The classic twin design aims to quantify the roles of genetic and environmental causes of variation in traits and in disease susceptibility.

• Estimate correlations rMZ and rDZ
• Compare MZ correlation with DZ correlation
• Divide total residual variance into components due to:
  A = (additive) effects of genes
  C = environmental (i.e., non-genetic) factors that are shared by twins in the same pair
  E = environmental effects specific to a person
  σ2 = A + C + E

In 1918,in his mid-20s, a twin called R. A. Fisher famously showed how the correlation between relatives (r) relates to A, C and E:
rMZ = A + C
rDZ = 0.5 A + C

Heritability = % of variation explained by genes
H = A / (A + C + E)
H = 2(rMZ – rDZ), provided H < rMZ
This equation assumes that MZ and DZ pairs share – to exactly the same extent – the non-genetic (environmental) factors specific to the characteristic of interest (C).
If rMZ > rDZ , then genetics might play a role.

Analytic approaches

• Pearson correlation (a good start but not ideal - the Intraclass Correlation Coefficient is better)
• Extensions of linear regression models:
   Variance components models
   Structural equation models
   Biometric models
   Mixed effects models
   Multivariate analyses

Advantages (not just heritability!)

• Very flexible models
• Adjust for exposures and confounders within families
• Variation perhaps more important than correlation
• Assess age and sex effects on variance and covariance

Limitations of classic twin approach

• Equal environments
• Crucial model assumption
• Can be difficult to test
• Low power to detect C effects
• ANY excess MZ correlation attributed to genetic effects
• Focus on h2 – other potentially interesting results ignored
• For non-normal outcomes, especially binary traits:
   Lower power
   More difficult to interpret results

References

Fisher, R. (1918). The Correlation Between Relatives On The Supposition Of Mendelian Inheritance. Transactions of the Royal Society of Edinburgh, 52, 399-433.

Hopper, J. L. (2005). Genetic Correlations and Covariances. Encyclopedia of Biostatistics.

Boyd, N. F., Dite, G. S., Stone, J., Gunasekara, A., English, D. R., McCredie M. R. E, Giles, G., Tritchler, D., Chiarelli, A., , Yaffe, M. J. and Hopper, J. L. (2002). The New England Journal of Medicine, 347(12), 886-94.