Genetic Epidemiology 30: 397–408 (2006)
Sex Differences in Genetic and Environmental Determinants of Pulse Pressure Katrina J. Scurrah,1,2 Graham B. Byrnes,2 John L. Hopper2, and Stephen B. Harrap1 1
Department of Physiology, The University of Melbourne, Parkville, Victoria, Australia Centre for Molecular, Environmental, Genetic and Analytic Epidemiology, The University of Melbourne, Parkville, Victoria, Australia
2
Pulse pressure (PP) is an independent risk factor for cardiovascular disease. PP rises with age, more so in women. We examined sex differences in the correlations and variance components of PP in adult subjects from 767 nuclear families, enriched with those containing twins, from the Victorian Family Heart Study. After adjusting for age, we found no significant differences in the means or variances of PP in males and females. Under the assumption of no sex differences, the proportions of variance due to shared genes, shared environment, and individual-specific environment were 20%, 23% and 57%, respectively. However, same-sex relative pairs had significantly higher correlations than opposite-sex pairs (P 5 0.005), implying the existence of sex-dependent effects. Extensions to the simple variance components model suggested three possible explanations for these differences: smaller genetic correlation between opposite-sex pairs (rG,MF 5 0.45, P 5 0.007); smaller environmental correlation between opposite-sex pairs (P 5 0.0003); or different environmental and genetic correlations obtained by estimating genetic, environmental, and individual variance components separately for males and females (not nested, Akaike’s Information Criterion (AIC) smaller by 6.69). Under the last model, the genetic component of PP variance is greater for males (1.62 vs 0.33) while the environmental component is greater for females (1.84 vs 0), which would have implications for the planning of gene discovery studies, since heritability would be higher in males. However, the second (environmental) approach best fits the data according to the AIC. Genetic explanations for sex differences in phenotypic correlations may be misleading unless shared environmental factors are also considered. PP illustrates a phenotype in which sex dependency represents an important component of phenotypic determination that can be revealed by detailed variance components modelling. Genet. Epidemiol. 30:397–408, 2006. r 2006 Wiley-Liss, Inc. Key words: variance components; coronary risk factors; family studies; blood pressure
Contract grant sponsor: Victorian Health Promotion Foundation and National Health and Medical Research Council of Australia. Correspondence to: Dr. Katrina Scurrah, Department of Physiology, The University of Melbourne, Parkville, Vic. 3010, Australia. E-mail:
[email protected] Received 27 November 2005; Accepted 27 February 2006 Published online 23 May 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/gepi.20156
INTRODUCTION Pulse pressure (PP) is the difference between systolic (SBP) and diastolic (DBP) blood pressure, representing the amplitude of the pressure wave generated by the heart with each contraction. PP is important because it is associated with increased risk of cerebrovascular and coronary heart disease, independently of other risk factors such as SBP and DBP [Franklin et al., 1997]. Although it is unclear whether this relationship represents cause or effect, PP might be a better predictor of future cardiovascular events than SBP alone in some circumstances [Franklin, 2004]. This might be because a higher PP not only implies higher SBP r 2006 Wiley-Liss, Inc.
and greater cardiac afterload and vessel stress, but also implies reduced DBP that might limit coronary artery blood flow. Physiologically, arterial compliance is the most important long-term determinant of PP. In general, PP increases with age, an effect thought to be attributable to reduced arterial compliance. Interestingly, the increase in PP with age [Burt et al., 1995] is exaggerated in women compared with men. It has been observed that even from a young age, females have stiffer large arteries than males [Ahimastos et al., 2003]. During the reproductive years, the female hormones ameliorate this difference by increasing the arterial compliance [Ahimastos et al., 2003]. With the onset of meno-
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pause the large arteries stiffen in females [Waddell et al., 2001] accounting for the greater increase in PP in older women than men. The possibility of sex differences in the shared genetic and environmental influences on PP has not been explored in detail. Most previous studies [Atwood et al., 2001; Adeyemo et al., 2002; Camp et al., 2003; DeStefano et al., 2004; Bochud et al., 2005] fitted separate means for each sex. This approach adjusts for overall mean differences between the sexes but presumes that the genetic and environmental components of variance of the trait do not differ between the sexes. Yet, gene regulatory sequences such as androgen or oestrogen responsive elements provide a means by which the expression of genes relevant to a phenotype could depend on sex. Constitutional sex chromosomal differences are obviously relevant. Furthermore, susceptibility to environmental factors such as diet and lifestyle might vary between men and women. There is a need for methods that can identify and partition sex-dependent effects on phenotypes and genotypes. Meaningful analyses of molecular genetic studies are predicated on statistical models that reflect the real world by accounting for genetic and environmental contributions. The development and testing of such models are best founded in biometric modelling that quantitates genetic and environmental effects and determines their dependency on sex. Carefully developed biometric models are likely to have direct application to genetic analyses, and can be directly included in linkage analyses of quantitative traits (as in Towne et al. [1997] and Weiss et al. [2006]). If heritabilities differ markedly between the sexes, strategic decisions might be made regarding the appropriate analytical framework to maximise the potential information obtained from genetic studies. In this study we have used data and material from the Victorian Family Heart Study (VFHS) to assess and model the familial aspects of PP. The VFHS is enriched for families containing twins, thereby increasing the informativeness of biometric analyses in providing estimates of the genetic and environmental components of variance [Harrap et al., 2000]. We describe and apply three specific extensions to commonly used models, so as to investigate the possibility of sex-dependent effects on covariances. These are 1) allowing unequal variance components for males and females; 2) allowing lower genetic correlations for opposite-sex than same-sex pairs; Genet. Epidemiol. DOI 10.1002/gepi
and 3) allowing different environmental correlations for male-male, female-female, and malefemale pairs.
