Multiple births are the rule rather than the exception in most mammals, though in these cases they are due to polyovulation. In man we see dizygotic (DZ) twins, due to polyovulation, and monozygotic (MZ) twins due to cleavage of the embryo at the 8 or 16 cell stage [Bulmer 1970]. Known risk factors for DZ twin pregnancy are high maternal age, maternal tallness, high fecundability, and fertility/gonadotropin therapy. MZ twinning has no known aetiological factors (though familial aggregation has been suggested in a few pedigrees). MZ twins are uncommon in other mammalian species, with the exception of the armadillo, used extensively as an animal model.
In Australia in 1982, there were 5.5 per 1000 DZ twin confinements and 4.8 per 1000 MZ twin confinements [Doherty & Lancaster 1986]. As in most developed countries, the DZ spontaneous twinning rate has fallen over time - from 8 per 1000 during the first half of this century. With increasing fertility treatment (esp IVF) in recent years, there is an increase in the total number of DZ and higher order multiples, but this also reflects increasing maternal age.
Twins at birth differ from singletons in a number of ways that have relevance to the analysis of disease. Risk of premature birth is increased. Pre-eclampsia and its effects on the fetus are increased [Beischer & Mackay 1983], as is maternal anaemia. Malpresentation of the fetus at delivery, particularly the aftercoming twin, is increased. Overall perinatal mortality is currently approximately four times higher than that for singletons in developed countries [eg Petterson et al 1993], and was higher still in earlier birth cohorts, as well as in less developed countries. Occurrence of a number of diseases are increased in premature or birth injured infants, such as respiratory illness [Drillien 1958; Rona et al 1993], and neurological disorders such as cerebral palsy [Petterson et al 1993]. In addition, there are conditions unique to multiple birth such as twin-twin transfusion syndrome.
I have outlined elsewhere how the observed correlation between pairs of individuals of differing degrees of genetic relatedness can be used to test genetic hypotheses. These same methods are also applied to twin data, with or without data from other relatives (twin-family study). The main advantage to using twins is the possibility of controlling and indirectly measuring unobserved shared environment. The types of twin study that have this property are the twin adoption design, the classical twin design, and the cotwin control design. The classical twin design is the study of MZ and DZ pairs where both members of the pair have been reared in the same (family or shared) environment. An older twin design that cannot differentiate (unmeasured) shared from unshared environment is the study of MZ twins reared together.
A second quality of the classical twin design is to some extent a contradiction to the first property I have mentioned. It is that the large MZ to DZ (and more distant relatives) difference in the intrapair correlation between dominance deviations makes the detection of nonadditive genetic variation in traits easier, in the case where shared environmental influences are smaller. Thus Penrose  states, "..a relatively strong likeness between monozygotic twin pairs, together with a weak likeness between dizygotic pairs or ordinary sibs, is suggestive of multiple gene causation with a sharp threshold controlling manifestation".
Sir Francis Galton  was the first author to suggest the examination of twins as a method for determining the contributions of heredity and upbringing. He was initially unaware of the distinction between MZ and DZ twins made by Dareste in 1874 [Vogel & Motulsky 1986], and believed opposite sex pairs could arise from a single ovum [Rende et al 1990]. By 1883 however, he would state that opposite-sex twins "[are] never due to the development of two germinal spots in the same ovum", and that the MZ/DZ dichotomy explained "...a curious discontinuity in my results...Extreme similarity and extreme dissimilarity between twins of the same sex are nearly as common as moderate resemblance". His main analyses were to examine changes in twin similarity over time in two groups: those who were similar when young - where he looked for divergence with increasing age; and those who were dissimilar when young, in both cases arguing that if such environmental factors were of importance, similar parental treatment would lead to increasing similarity with age until the twins moved apart, whereupon similarity would decrease. This was the method used in several early studies by Thorndike  and others.
