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Table S1: Results of Three Traits of the Trinity Students Study in the Region of An Enzyme Gene. The p-values of “Basis of both GVF and inline image” Were Based on the F-distributed Test Statistics of the Fixed Effect Model (3), the p-values of “Basis of FKST” Were Based on the Variance-Component Functional Kernel Score Test (7), and the p-values of SKAT Were Based of R Package SKAT. When Type of GVF = Add, Dom, and Rec, the Genetic Variant Function Was Taken as Additive, Dominant, and Recessive, Respectively. Abbreviation: GVF = Genetic Variant Function, FKST = Functional Kernel Score Tests.

Table S2: Simulation Results of Type I Error Rates of Four Tests Based on Sequence Data Generated by COSI, When The Genetic Variant Functions Were Taken as Additive. The Results of “Basis of both GVF and inline image” Were Based on the F-distributed Test Statistics of the Fixed Effect Model (3) and the Results of “Basis of FKST” Were Based on the Variance-Component Functional Kernel Score Test (7) of Mixed Effect Models, for B-spline Basis and Fourier Basis, Respectively. Abbreviation: GVF = Genetic Variant Function, FKST = Functional Kernel Score Tests.

Table S3: Simulation Results of Type I Error Rates of Four Tests Based on 36 SNPs of the Trinity Students Study When the Dominant Genetic Variant Functions Were Used. The Results of “Basis of both GVF and inline image” Were Based on the F-distributed Test Statistics of the Fixed Effect Model (3) and the Results of “Basis of FKST” Were Based on the Variance-Component Functional Kernel Score Test (7) of Mixed Effect Models, for B-spline Basis and Fourier Basis, Respectively. Abbreviation: GVF = Genetic Variant Function, FKST = Functional Kernel Score Tests.

Table S4: Simulation Results of Type I Error Rates of Four Tests Based on 36 SNPs of the Trinity Students Study When the Recessive Genetic Variant Functions Were Used. The Results of “Basis of both GVF and inline image” Were Based on the F-distributed Test Statistics of the Fixed Effect Model (3) and the Results of “Basis of FKST” Were Based on the Variance-Component Functional Kernel Score Test (7) of Mixed Effect Models, for B-spline Basis and Fourier Basis, Respectively. Abbreviation: GVF = Genetic Variant Function, FKST = Functional Kernel Score Tests.

Figure S1: The Empirical Power of the F-test Statistics of the Fixed Effect Models (3), (4), and (6), and SKAT and SKAT-O Using Rare Variants in Analysis, When Causal Variants Were Both Rare and Common, and All Causal Variants Had Positive Effects. The Simulations Were Based on COSI Sequence Data.

Figure S2: The Empirical Power of the F-test Statistics of the Fixed Effect Models (3), (4), and (6), and SKAT and SKAT-O Using Rare Variants in Analysis, When Causal Variants Were both Rare and Common, and 20%/80% Causal Variants Had Negative/Positive Effects. The Simulations Were Based on COSI Sequence Data.

Figure S3: The Empirical Power of the F-test Statistics of the Fixed Effect Models (3), (4), and (6), and SKAT and SKAT-O Using Rare Variants in Analysis, When Causal Variants Were both Rare and Common, and 50%/50% Causal Variants Had Negative/Positive Effects. The Simulations Were Based on COSI Sequence Data.

Figure S4: The Empirical Power of the F-test Statistics of the Fixed Effect Models (3), (4), and (6), and SKAT and SKAT-O Using Both Rare and Common Variants in Analysis, When Causal Variants Were only Rare, and All Causal Variants Had Positive Effects. The Simulations Were Based on COSI Sequence Data.

Figure S5: The Empirical Power of the F-test Statistics of the Fixed Effect Models (3), (4), and (6), and SKAT and SKAT-O Using Both Rare and Common Variants in Analysis, When Causal Variants Were only Rare, and 20%/80% Causal Variants Had Negative/Positive Effects. The Simulations Were Based on COSI Sequence Data.

Figure S6: The Empirical Power of the F-test Statistics of the Fixed Effect Models (3), (4), and (6), and SKAT and SKAT-O Using Both Rare and Common Variants in Analysis, When Causal Variants Were Only Rare, and 50%/50% Causal Variants Had Negative/Positive Effects. The Simulations Were Based on COSI Sequence Data.

Figure S7: The Empirical Power of Single Causal SNP Regression Model, Functional Linear Models, and SKAT and SKAT-O Based on Trinity Students Study SNP Data for Modes of Additive, Dominant, and Recessive Inheritance, Respectively, and a Sample Size of 250. Abbreviations: Add = Additive, Dom = Dominant, and Rec = Recessive, Respectively.

Figure S8: The Empirical Power of Single Causal SNP Regression Model, Functional Linear Models, and SKAT and SKAT-O Based on Trinity Students Study SNP Data for Modes of Additive, Dominant, and Recessive Inheritance, Respectively, and a Sample Size of 500. Abbreviations: Add = Additive, Dom = Dominant, and Rec = Recessive, Respectively.

Figure S9: The Empirical Power of Single Causal SNP Regression Model, Functional Linear Models, and SKAT and SKAT-O Based on Trinity Students Study SNP Data for Modes of Additive, Dominant, and Recessive Inheritance, Respectively, and a Sample Size of 1,000. Abbreviations: Add = Additive, Dom = Dominant, and Rec = Recessive, Respectively.

Figure S10: The Empirical Power of Single Causal SNP Regression Model, Functional Linear Models, and SKAT and SKAT-O Based on Trinity Students Study SNP Data for Modes of Additive, Dominant, and Recessive Inheritance, Respectively, and a Sample Size of 1,500. Abbreviations: Add = Additive, Dom = Dominant, and Rec = Recessive, Respectively.

Figure S11: The Empirical Power of Single Causal SNP Regression Model, Functional Linear Models, and SKAT and SKAT-O Based on Trinity Students Study SNP Data for Modes of Additive, Dominant, and Recessive Inheritance, Respectively, and a Sample Size of 2,000. Abbreviations: Add = Additive, Dom = Dominant, and Rec = Recessive, Respectively.

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