Joint genetic analysis using variant sets reveals polygenic gene-context interactions
[['Understanding genetic interactions with external context ( GxC ) , including environment , is a major challenge in quantitative genetics .', 'Linear mixed models ( LMMs ) have emerged as the framework of choice for many genetic analyses , mainly because the random effect component in this class of models provides robust control for population structure [1 , 2] and other confounding factors [3–5] .', 'More recently , random-effect models have also been shown to be effective to test for polygenic effects from multiple causal variants that are in linkage [6–9] ( variant sets ) .', 'Additionally , multivariate formulations of LMMs have been developed to test for genetic effects across multiple correlated traits , both in single-variant analyses [10 , 11] and more recently for joint tests using variant sets [12] .', 'However , these existing multivariate LMMs have primarily been designed to increase the statistical power for detecting association signals , whereas methods to test for interactions are only beginning to emerge [10 , 13] .', 'Classical single-variant models for GxC use fixed effects to test for differential effect sizes of individual variants between contexts , either using an ANOVA [14–16] or LMMs [10 , 17] .', 'The main advantages of set-based tests compared to single-variant models are twofold .', 'First , set tests reduce the effective number of tests and can account for effects due to multiple causal variants , thus increasing power for detecting polygenic effects [7 , 8 , 12 , 18] .', 'Second , we here show that joint tests across multiple contexts and sets of variants allow for characterizing the local architecture of polygenic-GxC interactions .', 'One way to generalize single-variant interaction tests to variant sets is using a model that assumes that context differences cause the same fold-differences in effect size across all genetic variants , such that all genetic effects in one context are proportional to the effects in a second context; a criterion that has also been considered to assess co-localization of multiple traits [19] ( Fig 1A , middle ) .', 'We denote this class of interactions rescaling-GxC .', 'More generally , however , there may also be differences in the configuration of causal variants between contexts ( Fig 1A , right ) , such that not all genetic variants show the same fold-difference between contexts , as some become more prominent in particular contexts and others less so .', 'We denote these complex interactions heterogeneity-GxC .', 'These two classes of interactions have different functional implications–the former suggest no difference in causal variants between contexts , and the latter suggest otherwise .', 'Distinguishing between them is only possible using multi-variant models such as set tests , and is important for identifying different potential causal variants in different contexts .', 'We here propose a multivariate LMM to test for interactions test between Sets of genetic variants and categorical contexts ( iSet ) and to distinguish between rescaling-GxC and heterogeneity-GxC .', 'We find that iSet yields increased power for identifying interactions and uniquely is able to robustly differentiate between rescaling-GxC and heterogeneity-GxC .', 'We first validate iSet using simulations before applying the model to test for gene-by-sex interactions in blood lipid levels [20] as well as gene-by-environment interactions in an expression quantitative trait loci ( eQTL ) study [21] .', 'We identify up to 20% of the stimulus-specific eQTLs as cases of heterogeneity-GxC , suggesting that context-specific causal variants are common .'], ['iSet generalizes previous multi-trait set tests [12] , while considering the same trait measured in two ( environmental ) contexts .', 'For a fully observed design , where the trait is measured in N individuals and each context , the phenotype matrix Y is modeled as the sum of a genetic effect from a set component and residual noise:', 'Y=FB⏟fixedeffects+Us⏟setcomponent+ψ⏟noise .', 'Here , F and B denote the design and the effect size matrices of additional fixed effect covariates and Us and ψ are random effects that follow matrix-variate normal distributions:', 'Us~MVN ( 0 , Cs , Rs ) , ψ~MVN ( 0 , Cn , IN ) ,', 'where Rs corresponds to a local realized relatedness matrix [22] of the set of interest s , and IN denotes a diagonal covariance , which corresponds to independent and Identically distributed residuals .', 'The trait-context covariance matrices Cs and Cn model correlations between contexts due to the set