A model of gene-gene and gene-environment interactions and its implications for targeting environmental interventions by genotype

Additional File 1:

Gene-gene and gene-environment interaction model. Contains the Visual Basic macro (Twincal), input and output datasheets and charts used to calculate the solutions described in the text. The program is run by entering parameters in the 'Inputs' sheet and clicking on the 'Run' button. Note that for the final chart ('fe') the number of categories on the horizontal axis changes depending on the environmental input parameters ε and PAF^E_e. If these parameters are changed it is therefore necessary to delete the lower part of the output sheet prior to running the model and, after the run, to redraw the chart using the source data option from the chart. All other charts are drawn automatically. The line γ_max = γ_min is calculated exactly for the chart 'fe' but is approximated in the charts 'pgdz' and 'pgdzneg' using Newton's method and an initial guess for f_ge (f0) and step (fet). For some input parameters it may be necessary to change these values by editing the Visual Basic code (Twincal) to obtain a valid solution.

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Additional File 2:

Supplementary Figure 1: Example model solution space with R_MD = 1.7 and U_ge ≥ 0. Model solution space with U_ge ≥ 0 for the same input parameters as Figure 2, apart from λ_MZ = 4.4.

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Additional File 3:

Supplementary Figure 2: Example model solution space with R_MD = 1.8 and U_ge ≥ 0. Model solution space with U_ge ≥ 0 for the same input parameters as Figure 2, apart from λ_MZ = 4.6.

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Additional File 4:

Supplementary Figure 3: Example model solution space with R_MD = 1.95 and U_ge ≥ 0. Model solution space with U_ge ≥ 0 for the same input parameters as Figure 2, apart from λ_MZ = 4.9.

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Additional File 5:

Supplementary Figure 4: Example model solution space with R_MD = 2.1 and U_ge ≥ 0. Model solution space with U_ge ≥ 0 for the same input parameters as Figure 2, apart from λ_MZ = 5.2.

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Additional File 6:

Supplementary Figure 5: Example full solution space with R_MD = 1.7. Full model solution space for the same input parameters as Figure 5, transformed so that f_ge is on the horizontal axis.

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Additional File 7:

Supplementary Figure 6: Example full solution space with R_MD = 1.8. Full model solution space for the same input parameters as Figure 6, transformed so that f_ge is on the horizontal axis.

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Additional File 8:

Supplementary Figure 7: Example full solution space with R_MD = 1.95. Full model solution space for the same input parameters as Figure 7, transformed so that f_ge is on the horizontal axis.

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Additional File 9:

Supplementary Figure 8: Example full solution space with R_MD = 2.1. Full model solution space for the same input parameters as Figure 8, transformed so that f_ge is on the horizontal axis.

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Additional File 10:

Supplementary Figure 9: Example model solution with c_MD > 1 and U_ge ≥ 0. Input parameters: λ_MZ = 5.2, λ_DZ = 3, λ_sib = 2, ε = 0.2, PAF^E_e = 0.5, c_MD = 2, r_t = 0.1.

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Additional File 11:

Supplementary Figure 10: Example model solution with c_MD > 1 and U_ge ≥ 0. Input parameters as for Figure 13.

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Additional File 12:

Supplementary Figure 11: Example full solution space with c_MD > 1. Full model solution space for the same parameters as Figure 13, transformed so that f_ge is on the horizontal axis.

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Additional File 13:

Supplementary Figure 12: Breast cancer solution space with U_ge ≥ 0. Input parameters are as shown in Table 5, with c_MD = 1. The solution space is shown (shaded) for positive f_ge, assuming the 'equal environments' assumption holds (c_MD = 1). The darker shaded area shows the part of the solution space for which γ_maxge < 1/2. Utility U_ge is at its maximum when γ = 1/2 except within this darker shaded area.

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Additional File 14:

Supplementary Figure 13: Breast cancer variances with f_ge = 0. Input parameters as for Figure 16. Additive model of G-E interaction (f_ge = 0). Variance components are genetic (V_g) or environmental (V_e).

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Additional File 15:

Supplementary Figure 14: Breast cancer variances with f_ge = 1. Input parameters as for Figure 16. Multiplicative G-E interaction model (f_ge = 1). Variance components are genetic (V_g), environmental (V_e) or due to gene-environment interaction (V_ge).

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Additional File 16:

Supplementary Figure 15: Breast cancer variances with f_ge = 1/PAF^E_e. Input parameters as for Figure 16. Maximum G-E interaction model (f_ge = 1/PAF^E_e). Variance components are genetic (V_g), environmental (V_e) or due to gene-environment interaction (V_ge).