Siemens' book "Die Zwillingspathologie" [1924; actually the full title is: "Die Zwillingspathologie: Ihre Bedeutung, ihre Methodik, ihre bisherigen Ergebnisse"] was perhaps the first systematic description of the classical twin design. The key features are firstly the method of collecting adequate representative samples of twins (in his case through schools); diagnosis of zygosity by the use of multiple criteria; and the comparison of MZ and DZ correlations on the trait of interest from twins that have been reared together. Siemens would conclude that a trait was under genetic control if MZ twins were strongly concordant for a trait, while DZ twins were less concordant. His comment on the finding of a correlation between MZ twins of 0.4 for number of naevi, and 0.2 for DZ twins was that "[t]hese results are exactly as one would anticipate in an idiotypical nevus disposition...". The German school of twin research which developed his methods however tended to discount genetic influences on traits for which less than perfect MZ concordance was observed.
In a classic paper , this author reviews earlier studies of fingerprints in "true duplicate" (ie MZ) twins, and then describes her own study. The 31 pairs of twins were divided into definite (on grounds of facial similarity) MZ and DZ groups, and two intermediate groups - probable MZ and DZ. Bonnevie hypothesised finger ridge count to be a polygenic trait (she attempted to fit five locus models to pedigree data). She concluded that the Pearson correlations seen for sib pairs (r=0.59), DZ twin pairs (r=0.53), MZ twin pairs (r=0.92), and within individuals (left versus right hand; r=0.86), strongly suggested genetic determination of this trait.
This group  described a ten year research program including a classical twin study of 100 pairs of twins, and a MZ twin adoption study of 19 pairs. Newman regarded MZ twins reared apart as the closest "natural" equivalent to an experimental design in which the influences of rearing on development could be assessed, controlling for genetic endowment. Holzinger developed analysis of variance methods to estimate heritability, which were in use until the 1970s.
The core of the classical twin method is the fact that MZ and DZ twins are two classes of relative pairs in which we can assume shared (and unshared) environmental influences would act in the same way if the pair has been reared together. The interpretation of the difference between MZ and DZ phenotypic covariances is then cleaner than that of differences between other classes of relatives, as unless zygosity- environment or gene-environment interaction or correlation is present, the effects of shared environment can be cancelled out in the analysis.
Therefore, as Siemens practiced, the classical twin study requires (1) collection of an appropriate sample of MZ and DZ twins reared together; (2) correct assignment of zygosity; (3) statistical analysis comparing means and variances of the measured trait in the MZ and DZ groups to exclude zygosity x environment effects; and (4) statistical analyses inferring the sources of resemblance among the twins based on the MZ/DZ difference in concordance.
Two broad sampling designs are used for the classical twin design - single (and complete) ascertainment, and population sampling. In the former case, pairs are included in the sample if one (or both) of the twins is expressing the trait of interest, whether discrete or at one extreme of a continuum. In the latter case, complete pairs of twins should be incorporated into the study sample regardless of their trait values. In both cases, a particular form of sampling bias may arise, where pairs that are more concordant for the trait of interest than the general population of twins are recruited. This may be self-selection by twins, or referral or selection by physicians or other research workers of twins for entry into the study. A number of clinic based studies of disease have obviously been affected by such processes.
Volunteer samples of twins tend to contain more MZ than DZ twins, and more females than males, both tending to be in ratios of 2:1 [Lykken et al 1978]. This is well known, and after appropriate stratification does not interfere with analysis. An obvious point is that both members of the twin pair need to be recruited into a twin study. In the case that recruitment of both members of the twin pair into the study is contingent upon the trait of interest, examination of "singles", where only one member has taken part, can suggest whether a sampling bias is in fact present. Models for correcting the analyses of data where this problem has been detected were described by Neale et al .
This is the most vexed question in study of twins reared together. MZ twins differ from DZ twins in a number of behaviours and environmental exposures that could modify the MZ phenotypic correlation. These include the biological mechanism of formation, nature of placentation, complications of the MZ pregnancy and delivery, parental treatment, amount of time spent together, and frequency of contact as adults.
