Logic of the Cotwin Control Design
Twin studies have long been a staple within the field of behavioral genetics. There are hundreds, perhaps thousands of twin studies of behavioral and social phenotypes (Bouchard & Propping, 1993
; McGue & Bouchard, 1998
). In most cases, these studies have sought to estimate heritability by comparing the phenotypic similarity of monozygotic (MZ) twins, who are genetically identical, with that of dizygotic (DZ) twins, who are no more genetically similar than ordinary siblings. Less widely recognized perhaps is the utility of twin studies to explore the environmental basis of individual differences in behavior (Kaprio et al., 1993
). Specifically, twins discordant for exposure approximate the alternative outcomes presumed under the counterfactual model. The basic logic of the approach can be illustrated by one of the earliest applications of the so-called cotwin control or discordant-twin design: Does smoking increase mortality?
The eminent statistician, R.A. Fisher, was skeptical that the association of smoking with lung cancer reflected a causal effect of the former on the latter: “that cigarette-smoking and lung cancer, though not mutually causative, are both influenced by a common cause, in this case the individual genotype” (Fisher, 1957
, p. 298). For Fisher, genetic confounding rather than true causation might be the basis of the association of smoking with lung cancer. In a subsequent letter to Nature
, Fisher (1958)
provided what he thought to be support for his genetic hypothesis: “that the smoking habits of monozygotic, or one-egg, twins were clearly more alike than those of twins derived from two eggs” (p. 596). But heritability of exposure does not preclude causality of effect. Fisher did not undertake the critical follow-up to his observation that smoking exposure was heritable. Namely, among twins who are discordant for smoking, is the smoking member of the pair more likely to suffer lung cancer and early mortality than the nonsmoking member? Subsequent research on MZ and DZ twin pairs discordant for smoking has adequately answered this question. Within discordant pairs, the smoking twin has significantly increased mortality relative to the nonsmoking twin (Carmelli & Page, 1997
; Kaprio & Koskenvuo, 1989
). Findings from the discordant-twin design led to the disconfirmation of Fisher’s genetic hypothesis by providing more powerful support for a causal influence of smoking than is possible with standard epidemiological designs.
It is helpful to analyze the logic of the cotwin control approach within the counterfactual framework. Let
be the outcome when the i
th twin is a smoker and
be the outcome when he or she is not. Then the causal effect of smoking for the i
th twin is given by
. Assume further that
is the outcome for the i
th twin’s nonsmoking cotwin (designated i
′). Then the cotwin control design involves estimating δi
. That is, the cotwin control design involves implicitly using the nonsmoking cotwin of a smoker to estimate what the smoker would have looked like had he or she not smoked. Of course the nonsmoking cotwin will not necessarily be a perfect match under this alternative outcomes scenario. Nonetheless, discordant MZ twins, who have both a common genotype and a common early rearing environment, are likely to be better matches than discordant DZ twins, who have a common early rearing environment but share only 50% of their segregating genetic alleles.
These expectations can be formalized within a biometric formulation. That is, the observed phenotype (P) or outcome can be assumed to be a function of (a) additive genetic effects (A), which are shared completely by MZ twins but are only 50% shared by DZ twins; (b) shared early environmental effects (C; e.g., the effects of rearing social class), which are shared completely by both MZ and DZ twins; and (c) non-shared environmental effects (E; e.g., the effects of adult social class), which are not shared by either MZ or DZ twins. Individual-level associations (e.g., as estimated from an individual-level regression of outcome on exposure) reflect potential confounding of exposure and outcome by A, C, and E effects. Associations within DZ twin pairs discordant for exposure (i.e., the exposure effect estimated comparing the two members of discordant DZ pairs), control for C effects and partially for A effects. Associations within MZ twin pairs discordant for exposure control for both C and A effects. Neither within-pair comparison controls for confounding due to E factors, an important point to which we return below. Regardless, if exposure is truly a cause of outcome, then we expect exposure to be associated with outcome at the individual level, as well as within DZ twin pairs discordant for exposure and within MZ twin pairs discordant for exposure.