component ( Cs ) , and residual noise ( Cn ) .', 'A key insight derived here is that different assumptions on the structure of the trait-context covariance CS correspond to alternative genetic architectures that can be explained by a polygenic model ( Fig 1B , Methods ) .', 'Persistent genetic effects across contexts ( no GxC ) can be modeled using an LMM with a constant block covariance ( Fig 1B ) ; rescaling GxC , where effect sizes in different contexts are proportional to each other , can be captured by a trait-covariance with rank one .', 'Note that genetic effects that act only in one context are a special case of this model and corresponds to a zero-rescaling coefficient .', 'Finally , the most general architectures with different relative effect sizes between contexts ( heterogeneity-GxC ) can be captured by an LMM with a full-rank trait-context covariance ( Methods ) .', 'By comparing LMMs with these alternative covariance structures , it is possible to define set tests for general associations ( mtSet ) , which identifies both persistent and context-specific effects , a test for genetic interactions , both with or without changes in the configuration of causal variants ( iSet ) , and finally a test for heterogeneity-GxC effects ( iSet-het ) , which is specific to differences between contexts that cannot be explained by rescaling ( Fig 1B ) .', 'These multivariate LMMs can be fit using principles that were previously derived for multivariate set tests [12] , and hence , provided the computations are suitable parallelized ( Methods ) , iSet can be applied to large cohorts with tens of thousands individuals ( S1 Fig ) .', 'Permutation schemes are not well defined for interaction models [23] , so we use a parametric bootstrap procedure [23] to estimate P values .', 'An important advantage compared to previous interaction tests [13 , 24–28] ( Methods ) , is that iSet can be applied both to study designs where all individuals have been phenotyped in each context and when stratifying populations into distinct subgroups using a context variable ( S2 Fig ) .', 'iSet also provides control for population structure , either using principal components that are included as fixed covariates , or using an additional random effect term ( Methods ) .', 'Finally , iSet can also be used to estimate the total phenotypic variance explained by variant sets and the relative proportions captured by persistent , rescaling-GxC and heterogeneity-GxC effects ( Methods ) .', 'To illustrate the polygenic interactions that can be detected using iSet , we first considered a basic simulated example ( Fig 1C ) .', 'We simulated genetic effects for one quantitative trait in two contexts , considering polygenic effects at three distinct loci ( Methods ) : a region with persistent genetic effects , a region with rescaling-GxC and a region with heterogeneity-GxC effects .', 'We tested consecutive regions ( 30kb region , 15kb step ) using the three tests provided by our model ( mtSet , iSet , iSet-het ) , finding that by combining these results , it was indeed possible to resolve the architecture of each of the simulated regions ( Fig 1C and 1D ) .', 'In particular , this example illustrates that , unlike single-variant tests , iSet-het can be used to discern heterogeneity-GxC effects specifically .', 'Next , we used simulations based on genotypes from the 1000 Genomes project [29] to assess the statistical calibration and power of iSet .', 'We generated a population of 1 , 000 individuals based on genotype data from European populations , initially simulating one quantitative trait measured in two distinct contexts in all individuals ( Methods ) .', 'First , we considered data with simulated persistent polygenic effects , confirming that both iSet and iSet-het are calibrated when no interaction effects are simulated ( Fig 2A , S1 Table ) .', 'Analogously , we also confirmed that iSet-het is calibrated when only rescaling-GxC effects are considered ( S3 Fig ) , and we assessed the robustness of iSet to different types of model misspecification ( S4 Fig , S1 Table ) .', 'We compared iSet to single-variant interaction tests [10] ( mtLMM-int ) ( Methods ) , considering a wide range of different settings ( S2 Table , Methods ) .', 'Because single-variant methods perform one test for each variant in the set ( S5 Fig ) , we adjusted for multiple testing using one of two approaches:', 'i ) conservative Bonferroni adjustment ( Bonferroni ) or', 'ii ) a recently proposed method that estimates the effective number of independent tests based on the local structure of linkage disequilibrium ( LD ) [30] ( eigenMT ) .', 'Note