1 Using genetic risk score approaches to infer whether an
2 environmental factor attenuates or exacerbates the
3 adverse influence of a candidate gene
4 5 Wan-Yu Lin 1,2*, Yu-Shun Lin 1, Chang-Chuan Chan 2,3, Yu-Li Liu 4, Shih-Jen Tsai 5,6,7, 6 Po-Hsiu Kuo 1,2 7 8 1 Institute of Epidemiology and Preventive Medicine, College of Public Health, National 9 Taiwan University, Taipei, Taiwan 10 2 Department of Public Health, College of Public Health, National Taiwan University, 11 Taipei, Taiwan 12 3 Institute of Environmental and Occupational Health Sciences, College of Public Health, 13 National Taiwan University, Taipei, Taiwan 14 4 Center for Neuropsychiatric Research, National Health Research Institutes, Zhunan, 15 Taiwan 16 5 Department of Psychiatry, Taipei Veterans General Hospital, Taipei, Taiwan 17 6 Division of Psychiatry, National Yang-Ming University, Taipei, Taiwan 18 7 Institute of Brain Science, National Yang-Ming University, Taipei, Taiwan 19 20 21 Running title: GRS approaches for GxE 22 23 24 * Corresponding author:
25 Wan-Yu Lin, Ph.D. 26 Room 501, No. 17, Xu-Zhou Road, Taipei 100, Taiwan 27 Phone/Fax: +886-2-33668106; E-mail: [email protected] 28 29 30 31 32
1
33 Abstract 34 Some candidate genes have been robustly reported to be associated with complex traits, such
35 as the fat mass and obesity-associated (FTO) gene on body mass index, and the fibroblast growth
36 factor 5 (FGF5) gene on blood pressure levels. It is of interest to know whether an environmental
37 factor (E) can attenuate or exacerbate the adverse influence of a candidate gene. To this end, we
38 here evaluate the performance of “genetic risk score” (GRS) approaches to detect
39 “gene-environment interactions” (GxE). In the first stage, a GRS is calculated according to the
40 genotypes of variants in a candidate gene. In the second stage, we test whether E can significantly
41 modify this GRS effect. This two-stage procedure can not only provide a p-value for a GxE test
42 but also guide inferences on how E modifies the adverse effect of a gene. With systematic
43 simulations, we compared several ways to construct a GRS. If E exacerbates the adverse
44 influence of a gene, GRS formed by the elastic net (ENET) or the least absolute shrinkage and
45 selection operator (LASSO) is recommended. However, the performance of ENET or LASSO
46 will be compromised if E attenuates the adverse influence of a gene, and using the ridge
47 regression (RIDGE) can be more powerful in this situation. Applying RIDGE to 18,424 subjects
48 in the Taiwan Biobank, we showed that performing regular exercise can attenuate the adverse
49 influence of the FTO gene on 4 obesity measures: body mass index (p = 0.0009), body fat
50 percentage (p = 0.0031), waist circumference (p = 0.0052), and hip circumference (p = 0.0001).
51 As another example, we used RIDGE and found the FGF5 gene has a stronger effect on blood
52 pressure in Han Chinese with a higher waist-to-hip ratio (p = 0.0013 for diastolic blood pressure
53 and p = 0.0027 for systolic blood pressure). This study provides an evaluation on the GRS
54 approaches, which is important to infer whether E attenuates or exacerbates the adverse influence
55 of a candidate gene.
56 Keywords: body mass index; elastic net regression; gene-environment interaction; lasso; ridge
2 57 regression.
58 Introduction 59 The detection of “gene-environment interactions” (GxE) is important and is even more
60 challenging than the detection of main effects of genes (Aschard 2016; Greenland 1983; Hunter
61 2005). Although some gene-based GxE methods have been developed (Chen et al., 2014; Jiao et
62 al., 2013; Lin, Huang, et al., 2019; Lin et al., 2013; Lin et al., 2016), very few GxE findings have
0.05 63 reached the genome-wide significance level (i.e., p < = 2.5 × 10−6. Because there are 20000
64 ~20,000 genes across the genome, 2.5 × 10−6 is the commonly used significance level in
65 genome-wide gene-based analyses) (Chen et al., 2014; Lin, Huang, et al., 2019). Most evidence
66 of GxE was discovered by candidate gene analyses in which genome-wide association study
67 (GWAS) hits were targeted. For example, physical activity has been found to attenuate the
68 influence of the fat mass and obesity-associated (FTO) gene on obesity risk (Kilpelainen et al.,
69 2011; Vimaleswaran et al., 2009). This means that the association of the FTO risk alleles with
70 obesity measures is weaker in physically active subjects than in physically inactive subjects.
71 Another example is related to blood pressure levels. The fibroblast growth factor 5 (FGF5)
72 gene is associated with blood pressure levels in Han Chinese (Lin, Huang, et al., 2019; Liu et al.,
73 2011). Obesity has been reported to exacerbate the adverse influence of FGF5 on blood pressure.
74 That is, the association of the FGF5 risk alleles with blood pressure is stronger in obese subjects
75 than in lean subjects (Li et al., 2015).
76 A candidate gene usually harbors multiple risk variants. It is of interest to know whether an
77 environmental factor (E) attenuates or exacerbates the effects of these risk variants. However,
78 most GxE methods provide only p-values without any inference for the direction of interaction
79 (Chen et al., 2014; Lin, Huang, et al., 2019; Lin et al., 2013; Lin et al., 2016). In contrast, a
3 80 genetic risk score (GRS) approach aggregates the effects among an ensemble of single-nucleotide
81 polymorphisms (SNPs) and can indicate whether the GRS interacts synergistically or
82 antagonistically with E. A GRS is a linear combination of risk allele counts, where risk alleles
83 and weights are usually retrieved from large published GWASs or meta-analyses. However, the
84 vast majority of genetic studies have been performed on subjects of European ancestry (Sirugo et
85 al., 2019). Appropriate external GWAS results may not be available for GxE studies in other
86 ethnic populations.
87 To address this issue, GRS approaches using internal weights have been proposed for
88 pathway-based GxE studies (Huls, Ickstadt, et al., 2017; Huls, Kramer, et al., 2017) and GWASs
89 (Lin, Chan, et al., 2019; Lin et al., 2020; Lin et al., 2018). The internal weights come from
90 marginal effects of SNPs that can be estimated by a multivariate elastic net (ENET) regression
91 (Huls, Ickstadt, et al., 2017; Huls, Kramer, et al., 2017).
92 In this study, we described how to use GRS approaches to infer whether E attenuates or
93 exacerbates the adverse influence of a gene (therefore, GRS here aggregates the effects among an
94 ensemble of SNPs in a gene). Moreover, we compared GRS approaches with the “Set-Based
95 gene-EnviRonment InterAction test” (SBERIA) (Jiao et al., 2013), the “interaction Sequence
96 Kernel Association Test” (iSKAT) (Lin et al., 2016), and our previously developed “ADAptive
97 combination of Bayes Factors method” (ADABF) (Lin, Huang, et al., 2019). These methods were
98 then applied to the Taiwan Biobank (TWB) data.
99 Materials and Methods
100 Genetic risk score approaches
101 Usually, a GRS combines information of multiple nearly independent SNPs across the
4 102 genome (Ahmad et al., 2013; Lin, Chan, et al., 2019; Lin et al., 2020; Rask-Andersen et al.,
103 2017). However, there have been few applications of using GRS in gene-based GxE tests. To
104 have a clear description, we first explain covariate adjustment in the GRS gene-based GxE
105 approach. Suppose there are L SNPs in a gene or a pathway. Let 푔[∙] be the link function, 푌푖 be
106 the phenotype that can be either continuous or binary, 퐺푖푗 be the number of minor alleles (0, 1,
th 107 or 2, by additive genetic model) at the j SNP (j = 1, …, L), 퐸푖 be the environmental factor, 푿풊
108 be the vector of non-genetic covariates such as the age and sex, and the subscript “i” represents
109 data for the ith subject (푖 = 1, ⋯ , 푛). In addition to the additive model (by counting the number of
110 minor alleles), 퐺푖푗 can also be coded according to the dominant or recessive genetic model.