MATERIALS AND METHODS STATISTICAL METHODS
Investigating within-family correlations and covariances using variance components models under a multivariate normal model for pedigree analysis is extremely flexible and allows for a variety of family structures and models. These models may be fitted using the software package Fisher [Lange et al., 1988; Hopper and Mathews, 1994]. This approach has been successfully applied to several phenotypes from the VFHS showing, for example, that variation in height in this study population appears to be controlled mainly by genes, while both genes and environmental factors influence variation in SBP [Harrap et al., 2000]. In this paper, we analysed PP and considered sex dependence of means, covariances, and variance components. We first considered a model which allows separate estimates of correlation between different pairs of relatives, without explicitly separating genetic and environmental contributions. We believe it is sound statistical practise to examine the correlations, and demonstrate differences in these before embarking on variance components modelling, as fitting variance components models alone can lead to spurious findings [Hopper, 1993]. This approach still allows an estimate of genetic contribution via the twin model: the heritability can be estimated as minðrMZ ; 2ðrMZ rDZ ÞÞ (ignoring the correlations between other relative pairs included in the model). It also allows simultaneous assessment of environmental influences via comparison of the correlations for the several types of firstdegree relative pairs, who share the same proportion of genes (ignoring the correlations between non-first-degree relatives included in the model). In order to make better use of the data to separate genetic and environmental factors, and estimate heritability using all observations rather than just twins, we then fitted a full variance components model in which the genetic covariances are determined by the kinship coefficients fjk [Lange, 2002]. The models considered in this paper build on those described previously by Towne et al. [1997] (which were also recently used by Weiss et al. [2006]), who allowed the genetic
Sex Differences in Correlations and Variance Components
females (Model 1.3). This model could be extended even further by allowing the father-daughter correlation to be different from the mother-son correlation. A different model was obtained by allowing separate (unequal) variances for males and females (Model 1.4). These models can all be considered as special cases of the most general correlation model for this type of data, in which the general form of the covariance Vjk for a relative pair j and k within a pedigree was Model 1, general
correlation between opposite sex pairs to be less than the kinship coefficient by a constant factor rG;MF. We expand them to incorporate a shared environmental variance component and environmental correlation coefficients that allow for different shared environmental effects between different types of relative pairs. In the majority of models we adjusted mean PP for sex, age, and age by sex separately for each generation, and we also considered covariates reported to be associated with PP such as body mass index (BMI), height, and mean arterial pressure (MAP) [Atwood et al., 2001; Adeyemo et al., 2002; Camp et al., 2003; Snieder et al., 2003; DeStefano et al., 2004; Bochud et al., 2005].
8 rjk;MM s2M > > > > rjk;MF sM sF < Vjk ¼ rjk;FF s2F > > 2 > > : sM s2F
CORRELATION MODELS
Within each family i, a multivariate normal distribution is assumed for the vector of phenotypes yi; conditional on covariates, yi NðbT Xi ; Vi Þ, where bT is a vector of regression coefficients, Xi is the covariate matrix, and Vi is the covariance matrix, with elements Vi,jk. Initially, under the assumption of no sex differences, a simple correlation model for this type of family data (i.e. nuclear families enriched with twin families) (Model 1.1) allowed a single variance component equal to the total residual phenotypic variance (s2 ), and five correlations for spouse (rSP ), parent-offspring (rPO ), sibling (rSIB ), DZ (rDZ ), and MZ (rMZ ) twin pairs. Therefore, for Model 1.1, the general form of the covariance between nuclear family relatives j and k was taken to be Vjk defined by Model 1.1, no sex differences rjk s2 j 6¼ k Vjk ¼ s2 j¼k
FULL VARIANCE COMPONENTS MODELS
We began with a model (2.1) in which total variance (s2 ) is partitioned into three variance components, representing: additive genetic effects (s2A ), shared family environmental effects (s2C ), and individual-specific effects (s2E ). The shared family environmental effects refer to those effects shared while all members of a nuclear family were living together. Although some of the offspring had left the family home, cohabitational effects appeared to persist for many cardiovascular phenotypes, as described by Harrap et al. [2000]. Spouse pairs are also assumed to be correlated, but we have not attempted to explain this correlation in terms of shared genetic and/or shared environmental effects. However, we have assumed that spouse correlation is not due to assortative mating. The general form of the covariance between nuclear family relatives j and k was taken to be Vjk defined by Model 2.1, no sex differences
8 rSP s2A þ s2C þ s2E > > < 2f r s2 þ g s2 jk G;MF
A
2f s2 þ g s2 > > : 2 jk A 2 jk 2C sA þ sC þ sE
j 6¼ k; j and k both male j 6¼ k; j and k opposite sex j 6¼ k; j and k both female j ¼ k; male j ¼ k; female
where rjk is again one of rSP , rPO , rSIB , rDZ , and rMZ . Note that rSP;MM , rSP;FF , and rMZ;MF are not defined. The constraints on the most general correlation model which are required to obtain Models 1.1–1.4 are shown in Table I.