MZ twins are often treated more similarly by their parents than are ordinary siblings or DZ twins. This includes being dressed identically as children, and parents having similar expectations in terms of behaviour and development. One test of whether such treatment induces greater similarity is to compare twins where zygosity has been misdiagnosed to twins of their correct zygosity. Several studies have shown that MZ twins believed to be DZ by themselves and their parents are as concordant as correctly diagnosed MZ twins for a number of personality traits [Scarr 1968; Matheny et al 1976; Matheny 1979]. Most recently, Kendler et al  have examined concordance for five major psychiatric conditions - generalised anxiety disorder, depression, bulimia nervosa, alcoholism and phobia. Out of 590 MZ twin pairs, both members of 64 (11%) pairs thought they were DZ, and a further 8% were uncertain (disagreed between themselves, or did not know). Of the 440 DZ pairs, 9.6% were uncertain. Fitting of an MFT model did not find any evidence that perceived zygosity altered twin concordance.
MZ twins are more likely to remain in close contact in adulthood than DZ twins, and high frequency of contact has been found to be associated with increased correlation for behaviours such as years of education, alcohol and cigarette usage, political and social opinions, and personality [Clifford et al 1984; Heller et al 1988; Rose & Kaprio 1990; Lykken et al 1990]. One hypothesis is that twins that are more similar in personality and behaviours tend to stay in contact with one another. Evidence supporting this view has been adduced by Lykken et al  and more recently Posner et al [unpublished]. This must be the case for such variables as education level in older twins. It should be noted that the magnitude of the association between contact and similarity is usually small.
The alternative view of "social contagion" has been supported by the work of Rose and Kaprio  for alcohol use and neuroticism on the Eysenck Personality Inventory. The analyses these groups have performed are actually Galton's paradigm, in that change in similarity versus changes in contact over time are examined to determine the direction of causation between the two variables. If intensity of contact causes MZ twins to become more similar, duration of contact will act to increase the difference in concordances between MZ and DZ twins. Rose and Kaprio  comment that models incorporating information on contact did not actually lower heritability of traits, but did increase the estimated effects of shared environment at the expense of a reduction in unshared environmental effects.
If social contact does in fact lead to increased similarity among twins, this must either act as a shared environmental factor, in that both twins are exposed to the same environments, or allow (competitive) interaction between the twins. In the latter case, one would expect phenotypic variance differences between different levels of contact, as well as among MZ and DZ twins.
Three quarters of MZ twins share a monochorionic placenta, while all DZ twins are dichorionic (Table). Reed et al [1989, 1991] have presented evidence that dichorionic MZ twins were less similar than monochorionic MZ twins on Apolipoprotein A1 level as well as Type A personality as measured by the Jenkins Activity Survey. Estimation of placental type was performed via discriminant function analysis of fingerprint data, a method not used by any other group to date. If these findings for quite different traits are replicable, then overall MZ concordance will be inflated due to these "maternal" effects not seen in other sibships.
|Study||Zygosity||Single Placenta||Two Placentae (DC)||Total|
|Husby et al ||MZ||59 (53%)||22||30||111|
|Derom et al [pers comm]||MZ||1001 (73%)||193||180||1374|
|Reed et al||MZ||70 (65%)||--- 38 ---||108|
|Ramos-Arroyo et al ||MZ||73 (72%)||11||17||101|
|von Verschuer ||MZ||32||24||--||56|
A number of MZ female twin pairs discordant for X-linked disorders have underlined the role of X inactivation in phenotypic expression of these traits. In these pairs "mirror lyonisation" or skewed X inactivation is present, with X chromosomes from the different parents inactivated in each twin. Discordance in MZ twins due to genetic imprinting has also been observed, and it has been suggested that somatic mutation early in development could affect yet other traits. Hall , and Burn , have used these observations to suggest that discordance between cell phenotype in the embryonal inner cell mass may lead to MZ twinning. Evidence to date has been limited to these monogenic conditions, and Trejo et al  found no evidence for such processes in 32 MZ pairs (in fact skewing was in the same direction in both members of the pair where extreme).
Another property of MZ twinning reported is mirroring of physical characteristics. Asymmetries in development of the skeletal system, congenital skin lesions, hair whorling, and colour of each eye have been noted to be to one side in one twin, and to the other in the cotwin. Mirroring is thought to reflect late cleavage of the inner cell mass, so that some lateralization of development has already occurred in the different sides of the embryo. An excess of left handedness in twins was reported early this century [Newman et al 1937], and was thought due to similar processes within the brain. For this trait at least, increased birth trauma in twin birth is an alternative mechanism.