111 Some GRS approaches involve SNP selection and then aggregate the information of selected
112 SNPs. Therefore, we leave 퐺푖푗 (푗 = 1, … , 퐿) later and first regress 푌푖 on 푿풊 by a linear model
113 or a logistic regression model, as follows:
114 푔[퐸(푌푖)] = 훼0 + 휶′푿풊 , 푖 = 1, ⋯ , 푛 . (1)
̂ 푒푥푝(훼̂푘+휶̂′푿풊) 115 Let 휇̂0푖 = 훼̂0 + 휶′푿풊 (for continuous 푌푖) or 휇̂0푖 = (for binary 푌푖) be the 1+푒푥푝(훼̂푘+휶̂′푿풊)
th 116 predicted mean of 푌푖 under model (1). Therefore, the covariate-adjusted phenotype for the i
117 subject is 휀̂푖 = 푌푖 − 휇̂0푖.
118 Subsequently, we regress 휀̂푖 on 퐺푖1, ⋯ , 퐺푖퐿, as follows:
퐿 119 푔[퐸(휀̂푖)] = 훽0 + ∑푗=1 훽푗퐺푖푗 , 푖 = 1, ⋯ , 푛. (2)
120 Let 휷′ = [훽0 ⋯ 훽퐿] be the vector of regression coefficients in model (2). The ordinary least
121 squares (OLS) estimate of 휷 is as follows:
2 ̂ 푎푟푔푚푖푛 ∑푛 ∑퐿 ( )−1( ) 122 휷 = 휷 [ 푖=1(휀̂푖 − 훽0 − 푗=1 훽푗퐺푖푗) ] = 푮′푮 푮′휺̂ , (3)
th 123 where n is the sample size, 푮 is the n × (퐿 + 1) matrix with the i row of 1GGi1 ... iL ,
5 124 and 휺̂ is the n-length vector of covariate-adjusted phenotypes. Because of linkage disequilibrium
125 (LD), the SNPs in a gene are usually highly correlated with each other. In this situation, 푮′푮
126 may be singular and not invertible.
127 Ridge regression (RIDGE) (Hoerl and Kennard 1970) is used to address the collinearity
128 problem in model (2), where the regression coefficients are estimated by minimizing the residual
129 sum of squares and an l2-norm penalty, as follows:
2 ̂ 푎푟푔푚푖푛 ∑푛 ∑퐿 ∑퐿 2 130 휷 = 휷 [ 푖=1(휀̂푖 − 훽0 − 푗=1 훽푗퐺푖푗) + 휆 푗=1 훽푗 ]. (4)
131 The regularization parameter 휆 controls the amount of shrinkage. When 휆 is close to 0, 휷̂
̂ ̂ ̂ 132 from RIDGE will approximate the 휷 from OLS. When 휆 is large, 훽1, ⋯ , 훽퐿 will approach 0,
133 and model (2) will be reduced to an intercept-only model.
134 LASSO was later proposed to estimate regression coefficients by minimizing the residual
135 sum of squares and an l1-norm penalty (Tibshirani 1996) as follows:
2 ̂ 푎푟푔푚푖푛 ∑푛 ∑퐿 ∑퐿 136 휷 = 휷 [ 푖=1(휀̂푖 − 훽0 − 푗=1 훽푗퐺푖푗) + 휆 푗=1|훽푗|]. (5)
137 The regularization parameter 휆 controls the amount of shrinkage. Moreover, variable selection
138 can be performed by shrinking some 훽푗푠 to 0 (푗 = 1, … , 퐿). Because equation (5) selects SNPs
139 that are marginally associated with the covariate-adjusted phenotype (휀̂푖, 푖 = 1, ⋯ , 푛), this is
140 called the marginal-association filtering by LASSO. The term “marginal” is used here because
141 the 퐸푖 and 퐺푖푗 × 퐸푖 interaction term have not been included in equation (5). If 훽푗 is shrunk to
142 0, the jth SNP is regarded as unassociated with the covariate-adjusted phenotype and will not be
143 used for the construction of a GRS.
144 ENET (Zou and Hastie 2005) strikes a balance between RIDGE and LASSO by estimating
145 regression coefficients while minimizing the residual sum of squares and a mixture of an l1-norm
146 and an l2-norm, as follows:
6 2 1 147 휷̂ = 푎푟푔푚푖푛 {∑푛 (휀̂ − 훽 − ∑퐿 훽 퐺 ) + 휆 ∑퐿 [ (1 − 훼)훽2 + 훼|훽 |]}. (6) 휷 푖=1 푖 0 푗=1 푗 푖푗 푗=1 2 푗 푗
148 The regularization parameter 휆 controls the amount of shrinkage, whereas 훼 is a penalty
149 weight ranging from 0 (RIDGE) to 1 (LASSO). As suggested by Hüls et al. (Huls, Kramer, et al.,
150 2017), α = 0.5 is used for ENET throughout this work to achieve an optimal balance between
151 RIDGE and LASSO. Equation (6) is the marginal-association filtering by ENET.
152 Similar to genetic studies using penalized regression approaches (Huls, Ickstadt, et al., 2017;
153 Huls, Kramer, et al., 2017; Waldmann et al., 2013), we used the R package “glmnet” (Friedman et
154 al., 2010) to obtain 휷̂. The optimal values of the regularization parameter 휆 in equations (4)-(6)
155 were determined by 10-fold cross-validation. GWASs (Waldmann et al., 2013) and
156 pathway-based GxE studies (Huls, Ickstadt, et al., 2017; Huls, Kramer, et al., 2017) have
157 recommended choosing the largest 휆 such that the mean squared error (MSE) is within 1
158 standard error of the minimum MSE, to avoid selecting too many SNPs in ENET or LASSO.
159 However, most complex traits are polygenic, and a single gene usually explains little phenotypic
160 variation. In our simulations and real data analyses, this criterion usually selected 0 SNPs for
161 ENET or LASSO. Therefore, in gene-based GxE studies, we recommend using the 휆 that leads
162 to the minimum MSE.
163 RIDGE, LASSO, and ENET are all techniques for regression models that suffer from
164 multicollinearity. Therefore, the pruning stage to remove SNPs with LD is not required here.
165 After obtaining 휷̂ from RIDGE, LASSO, or ENET, the GRS of the ith subject is constructed by
퐿 ̂ th th 166 퐺푅푆푖′ = ∑푗=1 훽푗퐺푖푗, where 퐺푖푗 is the number of minor alleles (0, 1, or 2) at the j SNP of the i
̂ 167 subject. A positive 훽푗 indicates that the minor allele is associated with an increase in phenotype.
168 Therefore, a subject with more copies of the minor allele (more phenotype-increasing alleles) will
̂ 169 obtain an increase in his/her 퐺푅푆′. In contrast, a negative 훽푗 indicates that the minor allele is
7 170 associated with a decrease in phenotype, and a subject with more copies of the minor allele (more
171 phenotype-decreasing alleles) will obtain a decrease in his/her 퐺푅푆′. The 퐺푅푆′ is then
172 transformed into a Z-score that represents how many standard deviations the 퐺푅푆′ is from the
173 mean. The standardized GRS Z-score is denoted as 퐺푅푆푖. A larger GRS is always associated with
174 an increased phenotype.
175 Afterwards, we fit the following generalized linear model (GLM):
176 푔[퐸(푌푖)] = 훾0 + 훾퐺퐺푅푆푖 + 훾퐸퐸푖 + 훾퐼푛푡퐺푅푆푖 × 퐸푖 + 휸푪′푿풊 , 푖 = 1, ⋯ , 푛, (7)
177 where 훾퐺 > 0 because a larger GRS is always associated with an increased phenotype. Adding a
178 constraint (훾퐺 > 0) is expected to improve power, although for simplicity we here perform a
179 GLM without this constraint. By testing 퐻0: 훾퐼푛푡 = 0 푣푠. 퐻1: 훾퐼푛푡 ≠ 0, we evaluate whether GxE
180 exists. For continuous traits, each 1 standard deviation (sd) increase in GRS is associated with a
181 훾̂퐼푛푡 change in phenotype for subjects exposed to E = 1 than for subjects exposed to E = 0. For
182 binary traits, each 1 sd increase in GRS is associated with an odds ratio of 푒푥푝(훾̂퐼푛푡) for
183 subjects exposed to E = 1 compared to subjects exposed to E = 0. A positive (negative) 훾̂퐼푛푡
184 indicates that E = 1, or a larger E, exacerbates (attenuates) the adverse influence of a candidate
185 gene.