where rjk is one of rSP , rPO , rSIB , rDZ and rMZ , depending on whether j and k are from a spouse, parent-offspring, sibling, DZ, or MZ twin pair. We first extended the simple model by allowing separate (unequal) correlations for same-sex and opposite-sex relative pairs (Model 1.2), and then by also allowing the correlations between two males to be different from that between two
Vjk ¼
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jk
C
j 6¼ k; j and k spouses j 6¼ k; j and k opposite sex and not spouses j 6¼ k; j and k same sex j¼k Genet. Epidemiol. DOI 10.1002/gepi
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TABLE I. Descriptions of main models Type Correlation
Full variance components
Number
Description
Constraints
1.1
Simple (no-sex-differences) correlation model
s2M 5 s2F 5 s2 rjk,MM 5 rjk,FF 5 rjk,MF
1.2
Different same-sex and opposite-sex correlations
s2M 5 s2F 5 s2 rjk,MM 5 rjk,FF
1.3
Different male-male, male-female and female-female correlations
s2M 5 s2F 5 s2
1.4
Different male and female total variances
rjk,MM 5 rjk,FF 5 rjk,MF
2.1
Simple (no-sex-differences) variance components model
s2AM 5 s2AF s2CM 5 s2CF s2EM 5 s2EF gjk,MM 5 gjk,FF 5 gjk,MF rG,MF 5 1
2.2
Different same-sex and opposite-sex shared genetic coefficient
s2AM 5 s2AF s2CM 5 s2CF s2EM 5 s2EF gjk,MM 5 gjk,FF 5 gjk,MF rG,MFr1
2.3
Different male-male, female-female and male-female shared genetic covariances
s2CM 5 s2CF s2EM 5 s2EF gjk,MM 5 gjk,FF 5 gjk,MF rG,MF 5 1
2.4
Different male-male, female-female and male-female shared genetic coefficient, and covariances
s2CM 5 s2CF s2EM 5 s2EF gjk,MM 5 gjk,FF 5 gjk,MF rG,MFr1
2.5
Different male and female variance components
gjk,MM 5 gjk,FF 5 gjk,MF rG,MF 5 1
2.6
Different same-sex and opposite-sex shared environment coefficients
s2AM 5 s2AF s2CM 5 s2CF s2EM 5 s2EF gjk,MM 5 gjk,FF rG,MF 5 1
2.7
Different male-male, female-female, and male-female shared environment covariances
s2AM 5 s2AF s2EM 5 s2EF rG,MF 5 1
2.8
Best combined G S and E S model
s2AM 5 s2AF s2CM 5 s2CF s2EM 5 s2EF gjk,MM 5 gjk,FF rG,MFr1
2.9
Separate male and female variance components and different same-sex and opposite-sex shared environment coefficients
gjk,MM 5 gjk,FF rG,MF 5 1
2.10
Most comprehensive model in this analysis; allows different same-sex and opposite-sex shared environment coefficients, different male and female variance components, and different same-sex and opposite-sex shared genetic coefficients
gjk,MM 5 gjk,FF rG,MFr1
Note that all models above include the additional constraints that gDZ,MM 5 gMZ,MM 5 1 and gDZ,FF 5 gMZ,FF 5 1 in order to satisfy the assumptions of the classic twin model.
The parameter rSP represents the combined (genetic and environmental) correlation for spouse pairs [Harrap et al., 2000]. The kinship coefficient fjk is 0.5 for MZ twin pairs and 0.25 for first-degree relatives. The symbol rG;MF allows the additive genetic covariance for an opposite-sex Genet. Epidemiol. DOI 10.1002/gepi
pair to be less than predicted by the kinship coefficients, as suggested by Towne et al. [1997]. The parameters gjk play a similar role, being the correlation of environmental effects in relative pairs. However, unlike the fjk they cannot be determined a priori from biological considerations
Sex Differences in Correlations and Variance Components
and must be estimated from the data. The shared family environmental variance s2C is defined by the covariance of MZ twin pairs, so gMZ ¼ 1 by definition. In order to distinguish genetic from environmental effects, a further assumption must be made: we assume the classical twin model in which same-sex DZ twins have the same environmental correlation as MZ pairs, gDZ ¼ gMZ ¼ 1. Where j and k are not same-sex twins, gjk is estimated and assumed to be no greater than 1. The classes of relationship explicitly considered are parent-offspring, sibling, DZ or MZ twin pair, represented by the symbols gPO , gSIB , gDZ , and gMZ . Further refinement is possible by considering different sex combinations separately: for example there are three possible types of sib-pairs and four types of parent-offspring pairs. Our most basic model (Model 2.1) assumes no sex dependence of either genetic or environmental effects. Thus the variance components s2A , s2C and s2E are identical for males and females, rG;MF ¼ 1 and gPO , gSIB and gDZ are independent of the sexes of the pair in question. Our initial aim was to assess evidence for genotype-by-sex (G S) interactions in PP, while ignoring environment-by-sex (E S) interactions. This was done by gradually relaxing constraints on only the genetic parameters in the model, as shown in Table I. We first allowed either rG;MF 1 (Model 2.2) or s2AM 6¼s2AF (Model 2.3), and then both of these (Model 2.4), following Towne et al. [1997]. The best model from these three was selected according to Akaike’s Information Criterion (AIC; see section on Model building and hypothesis testing below) and will be referred to as the ‘‘best G S model’’. 8 2fjk s2AM þ gjk;MM s2CM > > > > 2fjk rG;MF sAM sAF þ gjk;MF sCM sCF > > qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > > > r ðs2AM þ s2CM þ s2EM Þðs2AF þ s2CF þ s2EF Þ > SP > < Vjk ¼ 2fjk rG;MF sAM sAF þ gjk;MS sCM sCF > 2fjk rG;MF sAM sAF þ gjk;FD sCM sCF > > > > > 2fjk s2AF þ gjk;FF s2CF > > > > > s2AM þ s2CM þ s2EM > : 2 sAF þ s2CF þ s2EF Relaxing the equality constraint on a single variance component (s2A ) is likely to have little effect when the other two remain constrained, so we next considered models in which s2EM 6¼s2EF also. However, by allowing separate s2E for males and females, we are now allowing E S interac-
