρ DZ c 2 = 0 line c 2 = 1 line Figure 3: Additive-genetic and Common-environment variance components as functions of white and black MZ, DZ intrapair correlations in ACE model correlation coefficients is decomposed by two sets of parallel lines a 2 = 2(ρ MZ ρ DZ ) and c 2 = 2R DZ R MZ, the position of the (ρ DZ, ρ MZ ) combinations determines the estimated a 2 and c 2. Figure 3 shows that the close-to-zero Additive-genetic estimates for black derives from the relative position that ρ DZ is very close to ρ MZ. In the separate analyses on the racial and sex-composition groups, it seems that the absence of Additive-genetic components in black aggregate sample might be driven by the peculiarity of female same-sex group: the black female same-sex (ρ DZ, ρ MZ ) combination falling to the right of a 2 = 0 line. Figure 4 illustrate the problem, while male same-sex twins in black and white sample have comparable correlation coefficients. The deviations come from female same-sex twins in black and white sample pulling in opposite directions. The results appear to be in large part attributable to the differences in female same-sex twin across black and white sample. 23

24 Figure 4: Add Health twins sample distribution corresponding to the parameter estimates 24

25 The Add Health study was not designed to produce a representative sample of twins. 22 Furthermore, it is known that estimates of heritability are specific to a sample. In table 1, black female same-sex DZ twin pairs have higher birthweight than the comparable white group, which is different from the black-white birthweight difference in the general population. This and other irregularities on Add Health birthweight prompts examination on whether the birthweights in Add Health twin sample have other departures from the population distribution. To investigate whether the characteristics of the study sample are representative of the population, they are compard to the Matched Multiple Birth (MMB) data from National Center for Health Statistics (NCHS). The comparisons are not exact because the MMB data does not have information on zygosity. Only the different-sex pairs are known as DZ with certainty. The same-sex pairs are a mixture of MZ and DZ twins. 5.3 Compare Add Health Against Matched Multiple Birth Data I compare the Add Health twins sample in Table 1 to the summary statistics for the more inclusive Matched Multiple Birth (MMB) data from Center for Disease Control and Prevention (CDC) in Table 4. The comparison is illustrated in Figure 5. Note the comparison focuses on the relative patterns across the different racial and sex-composition groups for correlation coefficient ρ and mean birthweight, the comparison is not about the levels of birthweight because there have been secular changes in twin birthweight. Figure 5 illustrates the comparison on the correlation coefficient ρ and mean birthweight. The figure on the left plots the relative patterns for ρ and mean birthweight for the Matched Multiple Birth (MMB) data. In the Matched Multiple Birth data, the intrapair correlations for same sex pairs are higher than those for different-sex pairs. The 22 When studies examine the representativeness of their twin sample, they are mostly focused on the univariate distribution of individuals of the sample (Cesarini et al., 2008, 2009). Few studies consider the representativeness of the within-pair resemblance, which is the basic unit for analysis in Genetic Epidemiology models. 25

26 Figure 5: Irregularity in Add Health twins compared to Matched Multiple Birth twins dashed horizonal lines that separate ρ highlight this relative patterns: 23 the two same-sex correlation coefficients for white are higher than the white different-sex correlations, and the same holds for blacks. The figure on the right plots the patterns for Add Health. The Add Health sexcomposition catergories are aggregated to make them comparable to the left plot for MMB. 24 The Add Health female same-sex pairs break from the pattern in MMB: its correlation coefficient is lower than the different-sex. 25 The comparison of Add Health against MMB made it possible to infer that this abnormal result is specific to Add Health sample. Besides the relative pattern of ρ, there are other concerns regarding the Add Health birthweight: 1. MMB of Table 4 shows a consistent relative pattern of birthweight: mean birthweight of males from different-sex pairs > mean birthweight of males from same-sex 23 Note the female and male individuals from different-sex twin pairs are summarized with two points on the graph. These two points are necessary because male individuals from different-sex pairs have higher mean birthweight than the female individuals from these pairs. It is obvious that the two points share the same value of intrapair correlation coefficient. 24 Because MMB does not have MZ and DZ information, only same-sex or different-sex composition, the Add Health categories are also aggregated to this level. 25 This plot point also reflects the observation in Figure 3 that the black female same-sex ρ DZ, ρ MZ combination deviates from the rest by falling to the right of a 2 = 0 line. 26

27 MZ > DZ MZ < DZ MZ birthweight (gram) White female-female White male-male 2300 Black female-female Black male-male DZ birthweight (gram) Figure 6: Irregularity in Add Health Twins Birthweight pairs > mean birthweight of females from different-sex pairs > mean birthweight of females from same-sex pairs. This pattern holds for both black and white in MMB. Black female same-sex of Add Health breaks away from this relative rank: its mean birthweight is to the right of all other three. 26 Additionally, the left plot in Figure 6 shows Add Health ρ and birthweight, without aggregating to the crude level of MMB, it reflects information in Table 1: a) the mean birthweight for white female MZ pairs 27 is to the right of, or heavier than, that for white female same-sex DZ pairs, this deviation is shown in details in the right plot of Figure 6 ; b) the mean birthweight for white female MZ pairs is to the right of white male MZ pairs, c) the mean birthweights for black female MZ and black female same-sex DZ are to the right of black females from different-sex pairs 28 d) the mean birthweights for black male MZ and black male same-sex DZ are to 26 Mean birthweight are sensitive to outliers, I also check the results using median birthweight, the same pattern holds. 27 MZ pairs are always same-sex. 28 Different-sex pairs are always DZ. 27