186 The whole data can be used to estimate 훽1, ⋯ , 훽퐿 (equations 4-6) and then to test
̂ 187 퐻0: 훾퐼푛푡 = 0 푣푠. 퐻1: 훾퐼푛푡 ≠ 0 (model 7) without data splitting. Theoretically, 훽푗 (푗 = 1, ⋯ , 퐿)
188 and 훾̂퐼푛푡 are asymptotically independent under the null hypothesis of no SNP-by-environment
189 interaction, proved by corollary 1 of (Dai et al., 2012). A two-stage approach that first filters
190 SNPs by a criterion independent of the test statistic (훾̂퐼푛푡 estimated from model 7) under the null
191 hypothesis, and then only uses SNPs that pass the filter, can maintain type I error rates and boost
192 power (Bourgon et al., 2010; Frost et al., 2016). Empirically, our following simulation studies
8 193 confirmed that GRS using internal weights is a valid approach in the sense that type I error rates
194 match the nominal significance level. Moreover, studies on genes (Frost et al., 2016; Jiao et al.,
195 2013), pathways (Huls, Ickstadt, et al., 2017; Huls, Kramer, et al., 2017), and GWASs (Lin et al.,
196 2018) have presented the validity of using internally weighted GRSs to test for G×E.
197 Competing methods
198 The abovementioned GRS approaches with some form of penalized regression (RIDGE,
199 LASSO, or ENET) were compared with the SBERIA (Jiao et al., 2013), iSKAT (Lin et al., 2016),
200 and ADABF (Lin, Huang, et al., 2019) methods.
201 SBERIA is the first gene-based G×E test based on the GRS concept. The phenotype is first
202 regressed on each SNP separately, while adjusting for covariates such as sex, age, and ancestry
203 principal components (PCs), as follows:
′ 204 푔[퐸(푌푖)] = 훽0 + 훽푗퐺푖푗 + 휷푪푿풊 , 푖 = 1, ⋯ , 푛; 푗 = 1, ⋯ , 퐿. (8)
̂ th 205 Let 훽푗 be the estimated regression coefficient of the j SNP and 푝푗 be the p-value of
th 206 testing 퐻0: 훽푗 = 0 푣푠. 퐻1: 훽푗 ≠ 0. The GRS of the i subject is constructed by 퐺푅푆푖′ =
퐿 ̂ 207 ∑푗=1[퐼(푝푗 < 0.1)푠푖푔푛(훽푗) + 휈]퐺푖푗, where 퐼(푝푗 < 0.1) is an indicator variable with a value of 1
̂ ̂ 208 if 푝푗 < 0.1 and 0 otherwise, 푠푖푔푛(훽푗) is either 1 or −1 depending on the sign of 훽푗, and 휈
209 is a very small value (e.g., 0.0001). Therefore, SBERIA GRS includes both SNP selection (only
210 SNPs marginally associated with the phenotype are used to construct the GRS) and SNP
211 weighting (only the directions of how SNPs influence the phenotype are used in the GRS). The
212 standardized GRS Z-score is denoted as 퐺푅푆푖. Then, the following GLM is fitted:
[ ( )] ∑퐿 213 푔 퐸 푌푖 = 훾0 + 푗=1 훾퐺푗퐺푖푗 + 훾퐸퐸푖 + 훾퐼푛푡퐺푅푆푖 × 퐸푖 + 휸푪′푿풊 , 푖 = 1, ⋯ , 푛; 푗 = 1, ⋯ , 퐿. (9)
214 By testing 퐻0: 훾퐼푛푡 = 0 푣푠. 퐻1: 훾퐼푛푡 ≠ 0, we can evaluate whether GxE exists (Jiao et al., 2013).
215 There are two fundamental differences between SBERIA and ENET (or LASSO). First, in
9 216 the marginal-association filtering stage, SBERIA fits L regression models respectively (equation
217 8), whereas ENET and LASSO fit a multivariate model incorporating L SNPs simultaneously
218 (equations 5-6). Second, in the model for testing GRS×E, SBERIA includes the main effects of
∑퐿 219 all the L SNPs ( 푗=1 훾퐺푗퐺푖푗 in equation 9), whereas ENET and LASSO incorporate only a GRS
220 term as the aggregated genetic main effects (훾퐺퐺푅푆푖 in equation 7).
221 We compared the abovementioned GRS tests with iSKAT (Lin et al., 2016) and ADABF
222 (Lin, Huang, et al., 2019). In iSKAT, the following model is considered:
[ ( )] ∑퐿 ∑퐿 223 푔 퐸 푌푖 = 훿0 + 푗=1 훿퐺푗퐺푖푗 + 훿퐸퐸푖 + 푗=1 훿퐼푛푡푗퐺푖푗퐸푖 + 휹푪′푿풊 , 푖 = 1, ⋯ , 푛, (10)
th ( ) 224 where 훿퐼푛푡푗 is the interaction effect between the j SNP and E. Assuming 훿퐼푛푡푗푠 푗 = 1, ⋯ , 퐿
225 follow a distribution with a mean of 0 and a variance of 휏, the null hypothesis of all 훿퐼푛푡푗푠 =
226 0 (푗 = 1, ⋯ , 퐿) can be reduced to 휏 = 0. The iSKAT is a score statistic for testing the variance
227 component, i.e., 퐻0: 휏 = 0 vs. 퐻1: 휏 > 0. The statistic can be referred to as Equation (6) in (Lin
228 et al., 2016). The iSKAT method is regarded as optimal in the class of variance component tests
229 (Chen et al., 2014; Lin et al., 2013). Therefore, we chose iSKAT as the representative of variance
230 component tests.
231 In ADABF, we consider the following model for the jth SNP (푗 = 1, ⋯ , 퐿):
[ ( )] 232 푔 퐸 푌푖 = 훿0 + 훿퐺푗 퐺푖푗 + 훿퐸퐸푖 + 훿퐼푛푡푗 퐺푖푗퐸푖 + 휹푪′푿풊 , 푖 = 1, ⋯ , 푛 . (11)
th 233 The SNP×E interaction is of interest, and therefore, 퐻0: 훿퐼푛푡푗 = 0 vs. 퐻1: 훿퐼푛푡푗 ≠ 0 for the j
234 SNP (푗 = 1, ⋯ , 퐿). A Bayes factor (BF) was calculated for each SNP×E, where 퐵퐹 =
235 푃푟(퐷푎푡푎|퐻1)⁄푃푟(퐷푎푡푎|퐻0). A larger BF indicates that the relative evidence in favor of 퐻1
236 (SNP×E interaction exists) is stronger. Because the number of SNPs exhibiting interactions with
237 E varies gene by gene, ADABF exhaustively searches for the evidence of G×E interaction by
238 considering the largest BF, combining the largest 2 BFs, combining the largest 3 BFs, …, to
10 239 aggregating all the L BFs in the gene. The significance of G×E interaction is then determined by
240 the efficient sequential resampling procedure (Liu et al., 2016). ADABF was selected for
241 comparison because it was recommended as a powerful and robust gene-based GxE test in a
242 recent study (Lin, Huang, et al., 2019). The iSKAT and ADABF methods do not test for GxE
243 through a GRS term. Therefore, these two methods do not make inference for the direction of
244 G×E.
245 Simulation study
246 To reflect the real LD structures of the human genome, we used the genotypes of 18,424
247 TWB subjects as our simulation material. Three genes (i.e., TNNT3, RFX3, and FTO) were drawn
248 for simulations, including 48, 95, and 242 SNPs, respectively. It is common to see multiple
249 trait-associated SNPs to be included in the same gene (Fawcett and Barroso 2010; Willer et al.,
250 2007). Therefore, we randomly specified 4 trait-associated SNPs in each simulation replicate. We
251 considered binary and continuous exposures, respectively. For binary exposures, E was randomly
252 sampled from 1 (exposed) or 0 (non-exposed), with 푃(퐸 = 1) = 0.2 and 푃(퐸 = 1) = 0.5,
253 respectively. For continuous exposures, E was randomly selected from the normal distribution
254 with a mean of 0 and a standard deviation of 0.5.