illustrates three possible patterns of individual-level versus within-pair effects (cf. Bergen et al., 2008
). In Scenario A, the effect of exposure is the same at the individual level and within DZ and MZ pairs discordant on exposure. This is the pattern we would expect if exposure were causal and there was no confounding by either A
. In Scenario B, the within-pair effect is reduced in DZ twins relative to the individual-level effect and is completely absent in MZ twins. This pattern suggests that the association of exposure and outcome is due entirely to confounding by A
. In this case, failure to observe an effect within discordant MZ twin pairs is inconsistent with causality. In Scenario C, the exposure effect is reduced but not eliminated within both DZ and MZ pairs discordant on exposure relative to the individual-level effect. This pattern suggests that the association of exposure to outcome is due partially to confounding, whereas the existence of an exposure effect within discordant MZ pairs is consistent with at least a partial causal effect. Clearly the power of the discordant-twin design stems largely from the within-MZ pair analysis, because MZ comparisons afford the greatest control for confounding. Nonetheless, the biometric formulation also helps to identify one of the limitations of the discordant-twin approach. That is, only exposures on which MZ twins differ can be explored (i.e., exposures mediated by the non-shared environment), so that this design cannot be of help in exploring the impact of shared environmental exposures such as maternal depression and rearing social class—at least in the usual case when the MZ twins have been reared together.
Fig. 1 Logic of the discordant-twin design. We graphed the hypothetical effect of exposure on outcome when measured at the individual level (IL; i.e., without regard to twin-pair membership) and within monozygotic (MZ) and dizygotic (DZ) twin pairs discordant (more ...)
Discordant-Twin Studies in Gerontology
The extent to which the discordant-twin design will be of utility in gerontology will depend on the degree to which exposure to putative aging risk factors is heritable, just as Fisher (1958)
reasoned for smoking more the 50 years ago. That is, the power of the discordant-twin design is that it controls for potential genetic (and also shared environmental) confounding, and without heritability there can be no genetic confounding. In fact, twin studies have shown that a wide range of factors of relevance to aging are heritable. These include smoking (Li, Cheng, Ma, & Swan, 2003
), heavy alcohol consumption (Whitfield et al., 2004
), achieved social class (Plomin & Bergeman, 1991
), social engagement (McGue & Christensen, 2007
), and physical activity (Frederiksen & Christensen, 2003
). The heritability of these lifestyle factors may reflect selection effects, whereby individuals adopt lifestyles that complement and reinforce heritable characteristics (Scarr & McCartney, 1983
). We know, for example, that genetic factors contribute to individual differences in personality (Finkel & McGue, 1997
). We know further that individuals with outgoing and cheerful dispositions are more likely to have satisfying relations and a socially engaged lifestyle than are individuals who are withdrawn or sullen, in part because cheerful individuals strive to construct experiences that reinforce their sunny dispositions (Ozer & Benet-Martinez, 2006
). Thus, heritable influences on personality become translated as heritable influences on social engagement, raising the possibility that the association of social engagement with, for example, depression risk reflects genetic selection rather than true causation. But as with smoking exposure, the mere demonstration of heritability is not sufficient to establish genetic selection. If the association of social engagement with outcome is due entirely to genetic selection, then differences within genetically identical MZ twin pairs discordant for engagement should be unrelated to differences in outcome.
summarizes findings from discordant-twin studies in the psychological aging field in terms of the association between exposure and outcome at the individual level (i.e., without regard to twin-pair status) and the various within-pair estimates reported in each study. Although the number of studies is limited, a range of exposures and outcomes has been investigated. Several tentative conclusions seem appropriate. First, for most outcomes, findings from individual-level analyses are confirmed by showing exposure effects within discordant twin pairs, even if the magnitudes of the within-pair effects are smaller than those at the individual level. The one notable exception is adult social class, for which Osler, McGue, and Christensen (2007)
reported no association with health and cognitive outcomes in MZ twin pairs discordant for adult social class. Second, in most cases, the discordant-twin-pair analysis did not distinguish MZ from DZ twins, making it difficult to interpret the significance of the results (cf. ). Failure to report findings by zygosity presumably owes to the modest size of most of the discordant twin samples. Nonetheless, a pooled MZ and DZ analysis cannot totally rule out the possibility of genetic confounding since an association within discordant DZ pairs, who are not matched for genotype, is expected even under genetic selection. Finally, in the few studies that analyzed discordant MZ twins, findings generally confirm those found at the individual level. Thus, Carlson, Andersson, Lichtenstein, Michaelsson, and Ahlbom (2007)
reported that among MZ twins discordant for physical activity, the less active twin had higher mortality over a 29-year period; Kujala, Kaprio, and Koskenvuo (2002)
reported that smoking and heavy alcohol use were associated with mortality within MZ twin pairs discordant on exposure; and McGue and Christensen (2007)
reported that in MZ twin pairs discordant for social engagement, the least social twin had lower physical and cognitive functioning and higher rates of depression symptomatology.