that existing set-based interaction tests cannot be applied to complete designs with repeat measurements and hence were not considered ( Methods , S1 Text ) ; see below and Fig 5 for additional experiments where these methods were used .', 'As expected , the power advantages of iSet compared to single-variant models were largest when multiple causal variants were simulated ( Fig 2B , for constant total genetic variance , Methods ) .', 'However , iSet was better powered than mtLMM-int even for a single causal variant .', 'Identical simulations based on synthetic independent genotypes ( S6 Fig ) revealed that this effect is predominantly due to local LD and advantages due the reduced number of total tests .', 'We also considered the impact of different proportionality factors of genetic effects between contexts .', 'All models were best powered to detect GxC for negative proportionality factors ( opposite effects ) , or when the proportionality factor was close to zero ( context-specific effects ) ( Fig 2C ) .', 'Next , we simulated traits with context-specific causal variants ( heterogeneity-GxC ) .', 'Heterogeneity-GxC is detectable when there is a change in the local causal configuration , which corresponds to the absolute correlation of local genetic effects between contexts ( r ) smaller than 1; the greater the heterogeneity GxC effects , the smaller the absolute correlation .', 'Presence of GxC effects under tightly correlated genetic effects ( r ≈ ±1 ) cannot be distinguished from rescaling-GxC .', 'To simulate these different settings , we randomly selected two causal variants in each context and varied the extent of correlations of the genetic effect between contexts ( Fig 2D ) .', 'When using iSet-het for detecting heterogeneity-GxC effects , the model was best powered when there is a moderate to large change in causal configuration , corresponding to low correlated genetic effects ( >70% power for r2 < 0 . 16 , Fig 2D ) .', 'We also considered additional settings with larger numbers of causal variants ( S8 Fig ) , and we assessed the accuracy of iSet-het to classify interaction effects into heterogeneity-GxC or rescaling-GxC effects ( S7 Fig , Methods ) .', 'Taken together , these results confirm that iSet-het is a robust test for heterogeneity-GxC .', 'We also investigated the proportion of local genetic variance that can be explained by models with persistent , rescaling-GxC and heterogeneity-GxC for the corresponding simulations ( Fig 2C and 2D , Methods ) .', 'The persistent effect model explained large proportions of the simulated genetic variance , even in the presence of positively correlated GxC , but could not capture variance due to GxC effects with negative rescaling ( Fig 2C and 2D ) .', 'An LMM that models rescaling-GxC did account for negative and positive rescaling , and captured some of the heterogeneity-GxC effects ( Fig 2D ) .', 'Finally , variance contributions that were exclusively captured by a heterogeneity-GxC model were largest for uncorrelated context-specific genetic effects , the same regime where the corresponding test is best powered ( Fig 2D ) .', 'We also confirmed that the most flexible heterogeneity-GxC model yields unbiased estimates of the total genetic variance in genomic regions , whereas other models were biased for some simulated architectures ( S9 Fig ) .', 'Finally , we considered simulations where we varied both the size of the testing region and the simulated causal region , using a sliding window analysis ( S10 Fig , Methods ) .', 'Overall , iSet was markedly robust to the window size , and was best powered when the sizes of the testing region approached the size of the simulated causal region , which is in line with previous findings for set-based association testing [12] .', 'We also observed that iSet-het is best powered for small causal regions ( up to 100kb ) , and the power for detecting heterogeneity-GxC deteriorated when analyzing larger regions .', 'We next applied iSet to test for stimulus-specific genetic effects in a monocyte stimulus eQTL study [21] .', 'We considered gene expression profiles for 228 individuals in four stimulus contexts: naive state ( no stimulation ) , stimulation with interferon-γ for 24 hours ( IFN ) , and stimulation with lipopolysaccharide ( LPS ) for two and 24 hours .', 'We applied iSet to test for pairwise interaction effects , considering the naive monocyte state and each stimulus condition in turn , performing a single test using proximal cis acting variants ( plus or minus 50kb from the transcription start site; Methods ) .', 'After quality control , we considered 12 , 677 probes and tested for cis associations ( mtSet ) , GxC interactions ( iSet ) and for heterogeneity-GxC effects ( iSet-het ) .', 'For comparison , we also considered a conventional multi-trait LMM [10] and tested for associations and interactions in the same genomic regions , using eigenMT [30] to adjust for multiple testing ( Methods ) .', 'Although there was substantial overlap of the probes and stimulus conditions for which different methods identified significant interactions ( Fig 3B ) , iSet was better powered ( 32 . 