255 The continuous trait of the ith subject was simulated as follows:
∑4 ∑퐷 256 푌푖 = 푑=1 훽퐺푑퐺푖푑 + 훽퐸퐸푖 + 푑=1 훽퐼푛푡푑퐺푖푑 퐸푖 + 휀푖, (12)
th 257 where 훽퐺푑 is the SNP main effect of the d trait-associated SNP (푑 = 1, ⋯ ,4), 훽퐼푛푡푑 is the
258 effect size of interaction between the dth trait-associated SNP and E (푑 = 1, ⋯ , 퐷), D is the
259 number of trait-associated SNPs that also exhibit interactions with E (D = 4 or 2 in our
260 simulation), and 휀푖 is the random error term following the standard normal distribution.
261 The binary trait of the ith subject was simulated as follows:
11 ( ) 푃 푌푖=1 ∑4 ∑퐷 262 푙표푔 = 훽0 + 푑=1 훽퐺푑퐺푖푑 + 훽퐸퐸푖 + 푑=1 훽퐼푛푡푑퐺푖푑 퐸푖, (13) 1−푃(푌푖=1)
0.1 0.4 263 where the intercept 훽0 was 푙표푔( ⁄0.9) = −2.2 or 푙표푔( ⁄0.6) = −0.4. 푌푖 = 1 represents
th 264 that the i subject was diseased whereas 푌푖 = 0 indicates that he/she was non-diseased. This
265 setting corresponds to a disease prevalence of 10% or 40%. A disease prevalence of 40% is also a
266 reasonable setting for some complex diseases. For example, the worldwide prevalence of
267 hypertension among adults aged 25 years was ~40% (Abebe et al., 2015).
268 The magnitudes of SNP main effects, |훽퐺푑|s (푑 = 1, ⋯ ,4), were uniformly sampled from
269 0.04 to 0.08 for continuous traits or uniformly sampled from 푙표푔(1.05) to 푙표푔(1.15) for
270 binary traits. This simulation setting for binary trait (odds ratios uniformly sampled from 1.05 to
271 1.15) concurs with broad GWAS findings, where most odds ratios < 1.5 and many odds ratios <
272 1.2 (Baxter and Jordan 2012; Hodge and Greenberg 2016).
273 Unlike small effect sizes for SNPs, the effect size of E was assumed to be larger, because
274 some E is critical to traits (e.g., regular exercise and dietary habits are important to obesity
275 measures). The magnitude of E, |훽퐸|, was assigned to be 0.3 for continuous traits and
276 푙표푔(1.3) = 0.2624 for binary traits, respectively. When evaluating type I error rates, data have
277 to be generated from the null hypothesis of no 푆푁푃 × 퐸 interactions, and therefore we specified
278 all 훽퐼푛푡푑s = 0 (푑 = 1, ⋯ , 퐷). When assessing power, the magnitudes of 푆푁푃 × 퐸 interaction
279 effects, |훽퐼푛푡푑|s (푑 = 1, ⋯ , 퐷), were uniformly sampled from 0.04 to 0.08 for continuous traits
280 or uniformly sampled from 푙표푔(1.05) to 푙표푔(1.15) for binary traits. To not favor GRS-based
281 approaches that construct GRSs with SNPs marginal effects, the sampling of |훽퐼푛푡푑 |푠 (푑 =
282 1, ⋯ , 퐷) was independent of the sampling of |훽퐺푑|푠 (푑 = 1, ⋯ ,4). Power was evaluated under
283 14 simulation scenarios listed in Table 1, in which “+” indicates a positive effect and “−” means
12 284 a negative effect. As summarized by Table 1, we always assumed 4 trait-associated SNPs, but the
285 number of trait-associated SNPs that also exhibited interactions with E could be 2 or 4. This
286 setting mimics the common situation that some trait-associated SNPs may also present
287 interactions with E (Chen et al., 2014; Jonsson et al., 2009; Li et al., 2015).
288 Scenarios 1-7 describe that a larger E is associated with an increase in trait, whereas
289 scenarios 8-14 represent that a larger E is associated with a decrease in trait. Suppose that a
290 higher trait is linked to a less healthy situation, e.g., 푌푖 = 1 in binary traits. Scenarios 1, 3, 6, 8,
291 10, and 13 indicate that a larger E exacerbates the adverse effect of a candidate gene, whereas
292 scenarios 2, 4, 7, 9, 11, and 14 present that a larger E attenuates the adverse effect of a candidate
293 gene. Scenarios 5 and 12 are cross-over situations, representing that a larger E exacerbates the
294 adverse effect of 50% of trait-associated SNPs while attenuating the adverse effect of the
295 remaining 50% of trait-associated SNPs.
296 [Table 1 is approximately here]
297 Application to the Taiwan Biobank Data
298 The TWB aims to build a research database that integrates the genomic profiles and lifestyle
299 patterns of residents aged 30 to 70 years in Taiwan (Chen et al., 2016). Community-based
300 volunteers provided blood samples and a range of information via a face-to-face interview and
301 physical examination. This study included 20,287 TWB individuals and was approved by the
302 Research Ethics Committee of the National Taiwan University Hospital (NTUH-REC No.
303 201805050RINB). To remove cryptic relatedness, we used PLINK 1.9 (Purcell et al., 2007) to
304 calculate the genome-wide identity by descent (IBD) sharing coefficients between any two
305 subjects. Similar to many genetic studies (Lowe et al., 2009; Mok et al., 2014; Ombrello et al.,
306 2014), we excluded one subject from each pair with PI-HAT 0.125, where PI-HAT =
13 307 Probability(IBD = 2) + 0.5 Probability(IBD = 1). Through this step, relatives within the
308 third-degree of consanguinity were removed. Finally, 18,424 unrelated subjects (9,093 males and
309 9,331 females) were remained in the following analysis. Table 2 shows basic characteristics of
310 TWB participants stratified by sex.
311 [Table 2 is approximately here]
312 The majority of TWB subjects were of Han Chinese ancestry (Chen et al., 2016). The
313 Axiom Genome-Wide TWB genotyping array was designed for Han Chinese in Taiwan, which
314 was run on the Axiom Genome-Wide Array Plate System (Affymetrix, Santa Clara, CA, USA).
315 A total of 646,783 autosomal SNPs were genotyped in this TWB array. After removing 51,293
316 SNPs with genotyping rates < 95%, 6,095 SNPs with Hardy-Weinberg test P-values < 5.7 107
317 (WTCCC 2007), and 1,869 variants with minor allele frequencies (MAFs) < 1%, 587,526 SNPs
318 were used to construct ancestry PCs. Because variants with MAF < 1% have been excluded, no
319 rare variants were included in our following analyses. Removing variants with MAFs < 1% is a
320 commonly-used quality control step in genetic association studies, because the chances of errors
321 in genotype calling increase with decreasing MAFs (Coleman et al., 2016; Goldstein et al., 2012).
322 Results 323 Type I error rates
324 To evaluate type I error rates, continuous traits and binary traits were simulated according to
325 models (12) and (13), respectively. Scenarios 1 and 8 in Table 1 were simulated, but all 훽퐼푛푡푑s
326 (푑 = 1, ⋯ ,4) have to be set at 0 in order to evaluate type I error rates. The main effects of SNPs,
| | 327 |훽퐺푑|s (푑 = 1, ⋯ ,4), and the environmental factor, 훽퐸 , have been described in section
328 “Simulation study”. Based on 10,000 replications for each scenario, Figures 1 and S1 show that
329 all methods were valid in the sense that their type I error rates matched the nominal significance
14 330 level.
