As research in genetics has advanced, some findings have been unexpected or shown to be inconsistent between studies or datasets. The reasons these inconsistencies arise are complex. Results from genetic studies can be affected by various factors including statistical power, linkage disequilibrium, quality control, confounding and selection bias, as well as real differences from interactions and effect modifiers, which may be informative about the mechanisms of traits and disease. Statistical artefacts can manifest as differences between results but they can also conceal underlying differences, which implies that their critical examination is important for understanding the underpinnings of traits. In this review, we examine these factors and outline how they can be identified and conceptualised with structural causal models. We explain the consequences they have on genetic estimates, such as genetic associations, polygenic scores, family‐ and genome‐wide heritability, and describe methods to address them to aid in the estimation of true effects of genetic variation. Clarifying these factors can help researchers anticipate when results are likely to diverge and aid researchers' understanding of causal relationships between genes and complex traits. Accordi. Determining whether a causal effect is present or absent is challenging and rests upon assumptions that can be encoded in structural causal models based on the judgement of researchers.In addition, it may help to think probabilistically about causal relationships in genetics. If a genetic variant changes the probability of the trait, it is said to have a causal effect on the trait. The genetic variant need not be necessary or sufficient for the trait to be seen—it may occur regardless of the presence of the genetic variant, and the genetic variant may not be sufficient to cause the outcome on its own For example, researchers may be interested in understanding whether a single‐nucleotide polymorphism (SNP) has an effect on traits, that is, whether a variant at the SNP increases or decreases the risk of developing them. They may also be interested in other parameters, such as polygenic scores  and heritability estimates (the degree to which differences in a trait are attributable to genetic variation).If a polygenic score for a trait estimated from a European sample predicts the trait less accurately in an Asian sample, does that imply the genetic basis of the trait varies between the two populations, or that the trait difference is caused by other factors? For example, a difference could arise because the relevant genetic variants have not been identified precisely, or because environmental factors, which differ in prevalence between populations, modify the causal effects of these genes. This leaves the question: how can these explanations be distinguished?Underlying these questions are assumptions of how variables are causally related to each other. Making these assumptions explicit can help researchers clarify why some associations translate well in new populations while others do not and anticipate which situations may reduce predictive accuracy. It can also help researchers recognise when it would be challenging to translate these associations into clinical practice and appreciate when differences in results might reveal important information about the mechanisms of complex traits and disease.This paper will review the reasons that different genetic association studies are consistent or not—from causal interactions and effect modifications to artefacts such as confounding, selection bias, phenotyping, linkage disequilibrium and statistical power. We will outline how these factors can be identified and apply direct acyclic graphs to visualise causal relationships between variables. Additionally, we will explain the implications these factors have on genetic parameters, and how they can determine why observed consistencies or inconsistencies have arisen.1.1p‐value threshold for statistical significance in multiple datasets. However, this inference is mistaken, as the difference between a significant finding (in one data set) and non‐significant finding (in another) may not be significant itself , and the variance of the estimator .Since association tests depend on the presence of variation in genotypes and phenotypes, the effects of genetic variants may be undetected if they are present at a low allele frequency in a sample. For a given effect size, the statistical power is highest when the exposure variable, in this case, the genotype, has the greatest population variance, which occurs when the variant frequency is 50% when the genotype is coded additively. A causal variant showing significant association in a population in which it is common may not be replicated in a second population where it is much rarer, even if it has the same effect size, due to the difference in power.In the Winner's curse phenomenon, the magnitudes of associations are attenuated in new samples, potentially resulting in non‐significant replications Kraft, . This phR2 (the proportion of variance in the trait predicted by the polygenic score) and the area under the curve (a measure of the ability of the polygenic score to classify a true positive as a positive at a higher rate than a true negative) in an external data set  can also affect the consistency of genetic associations. False‐positive associations arising from genotyping errors are unlikely to be replicated by other studies and can contribute to inconsistent results. These can be reduced by carrying out careful quality control procedures to exclude problematic SNPs and samples, and by mega‐analyses  that use standardised quality control measures and cut‐offs  is the correlation between genetic variants that arises due to the variants being inherited together, from parents to offspring, which is more likely between variants located close to each other in the genome. Variants that are associated with a phenotype through LD with a ‘causal variant’ are called ‘linked’ or ‘proxy’ variants. The association of linked variants with the phenotype is referred to as indirect association.Patterns of LD differ between populations  than the sum of effects of the two variables. In contrast, multiplicative interactions can be estimated by comparing the joint effect of both the variables in combination to the product of the individual effects of the two variables in isolation . Effect modifications can be estimated by comparing the effect of one variable on the outcome in the presence of the second variable versus in its absence Bours, . If the 3.1Many studies in genetics have focused on the impact of interactions, exploring effects such as epistasis, allelic dominance, candidate gene‐environment interactions, and environmental