7% power increase; 5 , 068 versus 3 , 818 probes and stimuli with an interaction; FDR<5% , Fig 3A , S11 and S12 Fig , S4 Table ) .', 'Additionally , iSet-het identified 1 , 135 probes and stimulus contexts with significant heterogeneity-GxC effects ( Fig 3A and 3B ) .', 'This shows that a substantial proportion of stimulus-specific eQTLs are associated differences in the configuration of causal variants , suggesting context-specific regulatory architectures .', 'Although on average the proportion of variance explained by GxC tended to be smaller than for persistent effects ( median 3 . 7% for GxC versus median 9 . 5% for persistent effects , for probes with significant GxC , Fig 3C ) , GxC was the driving genetic source of variation for 11 . 8% of the significant cis eQTLs ( Fig 3D; defined as explaining 50% or more of the cis genetic variance ) .', 'Consistent with previous reports [31 , 32] , we observed that genes with large relative GxC effects were associated with weak overall cis effects , whereas eQTLs with large effect sizes tended to be persistent across stimuli ( Fig 3D ) .', 'To better understand the mechanisms that underlie genes with detected heterogeneity-GxC effects , we used an LMM with step-wise selection [33] , identifying 15 , 756 , 2 , 690 and 457 eQTLs ( across all probes and contexts ) with a single significant association , significant secondary and significant tertiary associations respectively ( FDR < 5% , Methods , S4 Table ) .', 'Probes with significant heterogeneity-GxC were more likely to harbor multiple independent associations ( Fig 4A ) , confirming that heterogeneity-GxC eQTLs have complex genetic architectures .', 'When overlaying heterogeneity GxC eQTLs detected using iSet-het with the results obtained from the single-variant step-wise LMM , we could attribute 46 . 2% of the heterogeneity-GxC effects ( 524 out of 1 , 135 ) to context-specific lead variants ( defined using r2<0 . 2 , FDR<5% , Fig 4B and 4C , Methods ) .', 'For an additional 14 . 6% of the heterogeneity eQTLs ( 166/1 , 135 ) the lead variants from a single-variant analysis were in high LD ( r2>0 . 8 ) , with context-specific secondary effects ( Fig 4B and 4D ) .', 'The remaining 445 heterogeneity eQTLs ( 39 . 2% ) could not be annotated using single-variant models .', 'One reason why heterogeneity GxC effects cannot be annotated using a single-variant model are differences in power .', 'Indeed , for 22 . 2% of the heterogeneity-GxC cases without a single-variant interpretation ( 99/445 ) , the single-variant LMM did not yield a significant effect in either of the two contexts ( S13A Fig ) .', 'For an additional 58 . 2% of the unannotated heterogeneity GxC effects ( 259/445 ) , the single-variant LMM lead variants were in weak linkage ( 0 . 2<r2<0 . 8 example in Fig 4E ) , which neither confirms nor rules out distinct genetic effects .', 'One explanation for these instances are distinct polygenic architectures in both contexts .', 'Consistent with this possibility , we observed that genetic effects captured by a polygenic model in both contexts ( best linear unbiased predictor , Methods ) were markedly less correlated for probes with significant heterogeneity-GxC ( S13B and S13C Fig , Methods ) .', 'Finally , we explored the relationship between probes with heterogeneity GxC and opposite effects as defined using conventional single-variant models .', 'We classified associations as opposite effects when context-specific lead variant were in high LD ( r2>0 . 8 ) and the effect on gene expression was in different directions ( Methods ) .', 'This approach identified 67 eQTLs with reversed effect directions between contexts .', 'iSet-het detected significant heterogeneity-GxC for 8 of these eQTLs , a 2 . 