28 the right of the mean birthweight for black males from different-sex pairs 2. Within each sex-composition category of MMB, the mean birthweight of black is lower than that of white. The dashed vertical line in Figure 5 highlights the difference. In Figure 6, there are other crossing over in the birthweight differences between the black and white. Table 4: Birthweight of twin pairs that Survived the first Year, by race and sexcomposition, from CDC Matched Multiple Birth (MMB) Data (Year ) white sex-composition ρ (within pair) mean st.d. N same-sex female pair male different-sex female pair male black same-sex female pair male different-sex femal pair male Proportion of Different-sex Pairs Affects Estimates I next consider whether the sample correlations could be sensitive to the proportion of different-sex pairs, which represents 24% of all white twins, 30% of all black twins, 38% of white DZ twins, and 44% of black DZ twins for Add Health in Table 1. For Matched Multiple Birth File in Table 4, different-sex pairs represents of 34% of all white twins and 36% of all black twins. In other twin samples, 29 other reports on the number of different-sex twins as a proportion of the total number of twins include 26.4%, 2.4%, and 23.1%. 30 I estimate the change in the intrapair correlation coefficient from these reported 29 We have no information on zygosity in MMB so can not deduce the share of different-sex pairs in DZ twins paisr. 30 Tong et al. (1997) inferred the DZ ratio from Weinberg Difference Method which, which although has its detractors (Boklage, 1985), is a straightforward formula to calculate the different-sex proportion. 28

29 values of different-sex proportions. For a sample aggregated from heterogeneous sub-samples, the final correlation are not necessarily a convex combination of the sub-samples correlations. In Hassler and Thadewald (2003) s example, correlation coefficient r xy of two variables x, y from aggregating two sub-samples 1, 2 could be larger or smaller than any of the correlation coefficients of its sub-samples, depending on the sub-samples relative proportions λ, dispersions σx,1, 2 σx,2, 2 σy,1, 2 σy,2 2, and means µ x,1, µ x,2, µ y,1, µ y,2 : p λcov(x, y) 1 + (1 λ)cov(x, y) 2 + λ(1 λ)(µ x,2 µ x,1 )(µ y,2 µ y,1 ) r xy (14) λσx,1 2 + (1 λ)σ2 x,2 + λ(1 λ)(µ x,2 µ x,1 ) λσ 2 y,1 2 + (1 λ)σ2 y,2 + λ(1 λ)(µ y,2 µ y,1 ) 2 where λ is the proportion of the second group in the aggregate sample. Applying the formula to the birthweight twin pairs example, the two birthweights are denoted x and y, the two groups mean matrices are [µ x,1, µ y,1 ], [µ x,2, µ y,2 ], and covariance matrices are σ2 x,1 cov(x, y) 1, and σ2 x,2 cov(x, y) 2. The effect of sampling from the cov(x, y) 1 σy,1 2 cov(x, y) 2 σy,2 2 two sub-populations: same-sex and different-sex is explained using simulated samples. Figure 7 illustrates twin sample s birthweight correlation vary with the proportion of different-sex twin pairs. For a given combination of race and sex composition, I draw pseudo-random samples from the CDC Multiple Matched Birth file and synthesize samples from the three components: female same-sex, male same-sex, and different-sex. 31 The figures show a general negative relationship between the proportion of different-sex twins and the resulting correlation coefficients. The relationship better proxies for the sensitivity of DZ twin sample s correlation. If the different-sex proportion is increased from The method assumes half of DZ twins are different-sex, and the proportion of twins who are DZ twins is half the value of different-sex twin proportions. The DZ proportion is. Since DZ DZ+MZ = 1 1+ MZ DZ = DZ MZ Tong et al. (1997) reported that the observed DZ MZ ratio changed from 1.12 in 1960 to 0.05 in 1978, and rose to 0.86 in These numbers translate to DZ proportions of 52.8%,4.8%, and 46.2%, and conversely different-sex proportion is half the value at 26.4%, 2.4%, and 23.1%. 31 The three components vary in size from 500 to 3000 pairs, the different combinations give varying proportion of different-sex pairs. 29

30 Figure 7: The proportion of different-sex twin pairs lead to different correlation coefficient estimates. 20% to 40%, two values within the observed range, 32 the average correlation coefficients in the synthesized sample is reduced by If this change in correlation coefficient is in ρ DZ, the change in Additive-genetic variance components is about 4 percentage points, sufficient to shift the black estimates to the cross-hatched zone in Figure 1. This simple exercise shows that aside from the irregularities in black female same-sex observations, the initial diverging results between racial groups could be partially accounted for by a changes in the sample sex-composition. 5.5 Concerns on Different Mortality Profiles Lastly, I address the concern on different mortality profiles. It has been documented that twinning individuals with intrapair birthweight discordance have elevated risk for fetal death and neonatal death (Hollier et al., 1999; Rydhstrm, 1994). The elevated risk is 32 A proportion of 20% corresponds to 20 black different-sex pairs, or less than the current 42 pairs by 22 pairs; a proportion of 40% corresponds to 40 black different-sex pairs, or less than the current 42 pairs by 2 pairs. The proportions correspond to 47 and 95 white different-sex pairs, 43 pair less and 5 pairs more than the current 90 pairs. 30