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tions. This led us to fit a model which allowed G S and E S interactions for both shared and unshared environmental effects, in which only the equality constraints for all three variance components were removed (Model 2.5, Table I). We then focused on E S effects, keeping all genetic parameters as in the simple Model 2.1. First the shared environment coefficients gjk were allowed to differ for same and opposite sex pairs, with all variance components once again constrained to be equal for males and females (Model 2.6). The next model (Model 2.7) allowed malemale environmental covariances to differ from female-female environmental covariances, by additionally allowing shared environment coefficients for male-male and female-female parentoffspring and sibling pairs to differ, and by simultaneously allowing s2CM 6¼s2CF (to allow male-male and female-female twin covariances to be different). The shared environment coefficients for father-daughter pairs could also differ from those of mother-son pairs. The best model from this set was again chosen according to the AIC and will be referred to as the ‘‘best E S model’’. Finally, we considered several models which included both G S and E S effects. Model 2.8 combined the best G S model with the best E S model, and this was compared with Model 2.5 which also allowed G S and E S effects, but through only variance components rather than correlations. The best E S model was then combined with Model 2.5. Remaining constraints on the best model were then relaxed to obtain the most general model. Model 2, general
j 6¼ k; j and k both male j 6¼ k; j and k opposite sex; not PO or SP j 6¼ k; j and k spouses j 6¼ k; j and k mother and son j 6¼ k; j and k father and daughter j 6¼ k; j and k both female j¼k; male j¼k; female MODEL BUILDING AND HYPOTHESIS TESTING All variance components were assumed to be non-negative and all correlations were assumed to lie between 0 and 1 inclusive, so we used the Self and Liang [1987] method when a parameter was on the boundary under the null hypothesis. Genet. Epidemiol. DOI 10.1002/gepi
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For the full variance components models, whenever a parameter was not statistically significantly different from a boundary point at the 5% level using this method, the parameter was set to that boundary and the model was refitted. The exception was rG;MF , which was considered a key parameter and which was therefore not set to 1 even when not significantly different from 1. However, all parameters were initially estimated for each of Models 2.1–2.10, even when the parameter was not different from a boundary value in the previous model. Results are shown only for the final model for each stage, with all nonsignificant parameters set to the boundary values. If two models are nested (for example, Models 1.1 and 1.2) their relative fits may be compared using a likelihood ratio test. If the models are not nested (for example, Models 1.2 and 1.4), the AIC can be used to assess the trade-off between fit and number of parameters. We focused more on building a model with sufficiently good fit to allow the estimated parameters to be used for other purposes (e.g. guiding future genetic or environmental studies), than on establishing the inequality of specific parameters (e.g. rSIB;MM 6¼rSIB;FF ) through hypothesis testing. Both the AIC and likelihood ratio test were used during the model-building process, while recognising that the AIC is inconsistent and may overfit [McQuarrie and Tsai, 1998, Section 4.7]. We took the approach of starting with a basic model and gradually relaxing the parameter constraints, rather than starting with the most general model and subsequently simplifying it, to avoid model instability due to over-parameterization. SUBJECT RECRUITMENT AND PHENOTYPE MEASUREMENT
The details of the recruitment of subjects for the VFHS have been published previously [Harrap et al., 2000]. In brief, a volunteer sample of 767 white adult families enriched with families containing twins (65 monozygotic pairs, 84 dizygotic pairs) was recruited from a variety of community-based sources. A family history of heart disease was not a prerequisite for recruitment. Families comprised both parents aged between 40 and 70 years and at least one natural offspring aged between 18 and 30 years. The Ethics Review Committee of the Alfred Hospital, Melbourne approved the study and informed consent was obtained from all participants. Participants attended research clinics where Genet. Epidemiol. DOI 10.1002/gepi
TABLE II. Observed and transformed pulse pressures of participants Participants Offspring Male Female Parents Male Female
Pulse pressure (mmHg)
10 ln (pulse pressure)
n
50.4 (10.8) 45.0 (9.2)
39.0 (2.1) 37.9 (2.1)
663 714
48.6 (11.7) 47.0 (10.6)
38.5 (2.3) 38.3 (2.2)
767 767
Data are mean (SD).
trained research nurses obtained relevant information regarding drug treatment and smoking, measured cardiovascular and other phenotypes such as height and weight, and took blood samples as detailed previously [Harrap et al., 2000]. After resting for 10 min, three measurements of both SBP and DBP were taken in the supine position, the last two of which were recorded. Subjects then stood for 2 min and three further measurements of SBP and DBP were taken, the last two of which were recorded. For subjects receiving antihypertensive treatments we adjusted the recorded pressures by adding 10 and 5 mmHg to SBP and DBP, respectively, as justified previously [Cui et al., 2003] and shown to provide an appropriate adjustment [Tobin et al., 2005]. The PPs were calculated as the difference between the average of the standing and lying SBPs and the average of the standing and lying DBPs. PP was log-transformed before analysis to approximate normality, and subsequently multiplied by 10 to increase the standard deviation to above 1 (as recommended in the Solar manual). This transformation enables more accurate estimation of model parameters. All models of means included age (centred at the mean of 40), sex, and age-sex interaction as covariates, and allowed for separate effects for each within each generation (parents and offspring). These covariates were included in all models regardless of statistical significance. All results, except the means and medians in Table II, refer to analyses performed on the log transformed phenotype multiplied by 10, which passed the Anderson-Darling omnibus test of departure from normality implemented in Fisher, P40.1 [Hopper and Mathews, 1982].
