1. Karri Silventoinen University of Helsinki Osaka University

2.  Genetic twin modeling, such as all statistical modeling, makes certain assumptions  In twin modeling, there are two types of assumptions  Some of the assumptions are technical and are based on the way we specify the model ◦ They can be tested statistically ◦ Violations may indicate complexity of the world not captured by the used model  However some assumptions do not affect the technical model specifications but rather how to interpret the results ◦ Violation of these assumptions may not affect the model fit but can lead to wrong conclusions ◦ In many cases, they cannot be tested directly ◦ The effects need to be considered when interpreting the results

3.  The most important technical assumption for twin modeling is that the variances are the for MZ and DZ twins as well as for the first and second twin in the pair  The technical reason for this was presented already in the previous presentations ◦ Same path coefficients are used both for MZ and DZ twins ◦ Necessary assumption for making possible to estimate the model ◦ The exception is sib-sib interaction we will treat later in this presentation  A real problem is, however, that greater variation, for example, in MZ twins may indicate that there is additional source of variation ◦ For example, intrauterine conditions may lead to greater variation of birth weight in MZ twins ◦ We cannot estimate the sources of this extra variation and thus cannot take it into account when specifying the model

4.  The assumption of similar variances in MZ and DZ twins is closely related to the equal environment assumption  This means that the same amount of environmental variation affects MZ and DZ twins ◦ MZ and DZ twins are thus samples from the same basic population  However this does not mean that MZ co-twins could not share more environmental variation than DZ twins ◦ It is very likely that environment of MZ twins is more similar than DZ co-twins ◦ Environment is partly reflection of genetic factors ◦ This part of environmental variation is (correctly) modeled as genetic variation

5.  In many cases twin models are written in the way that equal means are also expected  However because in twin studies we are interested in decomposing variation, this does not violate the basic assumptions  Different mean parameters can be given for different groups  Different means for MZ and DZ twins are typical for many anthropometric traits especially in childhood

6.  Take the script “ACE univariate model.R”  Modify the model in a way that it allows different means for MZ and DZ twins  When comparing the fit indexes, does the model indicates that different means are needed for MZ and DZ twins?

7.  A standard way to test the technical assumptions of genetic twin model is to compare the fit of twin model to the fit of saturated model ◦ This is the case for OpenMx ◦ For example, MPlus allows directly compare the model fit to observed data  Saturated model does not make these assumptions but estimates all statistics ◦ In practice it estimates means and variances for MZ and DZ twins as well as for first and second co-twin in the pair ◦ Genetic twin model, such as ACE model, can be interpreted to be a sub- model of the saturated model ◦ This allows to use -2LL statistics to compare models  If the fit of genetic twin model is not statistically significantly worse than saturated model, it indicates that these assumptions are fulfilled ◦ Using saturated model, it is possible to test these assumption separately

8.  Take the script “Saturated model.R”  Check what assumptions the model is testing  Run the model and check whether these assumptions are violated  Finally compare the fit of full saturated model to fit of ACE twin model

9.  Saturated model estimates 10 parameters ◦ Means for MZ and DZ and first and second co-twin (=4 parameters) ◦ Variances for MZ and DZ and first and second twin (=4 parameters) ◦ Covariances for MZ and DZ twins  ACE model estimates 4 parameters ◦ A, C and E components and one mean parameter  So the difference in -2LL follows χ 2 -distribution with 6 degrees of freedom  Naturally these numbers will be different, for example, for sex-limitation model  Good always to think beforehand the number of estimated parameters because discrepancy may indicate problems how the model is specified

10.  In addition to the assumptions related to the building the model, there are assumptions related to the interpretation of results  The violations of these assumption do not create technical problems but may affect how to interpret the results  The most important assumptions are random mating and lack of gene-environment interactions  Many models also assume that there is no sib-sib interactions

11.  As seen in the previous lectures, twin models assume that genetic correlation is 0.5 in DZ twins  This is because 50% chance that DZ twins have inherited the same allele from the same parents  However if there exists genetic correlation between parents, it inflates the genetic correlation of DZ twins  In practice this leads to the overestimation of common environmental factors ◦ Common environmental component is estimated if DZ correlation is more than half of MZ correlation ◦ If genetic correlation is more than 0.5 in DZ twins, this is estimated as common environmental influence if there is no dominance genetic inflluence