331 [Figure 1 is approximately here]
332
333 Power of 6 GxE methods
334 We compared the power of the 4 GRS-based tests and 2 GxE methods: iSKAT (Lin et al.,
335 2016) and ADABF (Lin, Huang, et al., 2019). The power of the 4 GRS-based tests is defined as
336 the probability of rejecting 퐻0: 훾퐼푛푡 = 0 (p-value < 0.05) and correctly specifying the sign of
337 훾퐼푛푡 (훾퐼푛푡 can be found from models 7 and 9). The iSKAT (Lin et al., 2016) and ADABF (Lin,
338 Huang, et al., 2019) methods can only provide a p-value for testing GxE, without an inference of
339 how E modifies the genetic effects. Therefore, their power is defined as the probability of
340 rejecting 퐻0: 훾퐼푛푡 = 0 (p-value < 0.05). Figure 2 presents the power based on 1,000 simulation
341 replications under each scenario, for continuous traits and 푃(퐸 = 1) = 0.2. If E exacerbates the
342 adverse effect of a gene, ENET and LASSO outperform the other methods (scenarios 1, 3, 6, 8,
343 10, and 13). If E attenuates the adverse effect of a gene, RIDGE is more powerful (scenarios 2, 4,
344 7, 9, 11, and 14). Moreover, ADABF was the optimal test under the cross-over scenario
345 (scenarios 5 and 12).
346 [Figure 2 is approximately here]
347 Among the 4 GRS-based tests, ENET, LASSO, and SBERIA first select SNPs marginally
348 associated with the phenotype. ENET and LASSO select SNPs according to the multivariate
349 ENET regression (equation 6) and multivariate LASSO regression (equation 5), respectively.
350 SBERIA selects SNPs based on regressions considering one SNP at a time (equation 8). The
351 performance of these three methods to detect G×E depends on their ability to find the true
352 trait-associated SNPs. Figures S2 and S3 summarize the sensitivity (SEN) and positive predictive
15 353 value (PPV) of the marginal-association filtering in ENET, LASSO, and SBERIA. As described
354 in equation (12) and Table 1, 4 trait-associated SNPs were randomly assigned in each simulation
355 replication. SEN is defined as the percentage of true positives among the 4 trait-associated SNPs,
356 whereas PPV is defined as the percentage of true positives among the total findings.
357 Because SBERIA takes a liberal p-value threshold of 0.1, in the filtering stage it usually
358 selects more SNPs than ENET and LASSO do. Therefore, as shown in Figures S2 and S3,
359 SBERIA generally has a higher SEN but a lower PPV, compared with ENET and LASSO. For
360 each method, SEN was much lower in attenuation scenarios than in exacerbation scenarios. This
361 means that pinpointing true trait-associated SNPs is more difficult in attenuation scenarios. In the
362 filtering stage (equations 5, 6, and 8), 퐺푖푑 × 퐸푖 cannot be included; therefore, a 훽퐼푛푡푑 in the
th 363 opposite direction to 훽퐺푑 will weaken the magnitude of the marginal effect of the d
364 trait-associated SNP. In contrast, a 훽퐼푛푡푑 in the same direction to 훽퐺푑 will strengthen the
365 magnitude of the marginal effect of the dth trait-associated SNP. Therefore, for each method, the
366 ability to pinpoint true trait-associated SNPs is inferior in attenuation scenarios than in
367 exacerbation scenarios (as shown in Figures S2 and S16 for continuous traits and binary traits,
368 respectively).
369 Because there is no SNP selection in RIDGE, true trait-associated SNPs are all reserved for
370 constructing GRS. Therefore, RIDGE is the optimal GRS-based test in attenuation scenarios
371 (Figure 2). In exacerbation scenarios, ENET and LASSO are the best 2 methods because of their
372 superior ability in finding trait-associated SNPs (Figures S2 and S16).
373 We then investigated the percentage of sign-misspecifications for each GRS-based method.
374 In the presence of G×E, we calculated the percentage of wrongly specifying the sign of 훾퐼푛푡 (in
375 models 7 or 9) among all rejections of 퐻0: 훾퐼푛푡 = 0 (p-value < 0.05). With 1,000 simulation
16 376 replications under each scenario, Figure 3 presents the percentages of sign-misspecifications, for
377 continuous traits and 푃(퐸 = 1) = 0.2. The true 훾퐼푛푡 is positive under scenarios 1, 3, 6, 8, 10,
378 and 13; negative under scenarios 2, 4, 7, 9, 11, and 14. The cross-over scenarios (5 and 12) were
379 not considered here, because the true sign of 훾퐼푛푡 was unclear when E = 1 (or a larger
380 continuous E) exacerbates the adverse effect of 50% of trait-associated SNPs but attenuates the
381 adverse effect of the remaining 50% of trait-associated SNPs.
382 [Figure 3 is approximately here]
383 Figure 3 shows that the signs of 훾퐼푛푡 were usually correctly specified except scenarios 4
384 and 11. SBERIA generally makes more mistakes in indicating the true direction for 훾퐼푛푡, because
385 it filters SNPs by considering only one SNP at a time (equation 8). Figures S4-S7 present the
386 power and percentages of sign-misspecifications in continuous-trait simulations, given
387 푃(퐸 = 1) = 0.5 and a continuous E, respectively. Each method under 푃(퐸 = 1) = 0.5 was
388 slightly more powerful than that under 푃(퐸 = 1) = 0.2, but the comparisons across methods
389 were similar to those shown in Figures 2-3.
390 The performance of each method for binary-trait simulations can be found in Figures
391 S8-S21. Regarding different prevalence values, each method was more powerful under
392 푃(푌 = 1) = 0.4 than under 푃(푌 = 1) = 0.1. Concerning different probabilities of being
393 exposed, each method was more powerful under 푃(퐸 = 1) = 0.5 than under 푃(퐸 = 1) = 0.2.
394 Nonetheless, the comparisons across methods were similar to those described for continuous
395 traits.
396 Regarding the 14 simulation scenarios listed in Table 1, only 2 SNP×E interactions (rather
397 than 4) were simulated in scenarios 4 and 11, and 훽퐼푛푡s were in the opposite direction to 훽퐺푠.
398 Therefore, detecting G×E and correctly specifying the sign for 훾퐼푛푡 were more challenging
17 399 under scenarios 4 and 11.
400 Regarding the computation time (Figures S22-S29), SBERIA is the fastest method, followed
401 by the 3 penalized regression methods: RIDGE, ENET, and LASSO. ADABF uses the sequential
402 resampling procedure (Liu et al., 2016), and therefore, it takes a longer time in the presence of
403 G×E. A recent study concluded that ADABF is a computationally feasible method in a GWAS
404 context (Lin, Huang, et al., 2019). This is because in a real GWAS usually very few genes can be
405 detected to interact with E. Therefore, a genome-wide analysis using ADABF takes a much
406 shorter time than the power evaluation performed here (power is always evaluated in the presence
407 of G×E). On average, the iSKAT method requires the longest time in most situations (Figures
408 S22-S29).
409 FTO x exercise interaction on 5 obesity measures
410 The FTO gene is obesity-associated and has been replicated by many studies (Fawcett and
411 Barroso 2010; Frayling et al., 2007; Scuteri et al., 2007). It spans from 53,737,875 to 54,148,379
412 base pairs on chromosome 16, according to the human genome GRCh37/hg19 assembly. Similar
413 to many gene-based tests (Alonso-Gonzalez et al., 2019; Lin, Huang, et al., 2019; Liu et al., 2010;
414 Wray et al., 2012), 50 kb in the 3’ and 5’ regions that might regulate a gene were also
415 incorporated in our analysis. Specifying a large boundary would be difficult to pinpoint the exact
416 gene interacting with E, whereas a small boundary may not fully capture the regulatory regions
417 (Liu et al., 2010). A total of 242 SNPs (all with MAF > 1%) were included in this chromosomal
418 region. Here, we used the 6 G×E tests to investigate whether the influence of FTO can be
419 modified by performing regular physical exercise. A total of 5 obesity measures were analyzed:
420 body mass index (BMI), body fat percentage (BFP), waist circumference (WC), hip
421 circumference (HC), and the waist-to-hip ratio (WHR).