RESULTS The descriptive statistics for PP are shown in Table II. After adjustment for age, differences
Sex Differences in Correlations and Variance Components
in means between males and females were not statistically significant in either the parental or the offspring generation (P 5 0.9 and 0.4, respectively). There was a small but statistically significant negative association between PP and age in the offspring (b 5 0.06, P 5 0.01) and a significant positive association between PP and age in the parents (b 5 0.12, P 5 0.001). Age-sex interactions were not statistically significant in either the offspring (P 5 0.2) or the parental (P 5 0.9) generations. CORRELATION MODELS
Results for selected fitted correlation models (Models 1.1–1.3) are shown in Table III. MZ twin pairs had the highest correlation with progressively lower correlations for DZ twin, sibling, parent-offspring and spouse pairs. When DZ twin, sibling and parent-offspring pairs were divided according to whether they were samesex or opposite-sex pairs (Model 1.2), higher correlations were observed between same-sex pairs (Table III) (P 5 0.005). This was true for all relative types, although these individual differences were not always statistically significant. In Model 1.2, the correlation for same-sex DZ twin pairs (0.44, SE 0.10) was much closer to that of MZ twin pairs (0.53, SE 0.09) than was the correlation for DZ opposite sex pairs (0.14, SE 0.12). There appeared to be little difference in correlation between male-male and female-female relative pairs (Model 1.3, Table III). The exception was parent-offspring pairs, in which the father-son correlation was higher than the mother-daughter correlation, for which there is no immediate explanation. This model was not an improvement over Model 1.2 (P 5 0.61). Separate male and female estimates of residual variance were very
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close (Model 1.4, results not included in Table III); s2M 5 4.58 (SE 0.17), s2F 5 4.35 (SE 0.16) and this model did not improve on the simple Model 1.1 in which male and female residual variances were constrained to be equal (P 5 0.3). FULL VARIANCE COMPONENTS MODELS
The models appear to have relatively flat likelihood surfaces in regions where environmental variance components and correlations were near zero. As these boundaries are dependent on the classical twin model assumptions, we also investigated models in which the lower bounds were negative (1 for correlations and unconstrained for variance components). However, these models did not fit appreciably better (results not shown) and in some cases could not be fitted at all. Hence the analyses presented assumed a lower bound of 0 for these parameters. In view of the flat likelihoods, we have chosen to fix estimates to zero in the absence of contrary statistical evidence. Parameter estimates for selected models are shown in Table IV. In the simplest model (Model 2.1), neither the parent-offspring nor sibling shared environment coefficients were significantly different from 0 (P40.1). In the no sex differences variance components model (Model 2.1), genetic effects accounted for 20% of the total residual variance while shared environmental effects contributed 23%. The majority of the variance was attributable to individualspecific factors, with s2E accounting for 57% of the total variance. After additional adjustments for BMI height, oral contraceptive/hormone replacement therapy use, and MAP, the estimates of genetic (19%), shared environmental (22%), and individual-specific (59%) variance components were not appreciably different.
TABLE III. Correlations between relative pairs Relative pair Derived from model MZ twin pairs (n 5 65) DZ twin pairs (n 5 84) Sibling pairs (n 5 651)a Parent-offspring pairs (n 5 2754)a Spouse pairs (n 5 767)
All
Same sex
Male pairs
Female pairs
Opposite sex
1.1 0.53 (0.09)
1.2 0.53 (0.09)
1.3 0.50 (0.13)
1.3 0.56 (0.13)
1.2
0.18 (0.06)
0.44 (0.10)
0.48 (0.22)
0.44 (0.11)
0.14 (0.12)
0.16 (0.05)
0.23 (0.05)
0.22 (0.08)
0.25 (0.07)
0.05 (0.06)
0.09 (0.02)
0.11 (0.03)
0.15 (0.04)
0.06 (0.04)
0.07 (0.03)
0.07 (0.04)
—
—
—
0.07 (0.04)
—
Data are correlations (SE) obtained from three different models as indicated. a Not all pairs of this type were independent. For example, a sibship of size 3 includes three distinct sibpairs, but only two of these pairs are independent. Genet. Epidemiol. DOI 10.1002/gepi
1.23 (0.23)
Males 1.07 (0.22) Females 0.76 (0.20)
Males 1.38 (0.26) Females 1.08 (0.25)
Males 1.62 (0.36) Females 0.33 (0.20)
0.78 (0.19)
0.61 (0.20)
0.94 (0.26)
Males 1.35 (0.39) Females 0.39 (0.23)
Males 1.39 (0.39) Females 0.55 (0.34)
2.2 (3599.641) 7225.28 (best G S model)
2.3 (3601.749) 7229.50
2.4 (3598.807) 7225.61
2.5 (3596.328) 7222.66
2.6 (3596.850) 7219.70 (best E S model)
2.7 (3594.624) 7221.25
2.8 (3596.431) 7220.86
2.9 (3594.879) 7221.76
2.10 (3594.585) 7225.17
Males 0.99 (0.59) Females 1.71 (0.43)
Males 1.00 (0.59) Females 1.82 (0.40)
1.46 (0.36)
Males 1.86 (0.37) Females 1.61 (0.35)
1.5883 (0.3349)
Males 0 Females 1.84 (0.40)
0.9827 (0.2991)
1.02 (0.30)
0.98 (0.30)
1.01 (0.31)
s2C
1 0.75 (0.35)
Males 2.22 (0.49) Females 2.07 (0.37)
0.69 (0.29)
1
1
1
0.45 (0.19)
1
0.45 (0.19)
1
rG,MF
Males 2.24 (0.48) Females 2.12 (0.36)
2.06 (0.30)
2.12 (0.30)
2.09 (0.30)
Males 2.96 (0.33) Females 2.16 (0.37)
2.25 (0.30)
2.53 (0.30)
2.25 (0.30)
2.54 (0.30)
s2E
0.06 (0.04)
0.06 (0.4)
0.07 (0.04)
0.06 (0.04)
0.06 (0.04)
0.07 (0.04)
0.07 (0.04)
0.07 (0.04)
0.07 (0.04)
0.07 (0.04)
rSP
Same-sex 0 Opposite-sex 0
Same-sex 0 Opposite-sex 0
Same-sex 0 Opposite-sex 0
Male-male 0.22 (0.11) Female-female 0 Father-daughter 0 Mother-son 0
Same-sex 0 Opposite-sex 0
0
0
0
0
0
gPO
Same-sex 0.44 (0.18) Opposite-sex 0
Same-sex 0.46 (0.17) Opposite-sex 0
Same-sex 0.38 (0.18) Opposite-sex 0
Male-male 0.40 (0.21) Female-female 0.46 (0.20) Opposite-sex 0
Same-sex 0.41 (0.16) Opposite-sex 0