For the case of continuous traits where bivariate normality within twin pairs, standard biometrical genetic theory holds. Specifically, neglecting gene x environment interaction and epistatic effects, and assuming panmixia, we write,
where Pij is the phenotypic value of the ith member of the jth twin pair (MP and VP are the population means and variances). Then, we can write expressions for the means, variances and covariances of the trait within twin pairs of different zygosities:
The solution of these equations is optimally carried out by maximum likelihood methods, and can be performed by iteratively reweighted least squares (eg GLIM), or numerical maximisation of the likelihood expression, either for the summary moments for the entire sample (as in LISREL), or by summing over twinship likelihoods (eg FISHER).
Falconer  suggested a simple estimator for the heritability of a trait applicable to the classical twin design, given that the effects of dominance are small or absent,
where r denotes the intraclass correlation. From this, if significant dominance is absent, the domesticity or cultural transmissibility can also be calculated by subtraction. The other "traditional" approach is an ANOVA. This model, after Kempthorne  and Haseman and Elston  is derived from the above equations,
|Source of Variation||df||Expected Mean Square|
|Among MZ pairs||NMZ-1||2 VA+2 VD+VE+2 VC|
|Within MZ pairs||NMZ||VE|
|Among DZ pairs||NDZ-1||1.5 VA+1.25 VD+VE+2 VC|
|Within DZ pairs||NDZ||0.5 VA+0.75 VD+VE|
and two unweighted F tests for the presence of genetic variation can be performed, the most powerful of which is,
Again, if dominance is absent, MWDZ-MWMZ is half the additive genetic variance, VA. A preliminary F test to test for equality of the total variance of the trait in MZ and DZ twins should be performed, one form of which is [Christian 1974]:
but more usually, simply,
In both cases, the degrees of freedom have to be adjusted for the dependent nature of the data. An alternative, that I have used, is to perform a randomization test on these F ratios. These models give rise to simple heuristics for intraclass correlations for a single variable (Table).
|rMZ > 4rDZ||Epistasis|
|rMZ > 2rDZ||Genetic dominance (or epistasis; shared environment small)|
|2rDZ > rMZ > rDZ||Additive genes and shared environment (genetic dominance small)|
|rMZ = 2rDZ||Additive genetic effect - either monogenic or polygenic|
|rMZ = rDZ > 0||No genetic contribution - effects of family environment|
|rMZ = rDZ = 0||No familial aggregation|
This is a relatively simple model for analysis of variation of quantitative variables in pairs of relatives [LaBuda et al 1986; DeFries & Fulker 1985; Cherny et al, 1992]. An advantage is that ascertainment correction is straightforward. Briefly, it quantifies the regression to the mean in the (correlated) MZ and DZ cotwins of selected probands. More formally, the method requires the fitting of a regression equation:
where P=Proband score, C=Cotwin Score, R=Coefficient of relationship for pair, and A=intercept. Then:
If both twins are probands, or the sample is unselected, the pair is double entered - t-tests and standard errors must be appropriately corrected for this. In the case of unselected pairs, the estimates of heritability are unbiased, but less efficient than the full ML approach. Hierarchical models can be fitted - shared environmental and additive genetic. The approach standardises the trait variances and means across the zygosity groups, and so preliminary testing for equality of means and variances are required. Robust covariance estimators such as those provided by SAS PROC REG make this method attractive in the face of heteroscedasticity and non-normality of the trait [White 1980].
The usual statistic calculated for binary traits in twins is the twin concordance. Different estimators have been used. Under the assumptions of complete ascertainment and interchangeability of twins, the probandwise concordance (PC) is the maximum likelihood estimator for the recurrence risk, and is identical to the casewise concordance. For the entire population of twin pairs, following the usual notation for the cells of the 2x2 table,
PC = a/(a+0.5(b+c)) = 2a/(2a+b+c)
and is thus determined by the pairs containing at least one affected member. The asymptotic (MLE) variance of PC is,
VPC = (1/2N) PC (1-PC) (2-PC)2 = 4aN(N-a)/(a+N)4
where a is the number of concordant pairs, and N is the number of concordant and discordant pairs (a+b+c in the equation). I am grateful to Dr Camlin Tierney for the derivation of this result, which was stated in a more complex form by Hannah, Hopper and Matthews , and also arises directly from the estimator described by Li and Mantel . The closely agreeing jackknife alternative (derived by the author) is,
JVPC = 4 a (N-a) (N-1)3/[N2(a+N-1)2(a+N-2)2]
Under complete ascertainment, the pairwise concordance PPW (a/(a+b+c)) is related to PC as,
which allows construction of exact Pearson-Clopper confidence limits.
