Quantifying and Addressing Parameter Indeterminacy in the Classical Twin Design

Abstract

T he classical twin design (CTD) is the most common method used to infer genetic and environmental causes of phenotypic variation. As has long been acknowledged, different combinations of the common environment/assortative mating, and additive, dominant, and epistatic genetic effects can lead to the same observed covariation between twin pairs, meaning that there is an inherent indeterminacy in parameter estimates arising from the CTD. The CTD circumvents this indeterminacy by assuming that higher-order epistasis is negligible and that the effects of either dominant genetic variation or the common environment are nonexistent. These assumptions, however, lead to consistent biases in parameter estimation. The current paper quantifies these biases and discusses alternative strategies for dealing with parameter indeterminacy in twin designs. One strategy is to model the similarity among other relatives in addition to twins (extended twin-family designs), which reduces but does not eliminate indeterminacy in parameter estimates. A more general strategy, applicable to all twin designs, is to present the parameter indeterminacy explicitly, as in a graph. Presenting the space of mathematically equally likely parameter values is important, not only because it aids the proper interpretation of twin design findings, but also because it keeps behavioral geneticists themselves mindful of methodological assumptions that can easily go unexamined.

Estimating the Extent of Parameter Bias in the Classical Twin Design: A Comparison of Parameter Estimates From Extended Twin-Family and Classical Twin Designs

“…These comparisons between CTD and ETFD parameter estimates are consistent with the biases predicted to exist in CTD parameters Grayson, 1989;Keller & Coventry, 2005). While V G parameters from CTD studies tend to be only moderately overestimated, the estimates for V A and V NA from CTD studies appear to be substantially biased.…”

“…Grayson, 1989). Of the two sources of bias, we found that the inability to simultaneously estimate both V NA and V C , as opposed to the fixing of rˆto 1 ⁄4, generally has greater potential to bias parameter estimates (Keller & Coventry, 2005).…”

“…In addition to these four parameters, the correlation between DZ twins due to genetic nonadditivity, r, is also unknown, although it must range between 1 ⁄4 (when all genetic nonadditivity is due to additive-by-additive epistasis or dominance) to a theoretical lower limit of 0 (when genetic nonadditivity is due to extreme epistasis). However, there are possibly good reasons, based on the principles of biometrical genetics, to believe that r is typically closer to 1 ⁄4 than to 0 Keller & Coventry, 2005).Despite its popularity and convenience, it has long been understood that the CTD is limited in its ability to distinguish many potential causes of phenotypic variation Jinks & Fulker, 1970;. A primary limitation of the CTD stems from the fact that it offers only three observations, the total phenotypic variance (V P ), the covariance between MZ twins (CV MZ ), and the covariance between DZ twins (CV DZ ), from which to estimate five unknown parameters 1 .…”

“…Algebraically, five unknowns cannot be estimated from only three knowns. This limitation is circumvented in the CTD by fixing two of the unknown parameters at assumed values (rˆto 1 ⁄4 and either V C or V NA to 0), enabling the other three parameters to be estimated.In a companion report (Keller & Coventry, 2005), we derive the biases in the three estimated parameters that result from fixing (a) rˆto 1 ⁄4 and (b) either V C or V NA to 0 (see also Grayson, 1989). When V NA is set to 0 (often called 'ACE' models), V A tends to be overestimated while V NA (because it is set to 0) and V C tend to be underestimated.…”

“…In addition to these four parameters, the correlation between DZ twins due to genetic nonadditivity, r, is also unknown, although it must range between 1 ⁄4 (when all genetic nonadditivity is due to additive-by-additive epistasis or dominance) to a theoretical lower limit of 0 (when genetic nonadditivity is due to extreme epistasis). However, there are possibly good reasons, based on the principles of biometrical genetics, to believe that r is typically closer to 1 ⁄4 than to 0 Keller & Coventry, 2005).…”