0.49 (0.19)
0
0
0
0
gSIB
Same-sex 1 Opposite-sex 0
Same-sex 1 Opposite-sex 0
Same-sex 1 Opposite-sex 0
Same-sex 1 Opposite-sex 0
Same-sex 1 Opposite-sex 0
1
1
1
1
1
gDZ
s2A =polygenic component of variance, s2C =shared environmental component of variance, s2E =unshared environmental component of variance, rG,MF=genetic correlation, rSP=correlation for spouse pairs, gSIB=shared environment coefficient for sibling pairs, gDZ=shared environment coefficient for DZ twin pairs. For these models gMZ (shared environment coefficient for MZ twin pairs) was 1 in accordance with the classic twin model. SEs of estimates are given in parentheses.
0.90 (0.18)
s2A
2.1 (3602.675) 7229.35
Model (loglikelihood) AIC
TABLE IV. Genetic and environmental components of variance
Sex Differences in Correlations and Variance Components
Of the three models which included only G S effects (Models 2.2–2.4) only Model 2.2, which removed the constraint rG;MF ¼ 1, resulted in a statistically significant improvement over the simple Model 2.1 (P 5 0.007) with rG;MF ¼ 0:45. Although the estimates of s2AM and s2AF were quite different in both Models 2.3 and 2.4, allowing these separate effects instead of or in addition to rG;MF 1 did not result in a better model (P 5 0.09, Model 2.3 vs 2.1, and P 5 0.1, Model 2.4 vs 2.2). This result is unsurprising, since a difference between males and females in a single variance component would be reflected in a difference in the total variance, and the correlation models showed that the total residual variances are approximately equal for males and females. Model 2.5, which allowed both G S and E S effects through separate variance components, provided a better fit than the simple (no-sexdifferences) Model 2.1 (AICs 7222.66 and 7229.35, respectively). Note that these models are not nested since gSIB ¼ 0 in Model 2.1 but gSIB 40 (P 5 0.004) in Model 2.5, so likelihood ratio tests cannot be used to compare them directly. We observed that although total variances were approximately equal for males and females, the additive polygenic variance was greater for males than females in this model (s2AM 5 1.62, s2AF 5 0.33, P 5 0.002), while the shared environmental variance was greater for females than males (s2CM 5 0, s2CF 5 1.84, Po0.001). Smaller sex differences were observed between the individualspecific variances (s2EM 5 2.96, s2EF 5 2.16, P 5 0.1). This model also fitted better than the best G S model (which had an AIC of 7225.28), suggesting that both G S and E S effects appear to be present, and models which include both of these are better than those that attempt to explain sex dependencies using genetics alone. The simplest E S model (2.6) was again a strongly significant improvement over Model 2.1 (P 5 0.0003). In this model, same-sex correlations were higher than opposite sex correlations for sibling and DZ twin pairs, and for both siblings and DZ twins, opposite sex correlations were set equal to the lower bound of 0 in the best model. However, relaxation of further environmental constraints did not result in significant improvements over this model (Table IV), suggesting that environmental correlations between male-male and femalefemale relative pairs tend to be approximately equal (P 5 0.22, Model 2.7 vs 2.6). The exception is parentoffspring pairs, where father-son pairs had higher environmental correlations than mother-daughter
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pairs (P 5 0.03), as was also apparent from the correlation models. Again, there appears to be no obvious explanation for this, and other results changed little regardless of whether constraints were gPO;MM 5 gPO;FF 5 0 or gPO;MM 0 and gPO;FF 5 0. The best E S model (2.6) had a lower AIC (7219.70) than both the best G S model (AIC 5 7225.28) and the separate variance components model (AIC 5 7222.66), suggesting that E S effects may explain the data better than either G S effects or a combination of E S and G S effects. To test this further, we combined Models 2.2 and 2.6 to produce Model 2.8. In this model, rG;MF was not significantly different from 1 (rG;MF 5 0.69, P 5 0.14) and overall this model did not significantly improve on the best E S model (P 5 0.18). This model had an AIC of 7220.86, which was close to the AIC of 7222.66 obtained from Model 2.5 (which also allowed both G S and E S effects, but through separate variance components), but lower than that of the best G S model. An alternative way to allow both G S and E S effects is to combine Models 2.6 and 2.5 to produce Model 2.9, allowing different same and opposite sex environmental coefficients and different additive polygenic, shared environment and unshared environment variance components for males and females. Again, although this model was not a statistically significant improvement over Model 2.6 (P 5 0.27), estimates of s2A and s2C were quite different for males and females (e.g. s2AM 5 1.35, s2AF 5 0.39, P 5 0.03). Finally we fitted a model that allowed: 1) different same-sex and opposite-sex shared environment correlations, 2) different shared genetic, shared environmental and individual-specific environmental variance components for males and females, and 3) shared genetic correlation less than 2fjk for opposite-sex pairs (rG;MF o1). In this model (Model 2.10, described in Table I and results presented in Table IV), rG;MF was estimated to be 0.75. While standard errors are quite large (Table IV), and the extension again did not result in a statistically significant improvement in the overall model fit in comparison with Model 2.9 (P 5 0.37) or 2.8 (P 5 0.30), this model also suggested that the covariance between males is due mainly to shared genetic effects (59% in men vs 24% in women) while the covariance between females is due mainly to shared environmental effects (76% in women vs 41% in men). Further extending Model 2.10 to allow different male-male and female-female environmental correlations did not result in an improvement (P 5 0.89, results not shown). Genet. Epidemiol. DOI 10.1002/gepi