18 422 Regular physical exercise was defined as engaging in 30 minutes of “exercise” 3 times a
423 week. “Exercise” indicated leisure-time activities such as jogging, yoga, mountain climbing, or
424 playing basketball. According to the TWB questionnaire, activities during work were not counted
425 in “exercise”. Among the 18,424 subjects, 7,652 (41.5%) reported performing regular exercise,
426 while 10,764 reported no regular exercise. A total of 8 subjects did not respond to this question.
427 Covariates adjusted in all models included sex, age (in years), educational attainment, drinking
428 status, smoking status, and the first 10 ancestry PCs.
429 [Table 3 is approximately here]
430 Table 3 presents the results of 6 methods. We may miss possibly important findings due to a
431 harsh penalty of multiple testing. Because this study focuses on G×E detection for candidate
432 genes, we set the significance level at 0.05. The results of RIDGE show that regular physical
433 exercise attenuates the adverse effect of the FTO gene on BMI, BFP, WC, and HC. The other
434 three GRS-based tests (ENET, LASSO, and SBERIA) provided significant results for three
435 obesity measures, respectively. All 훾̂퐼푛푡s were negative, indicating that regularly performing
436 exercise attenuates the adverse influence of FTO on obesity measures.
437 GRS-based tests are more powerful than iSKAT and ADABF because performing regular
438 exercise generally blunted the effects of the trait-increasing alleles in FTO. Take BMI-associated
439 SNPs as examples. A total of 12 out of the 242 SNPs reached the genome-wide significance
−8 440 (p-value < 5 × 10 ) when testing 퐻0: 훽푗 = 0 푣푠. 퐻1: 훽푗 ≠ 0 in the following model:
′ 441 퐸(푌푖) = 훽0 + 훽푗퐺푖푗 + 휷푪푿풊 , (14)
th 442 where 푌푖 is BMI, 퐺푖푗 is the number of minor alleles (0, 1, or 2) at the j SNP (j = 1, …, 242),
th ̂ 443 and 푿풊 is the vector of covariates of the i subject (푖 = 1, ⋯ , 18424). All 훽푗s of the 12
444 genome-wide significant SNPs were positive, representing that their minor alleles were
19 445 associated with increased BMIs.
446 When exercise (퐸푖 = 1 if yes; 퐸푖 = 0 if no) and the SNP×exercise interaction were
447 included in the 12 models, as follows:
′ 448 퐸(푌푖) = 훽0 + 훽푗퐺푖푗 + 훽퐸퐸푖 + 훽퐼푛푡푗퐺푖푗 × 퐸푖 + 휷푪푿풊 , 푗 = 1, ⋯ ,12, (15)
̂ ̂ 449 all 훽푗s were positive, and all 훽퐼푛푡푗s were negative (푗 = 1, ⋯ ,12). This indicated that the minor
450 alleles of the 12 SNPs were associated with increased BMIs, but their effects were blunted by
451 performing regular exercise. As mentioned above, a 훽퐼푛푡푗 in the opposite direction to 훽푗
̂ ̂ 452 weakens the magnitude of marginal effect of this SNP, and therefore 훽푗 from model (15) > 훽푗
453 from model (14). This is a situation similar to our simulation scenario 9 in Table 1, because
454 exercise is associated with a decrease in obesity measures. According to Figure 2 (scenario 9, 242
455 SNPs), RIDGE is the most powerful test. In real data, the FTO gene harbors more
456 BMI-associated SNPs than our simulation scenario 9, and these SNPs interact with E in the same
457 direction. Therefore, GRS-based tests are more powerful than iSKAT and ADABF.
458 According to RIDGE, each 1 sd increase in BMI-GRS was associated with a 0.1743 kg/m2
459 lower BMI in exercisers than in non-exercisers (p = 0.0009, Table 3). Each 1 sd increase in
460 BFP-GRS was associated with a 0.2661% lower BFP in exercisers than in non-exercisers (p =
461 0.0031). Each 1 sd increase in WC-GRS was associated with a 0.3854 cm lower WC in exercisers
462 than in non-exercisers (p = 0.0052). Each 1 sd increase in HC-GRS was associated with a 0.3868
463 cm lower HC in exercisers than in non-exercisers (p = 0.0001). As shown by Figure 4, except
464 WHR, GRS effect on each obesity measure was smaller in exercisers than in non-exercisers. For
465 each obesity measure, 훾̂퐼푛푡 in Table 3 is approximately equal to the length of blue bar – the
466 length of red bar in Figure 4. In the whole study population, each 1 sd increase in BMI-GRS was
467 associated with a 0.2420 kg/m2 (the length of orange bar in Fig. 3A) higher BMI (P = 1.1 ×
20 −20 468 10 ). This association was stronger in non-exercisers than in exercisers (PInt = 0.0009, Table 3).
469 In non-exercisers, each 1 sd increase in BMI-GRS was associated with a 0.3136 kg/m2 (the
470 length of red bar in Fig. 3A) higher BMI (P = 3.4 × 10−18); in exercisers, each 1 sd increase in
471 BMI-GRS was associated with a 0.1382 kg/m2 (the length of blue bar in Fig. 3A) higher BMI (P
472 = 1.4 × 10−4).
473 [Figure 4 is approximately here]
474 Performing regular exercises is associated with an attenuation of the adverse influence of the
475 FTO gene on both WC and HC, but not on WHR because it is a ratio of WC to HC. This negative
476 result for WHR is in line with the result from polygenic analyses (i.e., aggregating information of
477 multiple nearly independent SNPs across the genome) (Lin, Chan, et al., 2019).
478 FGF5 x WHR interaction on blood pressure levels
479 In addition to binary exposures, we also provide an example for continuous exposures. The
480 FGF5 gene is associated with blood pressure levels in Han Chinese (Lin, Huang, et al., 2019; Liu
481 et al., 2011). FGF5 spans from 81,187,742 to 81,212,171 base pairs on chromosome 4, according
482 to the human genome GRCh37/hg19 assembly. Similar to many gene-based tests (Liu et al.,
483 2010), our analysis region also included 50 kb in the 3’ and 5’ regions that might regulate the
484 gene. A total of 38 SNPs (all with MAF > 1%) were included in this chromosomal region. It has
485 been known that central obesity is a risk factor for hypertension (Parrinello et al., 1996).
486 Therefore, we used the 6 G×E tests to investigate whether the influence of FGF5 can be
487 modified by an indicator of central obesity, WHR. Covariates adjusted in all models included sex,
488 age (in years), drinking status, smoking status, and the first 10 ancestry PCs. As described above,
489 a total of 18,424 unrelated TWB subjects were included in our analysis, where 9,093 were males
490 and 9,331 were females.
21 491 [Table 4 is approximately here]
492 Table 4 presents the results of 6 methods. All 6 tests suggested the significance of
493 FGF5×WHR interaction on diastolic blood pressure (DBP) and systolic blood pressure (SBP)
494 (푃퐼푛푡 < 0.05). Positive 훾̂퐼푛푡s from GRS-based tests represent that a higher WHR acerbates the
495 adverse influence of FGF5.
496 The above two examples demonstrate using GRS-based methods to infer whether E
497 attenuates or exacerbates the adverse influence of a candidate gene (FTO and FGF5,
498 respectively).
499 Discussion 500 Detecting GxE has been an important but challenging issue. Although set-based GxE tests
501 have been evaluated in a genome-wide context, very few genes have been found to interact with
0.05 502 some exposures at the genome-wide significance level (i.e., p < = 2.5 × 10−6. Because 20000
503 there are ~20,000 genes across the genome, 2.5 × 10−6 is the commonly used significance level
504 in genome-wide gene-based analyses) (Chen et al., 2014; Lin, Huang, et al., 2019). Searching for
505 evidence of GxE for candidate genes may still be a more feasible strategy.