Discordant-Twin Studies in Social and Psychological Gerontology
It is important to recognize that the comparison of discordant MZ twins does not guarantee certain causal inference even if it is more powerful than individual-level analyses. The generalizability of findings from research on twins will always be questioned, even though research has repeatedly shown that twins are generally unremarkable with respect to their personalities (Johnson, Krueger, Bouchard, & McGue, 2002
), cognitive abilities (K. Christensen et al., 2006
), risk for mental disorders (Kendler, Pedersen, Farahmand, & Persson, 1996
), and adult mortality trajectories (K. Christensen, Vaupel, Holm, & Yashin, 1995
). In addition, the standard discordant-twin design cannot rule out reverse causation even if it addresses issues surrounding confounding. That is, if outcome differences lead to differences in exposure (e.g., as might occur when the outcome is cognitive ability and exposure is intellectual engagement), then we would still expect to observe within-pair associations. Ruling out reverse causation requires longitudinal designs.
A further significant limitation concerns the asymmetrical nature of causal evidence from a discordant-twin study. That is, although failure to observe a within-pair association would seem to disconfirm the existence of a causal effect (although even this can be debated; see discussion on reliability below), the observation of an association between exposure and outcome within discordant pairs cannot establish causality. A recent example from the substance abuse field can help to illustrate the issue. Lynskey et al. (2003)
reported that among MZ twins discordant for early onset cannabis abuse, the early-using twin was more likely to be a drug abuser or an alcoholic as an adult than the late-using or nonusing twin. These findings are consistent with, but do not establish, a causal effect of early cannabis use on adult substance abuse. This is because the factors that led to the twins being discordant in their cannabis use might also be the factors that account for their differences in outcome. This may be the case with early cannabis use. In a separate study, Vink, Nawijn, Boomsma, and Willemsen (2007)
reported that MZ twin discordance in cannabis exposure was associated with preexisting personality indicators of risk. That is, the early-using twin was more likely to be high in sensation seeking and neuroticism than his or her nonearly-using but genetically identical cotwin. Consequently, the association of early cannabis use with adult outcomes, rather than being causal, may arise because the personality factors that increase risk of early use also increase risk of adult substance abuse.
Thus the discordant-twin design does not obviate the need to consider the role of confounding factors even though it provides a basis for powerful tests of causality in observational settings. This is because MZ twins do not provide a perfect counterfactual pair. That is, even if they are matched on genotype and early rearing environment, the two members of an MZ twin pair are not matched on the nonshared experiences that make them psychologically unique. Consequently, a within-MZ pairs association of exposure with outcome may reflect true causality or, alternatively, the effect of the nonshared experiences that led to differences in exposure. Unfortunately, none of the studies included in systematically explored the factors associated with twin discordance in exposure.
Finally, in some cases the discordant-twin design may fail to observe a within-pair association even when there is a causal influence of exposure on outcome and the sample is large enough to provide adequate power. Specifically, measurement error in the exposure variable is expected to attenuate within-pair associations to a greater degree than individual-level associations because of the compounding of error inherent in taking a difference score (Ashenfelter & Krueger, 1994
). Under classical test score theory, if σ is the common estimate of the proportion of measurement error in the exposure variable and ρ is the twin correlation, then the regression coefficient of outcome on exposure is attenuated by σ at the individual level but by σ/(1−ρ) at the within-pair level (Griliches, 1979
; note that we implicitly assume here that there is no error of measurement in the outcome, because if it exists it would not have a differential effect on the alternative estimates discussed here). Thus, for example, if measurement error accounted for 10% in an exposure variable, then the individual-level estimate would be attenuated by 10%, but the within-pair estimate would be attenuated by 33% when the twin correlation on exposure is .7 and 20% when the twin correlation is .5. Consequently, we expect attenuation of within-pair estimates due to the compounding of measurement error. Moreover, since MZ twin correlations are typically higher than DZ twin correlations, we expect the within-pair attenuation to be greater for MZ than DZ pairs.