2 fold enrichment ( P<5e-2 ) compared to eQTLs with consistent effect directions between contexts ( 238 gene/stimulus pairs with significant heterogeneity-GxC out of 4 , 119 eQTLs with consistent direction , Fig 4F ) .', 'Similar enrichments were also observed when considering individual stimulus contexts , resulting in significant enrichments for two out of three stimulus contexts ( P<5e-2 , fold change>4 in naïve/IFN and naïve/LPS-24h , S5 Table ) .', 'Among the genes with significant heterogeneity-GxC are OAS1 , LMNA and PTK2B , opposite-effect eQTLs that have been reported in the primary analysis of the same data [21] ( S14 Fig ) .', 'Thus far , we have considered settings with repeat measurements , where the same phenotype is measured in all individuals and contexts .', 'Next , we considered applications of iSet to studies where individuals are phenotyped in only one of the two contexts ( S2 Fig , Methods ) .', 'This is a common strategy in investigation of genotype-context interactions , where a population is stratified using a context variable .', 'We considered simulations analogous to those for complete designs ( Fig 2 ) to validate iSet for this design .', 'We again confirmed statistical calibration of iSet ( S15A Fig ) and found similar power benefits as for complete designs ( Fig 5A and 5B , S15B and S15C Fig ) .', 'In addition to single-variant LMMs , we also compared to a recently proposed set test for interactions ( GESAT; [13] ) , which is designed for stratified populations .', 'Notably , iSet was consistently better powered than GESAT , most likely because GESAT does not model correlations of the local genetic effect between contexts ( Methods , S1 Text ) .', 'Next , we applied iSet to test for genotype-sex interactions in four lipid-related traits ( fasting HDL and LDL cholesterol levels , triglycerides and C-reactive protein ) measured in 5 , 256 unrelated individuals from the Northern Finland Birth Cohort ( NFBC1966 [20] ) .', 'We tested consecutive 100kb regions ( step size 50 kb; 52 , 819 genome-wide tests ) , and compared iSet to GESAT and the single-variant interaction test ( Methods ) .', 'iSet retrieved one genome-wide significant interaction ( C Reactive protein , chr1:40 , 450 , 000; P = 1 . 47x10-6; FWER<10% ) , whereas alternative set tests and the single-variant models did not yield significant effects ( Fig 5C , S16 and S17 Figs , S6 Table ) , even when using dense genotypes derived using imputation strategies ( S18 Fig ) .', 'This interaction was located within 400kb of an interaction identified in a large meta study ( 66 , 185 individuals [34] ) , which reports both an association for C-reactive protein at the same locus ( P<6x10-11 ) as well as a nominally significant interaction with sex ( P<5x10-3 ) .', 'Finally , a local single-variant analysis , separately for female and male individuals , provided evidence that this interaction reflects a male-specific genetic effect ( S19 Fig ) .', 'iSet revealed a second suggestive interaction with sex for LDL cholesterol levels ( chr3:121 , 850 , 000 , S16 Fig ) .', 'Although this effect failed genome-wide significance ( FWER<20% ) , iSet again yielded stronger evidence than other methods ( PiSet = 3 . 7x10-6 , PGESAT = 4 . 8x10-6 , PmtLMM-int = 3 . 2x10-5 ) .', 'Among the genes at this locus is ADCY5 , which has been linked to blood glucose levels in large meta-analyses [35 , 36] and hence is a plausible candidate to affect LDL via glucose regulation [37] .', 'Finally , we note that context stratification of quantitative traits can increase power for detecting associations rather than interactions , which is similar to previous strategies applied for single-variant analyses of quantitative [38] and categorical traits [39 , 40] .', 'Using this generalized association test , we identified three additional associations that were missed by conventional set tests and other methods ( S16 Fig , S6 Table ) .', 'These include the same locus with a sex-specific effect on C-reactive protein ( chr1:40 , 450 , 000 , P = 1 . 42x10-7 using mtSet , P = 1 . 89 x10-3 using a standard set test ) , and two associations for HDL cholesterol levels and triglycerides , both of which were replicated in larger meta analyses [41] .'], ['We have here proposed iSet , a method based on linear mixed models to test for gene-context interactions using variant sets .', 'On simulated data as well as in applications to gene expression and human lipid-related traits , we have demonstrated that iSet yields increased power and improved interpretation for interaction effects compared to previous methods .', 'Methods for the joint analysis of multiple traits , including tests for genetic interactions , are not new per se .', 'Most previous studies have used set-based methods to test for associations [7 , 8 , 12 , 18] , whereas tests for genotype-context interactions are still primarily carried out using single-variant models [10 , 17] .', 'iSet unifies several previous models ( Methods ) , and uniquely offers set-based interaction