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DISCUSSION The aim of this paper was to investigate genetic and environmental influences on PP, with particular regard to interactions between sex and environment, and between sex and genetic effects. In doing so, we demonstrated the importance of considering environmental factors in detail. Even though familial biometric studies allow the partitioning of variance into genetic and environmental components and offer the potential to examine the influence of sex differences, biometric analyses investigating sex-dependent effects are uncommon, even for cardiovascular risk factors. Sexual dimorphism is encountered frequently in quantitative cardiovascular risk factors. Men have higher average levels of blood pressure, weight, and cholesterol than women [Harrap et al., 2000] and die at younger ages from heart disease [Nikiforov and Mamaev, 1998]. We found no significant differences in the means or total variances of PP for males and females, but there was consistent evidence of sex-dependent covariances and sex-specific effects for shared familial factors, both genetic and environmental. These differences could arise from interactions between genetics and sex (G S), between environment and sex (E S) or from the interaction of both environment and genetics with sex (E,G S). Potential mechanisms for G S effects include different sex chromosomes and the contrasting hormonal milieux of males and females, which might modulate the impact of genetic factors and environmental exposures. The mechanisms for E S effects are potentially prosaic, arising from behaviours that are shared more strongly by same-sex relatives. The first clues to such sex-specific effects became evident when correlations between pairs were considered according to same-sex and opposite-sex pairs. Male-female pairs had consistently lower correlations than same-sex pairs (whether male or female) (P 5 0.005, Model 1.1 vs 1.2). This suggested differences in the underlying covariances in males and females. One previous study of adolescents also noted that the correlations between same-sex DZ pairs were greater than opposite sex pairs for a number of key cardiovascular traits including PP, cardiac index, and total peripheral resistance [Snieder et al., 2003]. We first considered G S effects and our results are consistent with those of Towne et al. [1997] Genet. Epidemiol. DOI 10.1002/gepi
and Weiss et al. [2006] in supporting reduced genetic phenotypic correlation between opposite sex relatives (rG;MF 5 0.45). The best G S model (2.2) fitted significantly better than the sexindependent model (P 5 0.007). However, this model excludes any role for shared environmental factors. The sex-independent model could also be improved by allowing environmental correlations to be sex dependent (Model 2.6). In particular, we found a significant improvement in fit (P 5 0.0003) by allowing nonzero environmental correlations only between same-sex siblings (including twins) and spouses. The spouse correlation is clearly the smallest of these (rSP 5 0.07), although it should be remembered that spouse correlations were defined relative to total variance rather than shared environmental variance alone. The third approach was to look at (E,G S) effects, via different partitions of variance into genetic, shared environment and individual components for males and females. This model (2.5) is not nested in the sex-independent model so we could not carry out a classical test of significance. The AIC did suggest an improved fit however (7222.7 vs 7229.4). Under this assumption the striking finding was that the proportion of PP variance ascribed to genetic causes was much higher in males (1.62 vs 0.32). The proportion explained by shared genetic factors was correspondingly higher in females (1.84 vs 0), while the residual component was less differentiated (males 2.96; females 2.16). Since these three approaches produce nonnested models, conclusions as to which is most appropriate must be based on a guide such as the AIC. Here it suggests that the E S is the best explanation of the data (AIC 5 7219.7), followed by the sex-specific variance E,G S model (AIC 5 7222.7) and then finally the rG;MF o1 model of G S. Hence it may be too early to assume that the Mendelian model underlying the kinship coefficients needs to be modified for opposite sex relative pairs. More complex combinations of sex-specific or sex-dependent genetic and environmental factors did not appear to improve model fit. We recognise that some of the models presented approach the limit of complexity given the sample sizes, even though this is one of the larger familybased studies and one of few world-wide to have over-sampled twin families. However, the consistent patterns of the parameter estimates in support of sex-specific genetic and shared environmental
Sex Differences in Correlations and Variance Components