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Additional File 17:

Supplementary Figure 16: Breast cancer γ values with f_ge = 0. Input parameters as for Figure 16. The proportion of the population in the 'high genotypic risk' group, γ, may take any value in the shaded area. γ_min occurs when R_ge = 1, i.e. when the Positive Predictive Value (PPV) of being in the 'ge' subgroup is 100%. γ_max occurs when R_oo = 1 for an additive G-E model and solutions with a Population Impact of 100% (PI = 1) cannot exist.

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Additional File 18:

Supplementary Figure 17: Breast cancer γ values with f_ge = 1. Input parameters as for Figure 16. The proportion of the population in the 'high genotypic risk' group, γ, may take any value in the shaded area. A solution with a Population Impact of 100% (PI = 1) may exist if γ = γ_max.

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Additional File 19:

Supplementary Figure 18: Breast cancer γ values with f_ge = 1/PAF^E_e. Input parameters as for Figure 16. The proportion of the population in the 'high genotypic risk' group, γ, may take any value in the shaded area. A solution with a Population Impact of 100% (PI = 1) may exist if γ = γ_max.

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Additional File 20:

Supplementary Figure 19: Breast cancer solution space with U_ge ≤ 0. Input parameters are as for Figure 16. The solution space is shown for negative f_ge (where the utility of targeting environmental interventions at the high genotypic risk group is negative, U_ge ≤ 0). Solutions exist only in the shaded area where γ_max ≥ γ_min.

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Additional File 21:

Supplementary Figure 20: Breast cancer: full solution space. Input parameters are as for Figure 16. The same solution space as Figures 16 and 23 is shown (shaded), transformed so that the G-E interaction factor is plotted on the horizontal axis. Again, each point in the shaded solution space represents a genetic model defined by p^DZ_g and a G-E interaction model defined by f_ge. The area of solutions with γ_maxge < 1/2 is highlighted with darker shading. The classical twin study solution lies on the vertical axis (f_ge = 0) at the point p^DZ_g = 1/2, and is slightly outside the solution space.

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Additional File 22:

Supplementary Figure 21: Lung cancer solution space with U_ge ≥ 0. Input parameters are as shown in Table 5, with c_MD = 1.

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Additional File 23:

Supplementary Figure 22: Lung cancer variances with f_ge = 0. Input parameters as for Figure 25. Note that the horizontal axis has been expanded to show high values of c_SD/R_SD only.

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Additional File 24:

Supplementary Figure 23: Lung cancer variances with f_ge = 1. Input parameters as for Figure 25. Note that the horizontal axis has been expanded to show high values of c_SD/R_SD only.

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Additional File 25:

Supplementary Figure 24: Lung cancer variances with f_ge = 1/PAF^E_e. Input parameters as for Figure 25. Note that the horizontal axis has been expanded to show high values of c_SD/R_SD only.

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Additional File 26:

Supplementary Figure 25: Lung cancer γ values for f_ge = 1. Input parameters as for Figure 25. The proportion of the population in the 'high genotypic risk' group, γ, may take any value in the shaded area.

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Additional File 27:

Supplementary Figure 26: Lung cancer γ values for f_ge = 1/PAF^E_e. Input parameters as for Figure 25. The proportion of the population in the 'high genotypic risk' group, γ, may take any value in the shaded area.

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Additional File 28:

Supplementary Figure 27: Lung cancer U_ge values for f_ge = 1. Input parameters as for Figure 25. The utility parameter, U_ge, may take any value in the shaded area, but is maximum when γ = 1/2.

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Additional File 29:

Supplementary Figure 28: Lung cancer U_ge values for f_ge = 1/PAF^E_e. Input parameters as for Figure 25. The utility parameter, U_ge, may take any value in the shaded area, but is maximum when γ = 1/2.

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Additional File 30:

Supplementary Figure 29: Lung cancer: full solution space. Input parameters as for Figure 25.

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Additional File 31:

Supplementary Figure 30: Schizophrenia U_ge ≥ 0, small environmental variance and c_MD ≥ 1. Input parameters are as shown in Table 5, with ε = 0.62, PAF^E_e = 0.15 and c_MD = 1.

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Additional File 32:

Supplementary Figure 31: Schizophrenia U_ge ≥ 0, small environmental variance and c_MD > 1. Input parameters are as shown in Table 5, with ε = 0.62, PAF^E_e = 0.15 and c_MD = 3.8.

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Additional File 33:

Supplementary Figure 32: Schizophrenia U_ge ≥ 0, large environmental variance and c_MD = 1. Input parameters are as shown in Table 5, with ε = 0.15, PAF^E_e = 0.86 and c_MD = 1.

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