Heritability Across the Distribution: An Application of Quantile Regression

Abstract

We introduce a new method for analyzing twin data called quantile regression. Through the application presented here, quantile regression is able to assess the genetic and environmental etiology of any skill or ability, at multiple points in the distribution of that skill or ability. This method is compared to the Cherny et al. (Behav Genet 22:153–162, 1992) method in an application to four different reading-related outcomes in 304 pairs of first-grade same sex twins enrolled in the Western Reserve Reading Project. Findings across the two methods were similar; both indicated some variation across the distribution of the genetic and shared environmental influences on non-word reading. However, quantile regression provides more details about the location and size of the measured effect. Applications of the technique are discussed.

Appendices

Appendix 1

SAS code: Data setup

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This code requires a data set that has one variable (column) per twin. In this first data preparation step, the data is called in, and the scores on the desired variable for twin 1 and their cotwin (twin 2) are renamed as “Var1” and “Var2”.

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libname df ‘C:\yourpath\’; Data abc; set df.your_dataset; Var1 = your_twin1_variable; Var2 = your_twin2_variable; run;

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For this next step, change the words “your_zygosity” to the name of the zygosity variable in your dataset. Change “MZ” to read however MZ is coded in your dataset (i.e., 1). Do the same for DZ.

The “proc standard” z-scores the variables (var1 & var2) prior to entry in the analysis.

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data abc2; set abc; if (your_zygosity = MZ) then rel = 1; if (your_zygosity = DZ) then rel = 0.5; run;

proc standard data = abc2 m=0 std=1 out = z1; var var1 var2; run;

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Appendix 2

SAS code: Cherny method

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The Cherny method can be conducted using the GLM procedure. This is done by using twin 1’s score (var1) to predict twin 2’s score (var2), along with an interaction of twin 1’s score with degree of relatedness (established in Appendix 1).

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proc glm data = abc2;

model var2 = var1 rel var1*var1 var1*rel var1*var1*rel;

run; quit;

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From these results, the parameter estimate associated with:

“var1” represents the proportion variance attributable to shared environment

“var1*rel” represents the proportion of variance attributable to heritability

“var1*var1” represents the linear change of shared environment across the distribution

“var1*var1*rel” represents the linear change of heritability across the distribution

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Appendix 3

SAS code: Quantile regression

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After setting up the data, run the following code to obtain estimates of heritability and shared environmental effects. This is done using the variable “Rel,” created in step 2 of Appendix 1 (indicating the degree of relatedness).

The results are presented graphically via the ODS statements.

Replace “quantile = all” with the quantiles desired. For the analyses in the present study, this syntax read: quantile = 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90

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ods html; ods graphics on; proc quantreg ci=sparsity; model var1 = var2 | rel/quantile= all plot = quantplot; run; ods graphics off; ods html close;

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The shaded areas on the graph represent 95% confidence intervals of differences from zero. The graph labeled “var2” represents shared environment. The graph labeled “var2*zyg” represents heritability.

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