effects is perhaps a more important indication of the robustness of our inferences. This is particularly so when viewed in the light of the known pathophysiology of PP [Burt et al., 1995; Waddell et al., 2001; Ahimastos et al., 2003] that adds biological plausibility to the model results and our conclusions. Whatever the source of sex-dependence, it has implications for the magnitude of heritability, a key consideration in justifying and designing genomic studies. In the case of PP there is potential for spurious estimates of heritability. Mixed DZ twin pairs had a modest correlation for PP (0.18), while MZ twin pairs had much higher correlation (0.53). According to the classical twin model ignoring sex effects, genetic effects alone must explain the different correlations, and hence heritability would have been estimated as 53% under a variance components model that constrains heritability to be less than or equal to the MZ pair correlation, or 70% under the simplistic formula of H 5 2(rMZ rDZ ) [Falconer, 1989]. However, DZ twin pairs of the same sex (whether male-male or female-female) were more closely correlated (0.44 and 0.48, respectively, or 0.44 when the sexes were combined) and an estimate of heritability H based on same-sex DZ and MZ twin pairs was only of the order of 4% for males, 24% for females, or 18% when the sexes were combined. As all MZ pairs are same-sex, comparison of MZ correlation with all DZ pairs may be confounding the effect of shared genes with the effect of shared sex. The literature has been divided in terms of the heritability estimates for PP. In our analyses, we estimated heritability to be 20% using a standard variance components model (Model 2.1). This is in agreement with several other studies [Atwood et al., 2001; Adeyemo et al., 2002; Camp et al., 2003] and contrasts with a group of other estimates that are of the order of 40–50% [Snieder et al., 2003; DeStefano et al., 2004; Bochud et al., 2005]. The latter do not appear to have accounted for the sex effects in their analysis as we have, and indeed their estimates are consistent with the estimate from our simple twin correlation model without sex effects. Although the heritabilities reported by Bochud et al. [2005] were obtained from models which did not include a shared environmental component, these authors also reported that the heritability decreased by less than 12% when a common sibship component was included, and that the estimate of the common sibship component was non-significant
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at the 5% level. However, the standard errors for these heritabilities were large (e.g. 0.3770.12 for office-measured PP). The models used by DeStefano et al. [2004] do not appear to have allowed for shared environmental effects. Further reasons for these discrepancies are not immediately obvious. All studies included mixed sexes but do not appear to have accounted for the sex differences as we have here. Studies reporting high heritabilities included two in which the average of repeated measures of PP were used [DeStefano et al., 2004; Bochud et al., 2005], thereby decreasing measurement error and so increasing the proportion of total variance that could be explained by genes. We have shown previously using the VFHS that the cumulative measurement error for variables calculated from our measurements of SBP and DBP accounts for 11% of variance [Harrap et al., 2004] and is independent of sex. Although measurement error might contribute to the high individual-specific component of PP variance, it cannot account for the sex-specific differences observed for genetic and shared environmental variance. When we consider the results of the variance components analysis, the estimates of the proportion of variance due to genes from Model 2.6 are 35% for males and 17% for females, inverting the relationship suggested by the correlation model. This implies that detailed genetic linkage and association analyses are less likely to be fruitful in females and the search for specific familial environmental factors relevant to a PP is likely to be more difficult in males. Note that this is precisely the opposite conclusion to that suggested by heritability estimates from the correlation model. It is worth noting that in this study, the effects of epistasis, dominance and shared environment may be confounded. One might equally say that epistasis and dominance are strongly confounded by the selection of an additive or multiplicative model. However, our analysis helps shed some light on this important issue. We expect that both male and female MZ twin pairs share the same patterns of epistasis and dominance, so excess correlation due to these causes would be present equally in both cases. Another possibility is that dominance or epistasis may act differently in males and females, just as Towne et al. [1997] have suggested for gene sharing in opposite sexes. However this seems rather tenuous, especially given our finding that sex differences may be more readily explained by behavioural differences Genet. Epidemiol. DOI 10.1002/gepi
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manifesting in different degrees of shared environment, than by putative new biological mechanisms. These analyses reveal that there is potentially much to be gained by ‘splitting’ rather than ‘lumping’ parameters in modelling of phenotypes in families, especially when this is done based on a priori biological knowledge. There are potentially important implications for the design of further molecular or epidemiological studies in search of genetic and environmental agents. Research design of such studies should anticipate the possibility that genetic and environmental factors might not be the same in males and females, and that simply pooling data from both sexes together would make it harder to identify those factors. Appropriate biometric analyses for sex dependency cannot only inform research design, but the sex-dependent models can be applied to linkage and association analyses to provide a more powerful analytical framework, as in Towne et al. [1997] and Weiss et al. [2006]. However, the final point that comes from our analyses is that one risks missing the point quite badly if focus is only on a genetic explanation for what might easily be explained by shared environmental factors.
ACKNOWLEDGMENTS We thank Margaret Stebbing, the general practitioners and research nurses, and the Australian Twin Registry and Professor Graham G. Giles and the Health 2000 Study for their contributions to subject recruitment. We also acknowledge the helpful comments of two anonymous referees which resulted in improvements to this paper.
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