tests on phenotypes in different contexts under the same or different ( stratified ) genetic backgrounds .', 'Additionally , we have shown that set-based interaction tests can be useful to disentangle the genetic architecture of such loci , discerning consistent changes of genetic effects between contexts ( rescaling-GxC ) and changes in the configuration of causal variants ( heterogeneity-GxC ) .', 'The heterogeneity GxC test we propose is related to co-localization tests [19 , 42 , 43] , however with a different objective .', 'In applications to a stimulus eQTL study , iSet has yielded increased power compared to single-variant tests ( Fig 3A and 3B ) , and we have shown that approximately 20% of the gene-stimulus interactions are associated with significant heterogeneity-GxC .', 'This suggests that changes in the genetic architecture between stimulus contexts are relatively common .', 'Additionally , we have observed that genes with opposite effects are enriched for heterogeneity-GxC .', 'This finding points to a possible bias whereby opposite effects identified using single-variant models may in part be due to context-specific causal variants that are LD-tagged by a shared lead variant .', 'Notably , although iSet is better powered overall , there may be true interactions that can be detected using single-variant models and are missed by set tests ( Fig 3B , S11 and S12 Figs , S4 Table ) .', 'Hence , iSet should be considered as a complementary method and not as a replacement of conventional single-variant tests .', 'The proposed iSet model is not free of limitations .', 'First , scalable inference in our model is achieved by exploiting the low-rank structure of variant sets , meaning that the number of variants in the analyzed region is typically small compared to the number of individuals .', 'Similar to previous set-based tests [12] , there are trade-offs between power and resolution , in particular when analyzing data from densely imputed or sequenced cohorts .', 'General strategies for the design of optimal testing regions , for example using genome annotations and LD information , are an important area of future work .', 'iSet is computationally efficient in cohorts with fully observed designs , or when stratifying a cohort using a context variable .', 'Intermediate designs , for example in fully observed designs with missing phenotypes , may also be considered , however currently require the use of separate imputation schemes [11 , 44] .', 'It is also worth noting that the test for heterogeneity-GxC ( iSet-het ) will be most accurate if all individuals are phenotyped in each context .', 'Although in principle the model can also be used in stratified designs , there may be concerns that false positive heterogeneity GxC effects can arise due to technical factors , for example due to differences in genotyping accuracy or variant allele frequencies in the corresponding sub populations .', 'A related issue is the need to choose the size of the region-set appropriately .', 'While we find that the model is overall robust across a wide range of region sizes ( S10 Fig ) , the model will be best powered if the size of true causal regions approximately matches the testing region size , in particular for identifying heterogeneity-GxC effects .', 'Finally , we have here focused on pairwise analyses of different contexts .', 'In principle , the model could also be applied to analyze multiple related context and different traits , and the model could be extended to handle continuous environmental states , which currently require discretization .', 'A related extension of the model is to test for genetic effects that are exclusive to one of the considered contexts .', 'Developments in these directions are future work .'], ['iSet is freely available as part of the LIMIX package ( https://github . com/limix/limix ) .', 'Tutorials for using iSet either as command line tool or via a Python API can be found at https://github . com/limix/limix-tutorials/tree/master/iSet .', 'To derive the model , we start assuming a fully observed design , where phenotypic measurements are available for all individuals and for each context .', 'Briefly , the N × C phenotype matrix Y for N individuals and two or more contexts ( C ) is modeled as sum of fixed effects of K covariates , effects from S genetic variants in the region of interest ( set component ) and residual noise:', 'Y=FB⏟fixedeffects+GW⏟setcomponent+ψ⏟noise .', '( 1 )', 'Here F ( N × K ) and G ( N × S ) denote respectively the fixed-effect covariates and the standardized genotypes of the variant set and B ( K × C ) and W ( S × C ) denote the