Multivariate Structural Equation Models

Structural equation models of twin family data can very easily be extended from the univariate to the multivariate case, which allows a whole new set of hypotheses to be tested because the observed information now includes all cross-twin cross-trait correlations. In addition to estimating the heritability of multiple traits, we can test the extent to which the heritability of these traits is caused by common genetic factors that influence all of the traits, and the extent to which heritability is caused by genetic factors that are specific to each trait. To illustrate this, Fig. 28.5 presents a bivariate extension of the ACE model of two different phenotypes: SBP measured at rest and SBP during mental stress. There are now two genetic factors, common genetic factor A influences SBP in both conditions, whereas specific genetic factor As influences only SBP under stress. Path coefficient a11 quantifies the effect of genetic factor A on SBP at rest, a21 quantifies the effect of A on SBP during stress. Coefficient a22

Table 28.8 Heritability estimates for cardiovascular disease risk factors in the Netherlands

Heritabilitya

Reference

Smoking

- Initiation 44%

- Quantity smoked 51%

- Nnicotine dependence 75% Physical inactivity

- Exercise less than 60 min weekly 50-68% Blood pressure

- Systolic blood pressure 48-60%

- Diastolic blood pressure 34-67% Lipids

- LDL cholesterol 77-83%

- HDL cholesterol 61-80% Obesity

-Body Mass Index 64-81%

-Waist-to-Hip ratio 70% Insulin resistance and beta cell function

-Fasting glucose 38-66%

-Insulin sensitivity (hyperinsulinemic 60%

euglycemic clamp) -Insulin response during hyperglycemic clamp 52%

First phase 77% Second phase Inflammation

-Cytokine response to LPS 55-68%

-Fibrinogen 39% Coagulation and Fibrinolysis

-Tissue plasminogen activator 67%

-Von Willibrand factor 72% Cardiac autonomic control

-Heart rate 37-68%

-Sympathetic control (pre-ejection period) 40-70%

-Parasympathetic control (respiratory sinus 28-55%

arrhythmia) Personality

-Type A behavior 45%

-Type D personality 52% Psychopathology

-Major depression 36%

-Anxiety disorders 36-51%

Vink et al (2005) Vink et al (2004) Vink et al (2005)

Stubbe et al (2006)

Kupper et al (2005b); Hottenga et al (2005);

de Geus et al (2007) Hottenga et al (2005); Kupper et al (2005b); de Geus et al (2007)

Beekman et al (2002) Beekman et al (2002)

Schousboe et al (2003) Unpublished

Simonis-Bik et al (2008) Unpublished

Unpublished

Posthuma et al (2005) de Lange et al (2006)

Kupper et al (2005a); Snieder et al (1997) Kupper et al (2006); de Geus et al (2007) Kupper et al (2005a) ; Snieder et al (1997)

Rebollo and Boomsma (2006) Kupper et al (2007)

Middeldorp et al (2005)

Distel et al (2008); Middeldorp et al (2005)

a Heritability estimates are ranged for some traits (e.g., 50-68%) because they were assessed in multiple studies in non-overlapping samples, e.g., young adults versus middle-aged, or by different assessment strategies, e.g., ambulatory recording versus laboratory-based measurements quantifies the additional effect of genetic factor As on SBP during stress. In a similar way, path coefficients en, cn, e2i, c2i, e22, and c22 quantify the effects of common and specific factors E and C on SBP at rest and during stress. The heritability of SBP at rest is the variance due to the genetic factor A divided by the total variance in SBP at rest and obtains as the ratio of a21/(a21 + c21 + e21). The heritability of SBP during stress is the variance due to the genetic factors A and As divided by the total variance

Fig. 28.5 A bivariate ACE model for SBP

in SBP under stress and obtains as the ratio of

We used the model depicted in Fig. 28.5

to test the hypothesis that stress increases the variance in SBP due to amplification of existing genetic variance and the emergence of new genetic variance (de Geus et al, 2007). Amplified genes are genes that have an effect on individual differences in a cardiovascular trait at rest, but these effects become stronger under stress. Emerging genes are genes that are expressed only during stress. To test for amplification (or deamplification) of genetic factors we compared the fit of a model in which a21 is freely estimated to the fit of a model in which a21 is constrained to be the same as an. If an and a2i are the same there is no evidence of amplification, but if a21 is significantly larger than a11 the effects of the genes acting on SBP at rest are amplified during stress. To test for emergence, we compared a model in which the path loading a22is freely estimated to a model in which a22 was constrained to be zero.

Results first of all showed that the total variance in SBP increased from 59.5 mm Hg2at rest to 94 mm Hg2 during stress. In both conditions DZ correlations were about half of the MZ correlations and model fitting confirmed that C did not influence SBP at rest or during stress and that an AE model fitted best. Under the AE model, the a21 coefficient was significantly larger than the a11 coefficient (ratio a21/a11 = 1.23) providing evidence for the amplification of the genetic factors active at rest during times of stress. The a22 coefficient was significantly different from zero (a22 = 4.0) providing evidence for the emergence of stress-specific genetic variation in SBP in a cohort of adolescent twins. Total heritabil-ity of SBP was 59% at rest but increased to 72% during stress. The ratio of genetic variance at rest and under stress was 35.1/67.8 = 1.9, whereas the ratio of unique environmental variance at rest and under stress was 24.4/26.4 = 1.1. Hence the increase in heritability reflected a true increase in genetic variance, not simply a reduction in environmental variance (e.g., because stress is a more standardized condition).

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