12.  However, assortative mating does not necessarily create genetic correlation between spouses  Trait correlation between spouses can be because of environmental factors ◦ For example there are clear differences in height between educational categories ◦ So if there is educational correlation between the spouses, it may lead to correlation in height which is totally caused by environmental factors  However there is also clear evidence that assortative mating can be directly based on traits ◦ For example it is very likely that height affects directly spouse selection ◦ This creates genetic correlation between spouses  These different hypotheses are difficult to test even if information on parents are available in data ◦ Two generation models are available but in practice complicated

13.  Twin models make usually the assumption of lack of gene environment interactions  However there is accumulating evidence that genetic and environmental factors interact ◦ Tomorrow a lecture on this specific topic  It is not possible to test all possible G*E interactions  However when interpreting the results, the possible role of G*E needs to be considered

14. Contributions of Genetic, Shared Environment, Genotype x Shared Environment Interaction Effects to Twin/Sib Resemblance Shared Environment Additive Genetic Effects Genotype x Shared Environment Interaction MZ Pairs111 x 1 = 1 DZ Pairs/Full Sibs1½1 x ½ = ½ In other words—if gene-(shared) environment interaction is not explicitly modeled, it will be subsumed into the A term in the classic twin model.

15. Contributions of Genetic, Unshared Environment, Genotype x Unshared Environment Interaction Effects to Twin/Sib Resemblance Unshared (Unique) Environment Additive Genetic Effects Genotype x Unshared Environment Interaction MZ Pairs010 x 1 = 0 DZ Pairs/Full Sibs0½0 x ½ = 0 If gene-(unshared) environment interaction is not explicitly modeled, it will be subsumed into the E term in the classic twin model.

16.  If G-E interaction is not modeled it naturally does not mean that it would not affect the results  In many cases we have not measured relevant environmental exposures, but we have to speculate whether they can still explain the found results  G-E interaction may well be one reason why common environmental influences are rarely seen even in the case when this in counterintuitive ◦ For example, the lack of common environmental effect in many psychological traits ◦ It may reflect rather that the effect of family related factors is modified by genetic factors than the lack of this effect ◦ This has important scientific and policy implications  However even if G*E effects are not modeled, it does not mean that the parameter estimates do not have interpretation  They describe heritability of the trait at the level of the environmental factors in the population ◦ This is comparable to the situation of all other statistics ◦ For example if we have the estimate of mean height in the Finnish population it applies in the given sex distribution but is different if the sex distribution will change

17.  Usually twin models assume that there is no interaction between co-twins  In some psychological trait this may not be the case  There can be collaboration and competition between twins  It can be shown that collaboration increases the estimates of common environmental effects whereas competition may increases the effect of dominance genetic effects  Sib-interaction effect can be modeled because collaboration increases MZ variation more and competition less as compared to DZ twins  So difference in variances between MZ and DZ twins may be because of sib-sib interaction and this can be tested  This is, however, a rare finding

18. Sib-sib interaction in ACE model A BMI TWIN1 CE a c e 1 / 0.5 1 1 1 A BMI TWIN2 CE a c e 1 1 1 1 s s

19.  Gene-gene interactions do not violate the assumptions of twin modeling, but their effect cannot be estimated  Gene-gene interactions are modeled in unknown proposition depending on linkage disequilibrium  If the interaction is between two genes closely linked, i.e. inherited together, it is modeled as part of additive genetic variation ◦ In the classical twin design they form only one unit  However if the genes are weakly linked, i.e. usually inherited separately, this effect mimics dominance genetic variation ◦ This is understandable because in that case the genes will be reshuffled between generations such as in the case for dominance genetic effect

20.  In the recent years epigenetics has become an important area in genetics  Discordant MZ twin pairs have been very important to study these issues  By using the classical twin design, it is also possible to study the heritability of RNA transcription of single genes  However otherwise epigenetics has only minor impact on twin design  Epigenetic variation is (correctly) modeled as part of A, C or E component related to factors behind this variation  The same applies to all environmental factors  Thus from the classical twin design point of view epigenetic is only one source of environmental variation ◦ Such as all environmental variation, part of it may be caused by genetic factors

21. Population Research Unit Department of Social Research University of Helsinki