Twins and Causal Inference: Leveraging Nature's Experiment

Abstract

In this review, we discuss how samples comprising monozygotic and dizygotic twin pairs can be used for the purpose of strengthening causal inference by controlling for shared influences on exposure and outcome. We begin by briefly introducing how twin data can be used to inform the biometric decomposition of population variance into genetic, shared environmental, and nonshared environmental influences. We then discuss how extensions to this model can be used to explore whether associations between exposure and outcome survive correction for shared etiology (common causes). We review several analytical approaches that can be applied to twin data for this purpose. These include multivariate structural equation models, cotwin control methods, direction of causation models (cross-sectional and longitudinal), and extended family designs used to assess intergenerational associations. We conclude by highlighting some of the limitations and considerations that researchers should be aware of when using twin data for the purposes of interrogating causal hypotheses.

Figure 1.

Path diagram of the univariate twin model. All of our path diagrams follow standard structural equation modeling conventions, whereby measured variables are represented with squares and latent variables are represented with circles. Although not included in the path diagram, the variances of all latent variables are fixed to unity. (a₁₁) Additive genetic effects on phenotype, (c₁₁) shared environmental effects on phenotype, (e₁₁) nonshared environmental effects on phenotype, (A₁) additive genetic variance component, (C₁) shared environmental variance component, (E₁) nonshared environmental variance component. In the classical twin design, the predicted variances of each trait (a₁₁² + c₁₁² + e₁₁²) and the predictions for the covariances (a₁₁² + c₁₁² for MZ and 0.5a₁₁² + c₁₁² for DZ pairs) are fitted to the observed variances and covariances to obtain the most likely estimates for the A, C, and E effects.

Figure 2.

Cholesky decomposition twin model.

Figure 3.

Modeling causality. In the above models, B_yx is the causal effect of X on Y. In model i, V_x denotes the variance of X, and R_y denotes the residual variance of Y (the variance of Y remaining after regressing out the effects of X). In model ii, V_z denotes the variance of Z, and R_x and R_y denote the residual variances of X and Y (variance remaining after regressing out the effect of Z (on X) and Z and X (on Y)). Twin models shown are partial path diagrams for a single individual. All latent factors have a variance of 1 (not shown).

Figure 4.

A phenotypic autoregressive cross-lagged model and partial path diagrams of a twin autoregressive cross-lagged model.

Figure 5.

The direction of causation (DoC) twin model.

Figure 6.

Children of twins structural equation model. (a₁) Additive genetic effects on parental phenotype, (c₁) shared environmental effects on parental phenotype, (e₁) nonshared environmental effects on parental phenotype, (a₁′) genetic effects common to parental phenotype and offspring phenotype, (c₁′) extended family environment effects on offspring phenotype, (a₂) genetic effects specific to offspring phenotype, (c₂) shared environmental effects on offspring phenotype (not estimable using cousin data), (e₂) nonshared environmental effects on offspring phenotype, (p) phenotypic effect of parent on offspring, (NB) the pathway between A₁ and A₁′ is fixed to 0.50 because parents and children share 50% of their genome. To avoid overcomplicating path diagrams, variance paths have been omitted but for all latent factors, variance = 1. For A₁′ this means that residual variance (after accounting for the path between A₁ and A₁′) is 0.75.