interactions with heritability. These fall under two groups: interactions between genetic variants and the environment (gene‐environment interactions) and interactions between genetic variants and other genetic variants (gene‐gene interactions).Gene–environment and gene–gene interactions are thought to consist of numerous genes and environmental pressures each with small effect sizes   in Figure In a DAG, an exposure refers to any factor of interest that may affect the outcome; exposures and outcomes relevant to the hypothesis are drawn with arrows pointing in the direction of the hypothesised effects , their reducibility (collapsed into a single variable if they can be described by a larger variable), their mediation (omitted if they mediate an effect but have no other effects or inputs), and their variation   on both exposure and outcome variables.A well‐known source of confounding in genetic studies is population stratification—systematic variation in allele frequencies between sub‐populations due to differences in ancestry and non‐random mating , can be identified using positive Hilgard,  and negaGenerally, confounders can be addressed in various ways: matching participants on their level of confounders (which can control confounding at baseline in a cohort study), covariate adjustment in a regression, stratification to examine the effect of the exposure at different levels of the confounder, restriction of the sample to a homogeneous group where the confounder does not vary, or adjustment for propensity scores  open, and do not open additional spurious paths between the exposure and outcome  are causally related to whether a participant is included in the sample (admitted into the university). In the DAG in Figure cannot occur  is treated as a covariate and is stratified, matched or adjusted for, then the relationship between the two variables that cause the collider become conditionally dependent on each other, resulting in a spurious association between them . That is, results may be inconsistent because the instrument itself measures the phenotype variably, increasing the rates of false‐negative results.Poor reliability can arise from various aspects of the measurement process, such as the reliability across raters , time , items  and forms   phenotype . In a latent factor model, this item had the lowest correlation with all the other items and a high residual variance that correlated with socioeconomic status, suggesting it related to sociocultural practices.Cultural differences in alcohol consumption worldwide . This can be problematic because the reliability of the test depends on the sample that is tested, and a respondent's standing on a test can vary substantially depending on which items are included on the measure. To address this issue, some tests use item response theory to test the likelihood that respondents will endorse a particular item Bech, .Reliability can be improved through different approaches, such as the use of more granular scales that better discriminate between levels of the phenotype, or by accounting for factors that affect measurement across raters, time or forms.In contrast to reliability, validity relates to systematic errors affecting measurement. Different types of validity can be tested, including convergent validity (the correlation with other measures of the phenotype), criterion validity (the correlation with other traits associated with the phenotype) and discriminant validity (the correlation with other traits that we would not associate with the phenotype) (Price et al., Approaches such as factor analysis can help test validity, as in the example of the AUDIT questionnaire, which distorted genetic correlations between its measure of alcohol use disorder and related phenotypes. Researchers may also test for measurement invariance: whether the instrument measures the construct equivalently between groups or over time Finch,  This is Measuring phenotypes is challenging because poor reliability and validity can affect the consistency of genetic results: low reliability can reduce the likelihood of replicating results by introducing noise into the measurement. As demonstrated by Wray et al. , low rel7Genetic association studies can be highly informative about the molecular basis of complex traits. However, identifying these effects and mechanisms from observational studies can be challenging, as these designs depend on assumptions about the relationships between variables. These assumptions inform decisions about study sampling, measurement and covariate adjustment, and can be made explicit with structural causal models using knowledge from other lines of evidence.Making these assumptions explicit is not only important for inferences about the causal effects of genes, but also because they influence estimates of heritability, the accuracy of polygenic scores, and the statistical power to detect genetic associations. Additionally, when studies are affected by confounding, selection bias or low phenotype validity, their design can also result in the detection of genetic variants associated with phenotypes that researchers do not intend to measure.Identifying the underlying factors for consistent and inconsistent findings increases our understanding of discrepant results in the literature. True differences in the effects of genes can arise from interactions and effect modifiers by other genes and the environment. But these differences can be masked by other factors, including the selection of samples, the measurement of phenotypes, the analytical method and adjustment of covariates, the statistical power of an analysis, quality control measures and population characteristics such as allele frequencies and LD. In parallel, consistent effects can be obscured by many of the same factors.These factors can be identified and addressed at various levels of research: from the design of a study and selection of participants to the measurement of phenotypes and the adjustment of confounders, but this can remain challenging.Our understanding of the causes of discrepancies between results can illuminate the mechanisms of complex phenotypes and disease. Recently, new software has been developed to quantify the impacts of bias on effect estimates. Future methods that improve our ability to estimate the propensity of individuals to participate in a study, identify confounders and measure phenotypes with greater reliability and validity may aid this progress even further.Saloni Dattani: Conceptualisation and design of the review, literature review, and writing of manuscript. David M. Howard and Cathryn M. Lewis: Design of the review and revision of manuscript. Pak C. Sham: Substantial revision of manuscript.Cathryn M. Lewis sits on the Scientific Advisory Board for Myriad Neuroscience.