506 It is common to see a GRS that aggregates information of multiple nearly independent SNPs
507 across the genome (Ahmad et al., 2013; Lin, Chan, et al., 2019; Lin et al., 2020; Rask-Andersen
508 et al., 2017). However, there have been few applications of using GRS in gene-based GxE tests.
509 In this work, we evaluate the performance of GRS gene-based GxE approach, with simulations
510 and real applications. GRS-based tests can outperform other methods if interactions tend to go in
511 the same direction (Aschard 2016). The filtering stage of SBERIA overlooks LD among SNPs
512 because it considers L SNPs in L respective regressions (equation 8). RIDGE has the advantage
513 of accommodating LD among SNPs and providing regression coefficients that lead to minimum
22 514 MSE. Although RIDGE has been used to address LD in genetic association analysis (Malo et al.,
515 2008), our study is the first attempt to use the ridge regression to construct a GRS for GxE
516 analyses. ENET and LASSO can not only accommodate LD among SNPs, but they also select
517 SNPs by shrinking some regression coefficients to 0.
518 Although ENET has been suggested as a powerful GxE test in pathway analyses (Huls,
519 Ickstadt, et al., 2017; Huls, Kramer, et al., 2017), in this study, we showed that its performance to
520 find trait-associated SNPs can be compromised if E attenuates the adverse effect of a gene
521 (simulation scenarios 2, 4, 7, 9, 11, and 14). As a result, RIDGE is recommended if E attenuates
522 the adverse effects of most SNPs in a gene, as shown in the application of FTO×exercise
523 interaction on obesity measures (Table 3). In contrast, if E exacerbates the adverse effects of most
524 SNPs in a gene, ENET and LASSO will be more powerful, as shown in the application of
525 FGF5×WHR interaction on SBP (Table 4).
526 In this work, we described how to use GRS approaches to infer whether E attenuates or
527 exacerbates the adverse effect of a gene. GRS approaches can not only provide a p-value for GxE
528 but also infer how E interacts with the gene. The signs of 훾퐼푛푡 were usually correctly specified
529 except scenarios 4 and 11, where only 2 SNP×E interactions were specified and their interaction
530 effects were in the opposite direction to the SNP main effects. SBERIA usually makes more
531 mistakes because its filtering stage overlooks LD among SNPs by considering L SNPs in L
532 respective regressions (equation 8).
533 In the cross-over situations (simulation scenarios 5 and 12), where E exacerbates the adverse
534 effects of some SNPs but attenuates the adverse effects of others, GRS approaches were
535 underpowered and ADABF became the most useful. None of the 6 methods could outperform the
536 others across all situations. In this work, we performed simulations to explore the relative
23 537 performances of these 6 tests in detecting GxE and correctly indicating the interaction direction.
538 To show the utility of GRS-based approaches, we provided an example for binary exposure
539 and an example for continuous exposure: (1) FTO x exercise interaction on 5 obesity measures
540 (Table 3); (2) FGF5 x WHR interaction on blood pressure levels (Table 4). The 훾퐼푛푡s in Table 3
541 were consistently negative, representing that performing regular exercise attenuates the adverse
542 influence of the FTO gene on 4 obesity measures. Moreover, 훾퐼푛푡s in Table 4 were consistently
543 positive, indicating that a higher WHR exacerbates the adverse effect of the FGF5 gene on blood
544 pressure levels.
545 This work provides contributions to an important issue: identify whether E attenuates or
546 exacerbates the adverse influence of a candidate gene. Genes exhibiting interactions with E are
547 usually difficult to detect and replicate (McAllister et al., 2017), especially at the genome-wide
548 significance level (2.5 × 10−6). When testing for many genes simultaneously, even true positive
549 GxEs would have difficulty in standing out among all the noise (Lin and Lee 2010). Therefore,
550 our discussions here are restricted to candidate genes. As TWB keeps recruiting more subjects, in
551 the future we look forward to performing genome-wide GxE analyses on a larger TWB cohort.
552 Author contributions 553 W.-Y.L. developed the methods and the analysis tools, designed and performed the simulation
554 studies, analyzed the TWB data, and wrote the manuscript. Y.-S.L. contributed to the
555 programming for the simulations and data analyses. C.-C.C., Y.-L.L., S.-J.T., and P.-H.K.
556 contributed to the writing of the manuscript. P.-H.K., Y.-L.L., and S.-J.T. provided the TWB data.
557 All authors reviewed the manuscript.
558 Acknowledgments 559 We would like to thank the reviewers for their insightful and constructive comments, and Mr.
24 560 Ya-Chin Lee for assisting with the acquisition of the TWB data. This study was supported by the
561 Ministry of Science and Technology of Taiwan (MOST, grant number MOST
562 107-2314-B-002-195-MY3 to Wan-Yu Lin). The acquisition of TWB data was supported by a
563 MOST grant (grant number MOST 102-2314-B-002-117-MY3 to Po-Hsiu Kuo) and a
564 collaboration grant (National Taiwan University Hospital: grant number UN106-050 to
565 Shyr-Chyr Chen and Po-Hsiu Kuo).
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28 701 Figure Legends 702
703 Figure 1 Empirical type I error rates under the nominal significance level of 0.05 (continuous
704 trait)
705
706 Figure 2 Power given a significance level of 0.05, for continuous traits and 푃(퐸 = 1) = 0.2
707
708 Figure 3 Percentages of sign-misspecifications for 훾퐼푛푡, under continuous traits and
709 푃(퐸 = 1) = 0.2
710
711 Figure 4 The effect of GRS on the 5 obesity measures
712 The regression model was built as 푂푏푒푠푖푡푦 푚푒푎푠푢푟푒 = 훽0 + 훽퐺푅푆퐺푅푆 + 휷푪푪풐풗풂풓풊풂풕풆풔 + 휀,
713 where GRS was obtained by RIDGE. Three regression models were built for each obesity
714 measure, one for all 18,424 subjects, one for 7,652 exercisers, and one for 10,764 non-exercisers.
̂ 715 The bars represent 훽퐺푅푆 on an obesity measure, and the black segments mark the 95%
716 confidence intervals, i.e.,
̂ ̂ ̂ ̂ 717 [훽퐺푅푆 − 1.96 × standard error of 훽퐺푅푆, 훽퐺푅푆 + 1.96 × standard error of 훽퐺푅푆]. Covariates
718 adjusted in all models included sex, age (in years), educational attainment, drinking status,
719 smoking status, and the first 10 ancestry PCs.
720
721
722
723
29 724 Tables 725
Scenario E 휷푮ퟏ 휷푮ퟐ 휷푮ퟑ 휷푮ퟒ 휷푰풏풕ퟏ 휷푰풏풕ퟐ 휷푰풏풕ퟑ 휷푰풏풕ퟒ 1 + + + + + + + + + Exacerbation 2 + + + + + − − − − Attenuation 3 + + + + + + + 0 0 Exacerbation 4 + + + + + − − 0 0 Attenuation 5 + + + + + + + − − cross-over 6 + + + − − + + − − Exacerbation 7 + + + − − − − + + Attenuation 8 − + + + + + + + + Exacerbation 9 − + + + + − − − − Attenuation 10 − + + + + + + 0 0 Exacerbation 11 − + + + + − − 0 0 Attenuation 12 − + + + + + + − − cross-over 13 − + + − − + + − − Exacerbation 14 − + + − − − − + + Attenuation 726
727 Table 1 The 14 simulation scenarios for power comparison, where “exacerbation” and
728 “attenuation” mean that E = 1 (or a larger continuous E) exacerbates or attenuates the adverse
729 effect of a candidate gene, respectively.