corresponding effect sizes .', 'The noise component ψ is assumed to follow a matrix-variate normal distribution , ψ∼MVN ( 0 , Cn , IN ) , where Cn is a C × C covariance matrix that models residual covariances between traits .', 'Note that in this formulation , population structure can be accounted for by including the leading principal component of the N × N ( global ) realized relatedness matrix [22] into the model as fixed effects [12] .', 'In human populations , 10–20 principal components are typically sufficient to adjust for such structure [45] .', 'Note that iSet can also account for population structure using an additional random effect term into the model ( see S1 Text ) .', 'While computationally more expensive , this approach provides for additional robustness and calibration when analyzing cohorts with related individuals ( see [12] for a discussion ) .', 'All experiments reported here have been carried out using adjustment based on principal components , considering 10 PCs .', 'Simulations were carried out using a synthetic cohort of 1 , 000 individuals derived from genotypes of European populations in the 1000 Genomes project [29] ( phase 1 , 1 , 092 individuals , 379 Europeans ) .', 'Following [12 , 47] , we composed synthetic genotypes as a mosaic of real genotypes from individuals of European ancestry , while preserving population structure ( S1 Text ) .', 'We considered single-nucleotide polymorphism with a minor allele frequency of at least 2% ( S4 Fig ) .', 'In all simulations , we simulated two contexts , modeled as the sum of a genetic contribution from a 30kb causal region , effects due to population structure , hidden covariates and identically distributed Gaussian noise .', 'Effects due to population structure and hidden confounders were simulated with partial correlations across contexts , explaining variable proportions of the total phenotypic variance in each context ( S2 Table , S1 Text ) .']]
['Introduction', 'Results', 'Discussion', 'Methods']
['Joint genetic models for multiple traits have helped to enhance association analyses .', 'Most existing multi-trait models have been designed to increase power for detecting associations , whereas the analysis of interactions has received considerably less attention .', 'Here , we propose iSet , a method based on linear mixed models to test for interactions between sets of variants and environmental states or other contexts .', 'Our model generalizes previous interaction tests and in particular provides a test for local differences in the genetic architecture between contexts .', 'We first use simulations to validate iSet before applying the model to the analysis of genotype-environment interactions in an eQTL study .', 'Our model retrieves a larger number of interactions than alternative methods and reveals that up to 20% of cases show context-specific configurations of causal variants .', 'Finally , we apply iSet to test for sub-group specific genetic effects in human lipid levels in a large human cohort , where we identify a gene-sex interaction for C-reactive protein that is missed by alternative methods .']
['Genetic effects on phenotypes can depend on external contexts , including environment .', 'Statistical tests for identifying such interactions are important to understand how individual genetic variants may act in different contexts .', 'Interaction effects can either be studied using measurements of a given phenotype in different contexts , under the same genetic backgrounds , or by stratifying a population into subgroups .', 'Here , we derive a method based on linear mixed models that can be applied to both of these designs .', 'iSet enables testing for interactions between context and sets of variants , and accounts for polygenic effects .', 'We validate our model using simulations , before applying it to the genetic analysis of gene expression studies and genome-wide association studies of human blood lipid levels .', 'We find that modeling interactions with variant sets offers increased power , thereby uncovering interactions that cannot be detected by alternative methods .']
['blood cells', 'medicine and health sciences', 'c-reactive proteins', 'immune cells', 'protein interactions', 'built structures', 'engineering and technology', 'immunology', 'random variables', 'covariance', 'simulation and modeling', 'mathematics', 'research and analysis methods', 'white blood cells', 'animal cells', 'proteins', 'genetic loci', 'probability theory', 'biochemistry', 'cell biology', 'monocytes', 'phenotypes', 'genetics', 'biology and life sciences', 'structural engineering', 'physical sciences', 'cellular types']