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Nonparametric Estimates of Gene × Environment Interaction Using Local Structural Equation Modeling

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Abstract

Gene × environment (G × E) interaction studies test the hypothesis that the strength of genetic influence varies across environmental contexts. Existing latent variable methods for estimating G × E interactions in twin and family data specify parametric (typically linear) functions for the interaction effect. An improper functional form may obscure the underlying shape of the interaction effect and may lead to failures to detect a significant interaction. In this article, we introduce a novel approach to the behavior genetic toolkit, local structural equation modeling (LOSEM). LOSEM is a highly flexible nonparametric approach for estimating latent interaction effects across the range of a measured moderator. This approach opens up the ability to detect and visualize new forms of G × E interaction. We illustrate the approach by using LOSEM to estimate gene × socioeconomic status interactions for six cognitive phenotypes. Rather than continuously and monotonically varying effects as has been assumed in conventional parametric approaches, LOSEM indicated substantial nonlinear shifts in genetic variance for several phenotypes. The operating characteristics of LOSEM were interrogated through simulation studies where the functional form of the interaction effect was known. LOSEM provides a conservative estimate of G × E interaction with sufficient power to detect statistically significant G × E signal with moderate sample size. We offer recommendations for the application of LOSEM and provide scripts for implementing these biometric models in Mplus and in OpenMx under R.

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Notes

  1. In this paper, we focus on measured, family-level moderators that are, by definition, the same across family members. This level of measurement is currently required for the statistical approach we introduce, and we return to this limitation in the discussion.

  2. “We prefer an exponential function rather than a quadratic one as a model of the variances. Exponential models share with quadratic models the desirable property of being positive, but have the additional advantage of being monotonic uniformly increasing or decreasing with respect to the moderator. Quadratic models of variances are by definition parabolic with respect to the moderator, and once again, biometric interaction models are difficult enough to explain without having to account for why a biometric variance first increases, and then decreases, as a function of SES” (Turkheimer and Horn 2014, p. 44).

  3. Other kernel forms are in use beside the Gaussian specification (e.g., bi-square, triangular, uniform, etc.). However, the choice of the type of kernel is largely unimportant for statistical inference (Eubank 1999 p. 177; Hart 1997, p. 11). The bandwidth is the primary determinant of smoothing.

  4. Due to ECLS-B data regulations, all sample sizes are rounded to the nearest 50.

  5. Importantly, note that standard software applications of sampling weights automatically rescale sampling weights such that the sum of the weights equals the number of observations (Asparouhov 2005).

  6. Of course, such an approach is inadequate to capture many of the nonlinearities found in the data.

  7. The possible significance level of a permutation test is limited by the number of permutated datasets that are created. Using an observed test statistic and 99 permutation datasets, the lowest possible significance level is .01. More precise significance levels can be obtained by analyzing more permutation datasets (e.g., 999). For the current purposes, this proved too computationally intensive when hundreds of models were under investigation.

  8. This complex form was accomplished by specifying that genetic influences on the phenotype took the form of: \(a = 1 + .25 \times M - .20 \times M^{2} - .05 \times M^{3}\).

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Acknowledgments

This research was supported by National Institutes of Health (NIH) research Grant R21-HD069772 to Dr. Tucker-Drob and R21-AA020588 to Dr. Harden. Daniel A. Briley was supported by NIH training Grant T32HD007081. The Population Research Center at the University of Texas at Austin is supported by NIH Center Grant R24HD042849.

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Correspondence to Daniel A. Briley.

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Daniel A. Briley, K. Paige Harden, Timothy C. Bates, and Elliot M. Tucker-Drob have declared that they have no conflict of interest.

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The ECLS-B was approved by state institutional review boards where testing was conducted. All participants provided informed consent before taking part in the study.

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Edited by Carol Van Hulle.

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Briley, D.A., Harden, K.P., Bates, T.C. et al. Nonparametric Estimates of Gene × Environment Interaction Using Local Structural Equation Modeling. Behav Genet 45, 581–596 (2015). https://doi.org/10.1007/s10519-015-9732-8

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