30 Overall Males Females
Total, n (%) 18,424 9,093 9,331
Age (years), mean (s.d.) 48.9 (11.0) 49.0 (11.0) 48.9 (10.9)
Smoking, n (%) 2,134 (11.6) 1,882 (20.7) 252 (2.7)
Drinking, n (%) 1,345 (7.3) 1,178 (13.0) 167 (1.8)
Regular exercise, n (%) 7,652 (41.5) 3,896 (42.8) 3,756 (40.3)
Educational attainment, 5.46 (0.99) 5.62 (0.92) 5.29 (1.02) mean (s.d.) BMI (kg/m2), mean (s.d.) 24.31 (3.66) 25.2 (3.4) 23.5 (3.7)
Body fat %, mean (s.d.) 27.29 (7.38) 22.9 (5.5) 31.5 (6.5)
Waist circumference (cm), 83.93 (10.03) 87.4 (9.1) 80.5 (9.7) mean (s.d.) Hip circumference (cm), 96.34 (6.90) 97.6 (6.5) 95.2 (7.0) mean (s.d.) Waist-hip ratio, mean (s.d.) 0.87 (0.068) 0.90 (0.06) 0.85 (0.07)
Diastolic blood pressure 73.11 (11.10) 76.9 (10.6) 69.4 (10.3) (mmHg), mean (s.d.) Systolic blood pressure 117.62 (17.37) 121.9 (16.1) 113.5 (17.6) (mmHg), mean (s.d.) 730
731 Table 2. Basic characteristics of TWB participants stratified by sex
732
733
31 Trait RIDGE ENET LASSO SBERIA iSKAT ADABF
훾̂퐼푛푡 -0.1743 -0.0821 -0.0964 -0.1482 BMI (kg/m2) PInt 0.0009 0.1192 0.0671 0.0067 0.2043 0.1700
훾̂퐼푛푡 -0.2661 -0.2069 -0.2081 -0.2259 Body fat % PInt 0.0031 0.0212 0.0205 0.0160 0.2430 0.2200
Waist circumference 훾̂퐼푛푡 -0.3854 -0.3719 -0.3760 -0.2786
(cm) PInt 0.0052 0.0069 0.0063 0.0512 0.5369 0.3700
Hip circumference 훾̂퐼푛푡 -0.3868 -0.3286 -0.3291 -0.2902
(cm) PInt 0.0001 0.0011 0.0011 0.0055 0.5061 0.3300
훾̂퐼푛푡 -0.000116 -0.000775 -0.000374 -0.000314 Waist-to-hip ratio PInt 0.8951 0.3773 0.6699 0.7308 0.7994 0.3100
734
735 Table 3 FTO x exercise interaction on 5 obesity measures. Significant results with PInt < 0.05
736 are highlighted. Negative 훾̂퐼푛푡s indicate that regular physical exercise attenuates the adverse
737 influence of FTO on obesity measures.
32 Trait RIDGE ENET LASSO SBERIA iSKAT ADABF
훾̂퐼푛푡 0.2419 0.1980 0.2141 0.2378 DBP (mmHg) PInt 0.0013 0.0082 0.0042 0.0014 0.0154 0.0096
훾̂퐼푛푡 0.3396 0.3548 0.3551 0.3261 SBP (mmHg) PInt 0.0027 0.0017 0.0017 0.0039 0.0482 0.0480
738
739 Table 4 FGF5 x WHR interaction on blood pressure levels. Significant results with PInt < 0.05
740 are highlighted. Positive 훾̂퐼푛푡s indicate that a higher WHR exacerbates the adverse influence of
741 FGF5 on blood pressure levels.
742
33 743 Supplementary Material 744 Figure S1 Empirical type I error rates under the nominal significance level of 0.05 (binary trait)
745 Figure S2 The sensitivity of the marginal-association filtering in ENET, LASSO, and SBERIA,
746 for continuous traits and 푃(퐸 = 1) = 0.2
747 Figure S3 The positive predictive value of the marginal-association filtering in ENET, LASSO,
748 and SBERIA, for continuous traits and 푃(퐸 = 1) = 0.2
749 Figure S4 Power given a significance level of 0.05, for continuous traits and 푃(퐸 = 1) = 0.5
750 Figure S5 Percentages of sign-misspecifications for 훾퐼푛푡, under continuous traits and
751 푃(퐸 = 1) = 0.5
752 Figure S6 Power given a significance level of 0.05, for continuous traits and a continuous E
753 Figure S7 Percentages of sign-misspecifications for 훾퐼푛푡, under continuous traits and a
754 continuous E
755 Figure S8 Power given a significance level of 0.05, for binary traits, 푃(푌 = 1) = 0.1, and
756 푃(퐸 = 1) = 0.2
757 Figure S9 Percentages of sign-misspecifications for 훾퐼푛푡, under binary traits, 푃(푌 = 1) = 0.1,
758 and 푃(퐸 = 1) = 0.2
759 Figure S10 Power given a significance level of 0.05, for binary traits, 푃(푌 = 1) = 0.4, and
760 푃(퐸 = 1) = 0.2
761 Figure S11 Percentages of sign-misspecifications for 훾퐼푛푡, under binary traits, 푃(푌 = 1) =
762 0.4, and 푃(퐸 = 1) = 0.2
763 Figure S12 Power given a significance level of 0.05, for binary traits, 푃(푌 = 1) = 0.1, and
764 푃(퐸 = 1) = 0.5
765 Figure S13 Percentages of sign-misspecifications for 훾퐼푛푡, under binary traits, 푃(푌 = 1) =
34 766 0.1, and 푃(퐸 = 1) = 0.5
767 Figure S14 Power given a significance level of 0.05, for binary traits, 푃(푌 = 1) = 0.4, and
768 푃(퐸 = 1) = 0.5
769 Figure S15 Percentages of sign-misspecifications for 훾퐼푛푡, under binary traits, 푃(푌 = 1) =
770 0.4, and 푃(퐸 = 1) = 0.5
771 Figure S16 The sensitivity of the marginal-association filtering in ENET, LASSO, and
772 SBERIA, for binary traits, 푃(푌 = 1) = 0.4, and 푃(퐸 = 1) = 0.5
773 Figure S17 The positive predictive value of the marginal-association filtering in ENET,
774 LASSO, and SBERIA, for binary traits, 푃(푌 = 1) = 0.4, and 푃(퐸 = 1) = 0.5
775 Figure S18 Power given a significance level of 0.05, for binary traits, 푃(푌 = 1) = 0.1, and a
776 continuous E
777 Figure S19 Percentages of sign-misspecifications for 훾퐼푛푡, under binary traits, 푃(푌 = 1) =
778 0.1, and a continuous E
779 Figure S20 Power given a significance level of 0.05, for binary traits, 푃(푌 = 1) = 0.4, and a
780 continuous E
781 Figure S21 Percentages of sign-misspecifications for 훾퐼푛푡, under binary traits, 푃(푌 = 1) =
782 0.4, and a continuous E
783 Figure S22 Average time spent (in seconds) for each simulation replication, under 퐻0, for
784 continuous traits.
785 Figure S23 Average time spent (in seconds) for each simulation replication, under 퐻0, for
786 binary traits.
787 Figure S24 Average time spent (in seconds) for each simulation replication, under 퐻1, for
788 continuous traits and 푃(퐸 = 1) = 0.2
35 789 Figure S25 Average time spent (in seconds) for each simulation replication, under 퐻1, for
790 continuous traits and 푃(퐸 = 1) = 0.5
791 Figure S26 Average time spent (in seconds) for each simulation replication, under 퐻1, for
792 binary traits, 푃(푌 = 1) = 0.1, and 푃(퐸 = 1) = 0.2
793 Figure S27 Average time spent (in seconds) for each simulation replication, under 퐻1, for
794 binary traits, 푃(푌 = 1) = 0.4, and 푃(퐸 = 1) = 0.2
795 Figure S28 Average time spent (in seconds) for each simulation replication, under 퐻1, for
796 binary traits, 푃(푌 = 1) = 0.1, and 푃(퐸 = 1) = 0.5
797 Figure S29 Average time spent (in seconds) for each simulation replication, under 퐻1, for
798 binary traits, 푃(푌 = 1) = 0.4, and 푃(퐸 = 1) = 0.5
36 799 800 801 Figure 1
37 802 803 804 Figure 2
38 805 806 807 Figure 3
39 808 809 Figure 4
40