When ascertainment is less than complete, and/or secondary ascertainment occurs (that is diagnosis in the cotwin is made after the pair is detected via the proband twin), the probandwise concordance is,
where C2 represents the number of concordant pairs containing two probands (both diagnosed on the first pass), C1 the number of concordant pairs where the cotwin was diagnosed after being ascertained via the proband, and D the discordant pairs [Allen & Hrubec, 1979]. Under single ascertainment, this approaches the pairwise estimator (PPW=C1/(C1+D)). Davies  gives a simple variance estimator for PC under incomplete ascertainment.
This approach leads directly into that of James  as extended by Risch , given an additive relationship between the effects of shared environmental factors and genes. Tabulated below (see Table) are the broad conclusions that may be reached by the comparison of MZ and DZ PRR's. The first line is supported by the relationship between PRRM, PRRD and PRR1 under a single gene model mentioned earlier.
|PRRM > 4 PRRD||Epistasis - must be polygenic|
|PRRM-1 > 2(PRRD-1)||Genetic dominance (or epistasis)|
|PRRM-1 = 2(PRRD-1)||Additive genetic effect - either monogenic or polygenic|
|PRRM = PRRD > 1||No genetic contribution - effects of family environment|
|PRRM = PRRD = 1||No familial aggregation|
Allen [see Cederlof et al 1971; Kaprio et al 1977] suggested the use of the coincidence "rate", a/(a+b+c+d), which was standardised as a ratio of that expected under the hypothesis of no association. It can be shown that this ratio equals half the population risk ratio.
One can apply essentially the same rules to binary correlation coefficients calculated from simple samples of twins as those for intraclass correlations for continuous traits. I will examine one particular example where a trait is solely under the control of a single low penetrance diallelic autosomal dominant gene, with gene frequency q(A)=0.2, and penetrances f(AA)=f(AB)=0.2, f(BB)=0 - this is the model for asthma proposed by Cookson et al . Using standard approaches, one can calculate the distribution of pairs in the population arising under this model (Table).
|Zygosity||Concordant Affected||Discordant||Concordant Unaffected||Odds Ratio||Relative Risk||Phi||Tetrachoric r|
The population prevalence of the trait is 7.2%. Under the James/phi model, the additive genetic variance is 0.008192 (12.3% of phenotypic variance) and the dominance variance 0.001024 (1.5%). The binomial heritability is the rMZ (13.8%), which is estimated as 14.6% using the Falconer formula. Analysis using the tetrachoric correlation would lead to the estimation of a small component of variation due to shared environment. A range of monogenic models give rise to exactly these same results (eg Table), thus confirming that segregation analysis using twins alone is limited (though not completely uninformative).
The MFT can be fitted to binary or ordinally classified traits as was outlined elsewhere. Analyses are either performed by direct model fitting to contingency tables, or by weighted least squares methods, as described by Muthen, and implemented in PRELIS [Joreskog & Sorbom 1989]. The current strengths of this latter approach are the ease in which multivariate genetic models can be fitted, and the ability to fit to ordered categories and to combinations of continuous and discrete traits. This is not yet the case for analyses using the binary correlation or population relative risk.
The twin-cotwin matched case-control design (cotwin control design) is seen as a useful method of assessing associations between traits of interest and covariables. Its main strength is the absence of a need for ascertainment correction when twin pairs are ascertained via a proband (since both twins become probands). Usually, the ascertained trait is dichotomous, therefore twin pairs are selected that are discordant for this trait. The test for association between a continuous covariable and the trait is then a t-test of the intrapair difference of the covariate. In the case of monozygotic (MZ) twins, interpretation of results is straightforward, but other classes of relatives are often used.