ANKH and calcium levels mediated by citrate levels and SLC6A12 and serum creatinine through modulation of the levels of the renal osmolyte betaine. We show that the signals missed by transcriptome-wide MR are found, thanks to the increase in power conferred by integrating multiple omics layer. Simulation analyses show that with larger molecular QTL studies and in case of mediated effects, our multi-omics MR framework outperforms classical MR approaches designed to detect causal relationships between single molecular traits and complex phenotypes.Despite the success of genome-wide association studies (GWASs) in identifying genetic variants associated with complex traits, understanding the mechanisms behind these statistical associations remains challenging. Several methods that integrate methylation, gene expression, and protein quantitative trait loci (QTLs) with GWAS data to determine their causal role in the path from genotype to phenotype have been proposed. Here, we developed and applied a multi-omics Mendelian randomization (MR) framework to study how metabolites mediate the effect of gene expression on complex traits. We identified 216 transcript-metabolite-trait causal triplets involving 26 medically relevant phenotypes. Among these associations, 58% were missed by classical transcriptome-wide MR, which only uses gene expression and GWAS data. This allowed the identification of biologically relevant pathways, such as between  Genome-wide association studies (GWASs) have identified thousands of single nucleotide polymorphisms (SNPs) associated with a wide range of complex traits . HoweverN>30,000). Availability of these datasets fostered the development of summary statistic-based statistical approaches aiming at identifying associations between transcripts and complex traits  data to compute the indirect effect of gene expression on complex traits mediated by metabolites in three steps . First, cis-eQTLs stem from the eQTLGen Consortium meta-analysis of 19,942 transcripts in 31,684 individuals (N = 6056) and KORA (N = 1768)  of the 133 associations were reported in HMDB, an automated literature review (see Methods) identified a match for 22 (16.5%) of the identified transcript-metabolite pairs  . After s = 1768)  and 242  = 1768)  (see Met = 1768) . By test = 1768) . Most inte pairs .Univariable metabolome-wide MR MWMR;  was usedWe applied univariable transcriptome-wide MR   and 132 metabolite-trait (FDR ≤5%) associations to pinpoint 216 transcript-metabolite-phenotype causal triplets (FDR = 1–0.95= 9.75%) . Among tFor each of these 216 putative mechanisms, an MVMR approach to compute the direct effect of gene expression on the phenotype was applied , 1-arachidonoylglycerophosphoethanolamine (LPE(20:4);HMDB0011517; –37; –07; –18), and 1-arachidonoylglycerophosphoinositol (LPI(20:4); HMDB0061690; –18; –16) levels  levels . These rnd FADS2 . Recentlnd FADS2 . OverallImportantly, only 42% (90/216) of the causal triplets showed a significant total transcript-to-phenotype effect , suggesting that the method lacks power under current settings. To characterize the parameter regime where the power to detect indirect effects is larger than it is for total effects, we performed simulations using different settings for the mediated effect. In each scenario we evaluated 500 transcripts and 80 metabolites and varied two parameters characterizing the mediation:The proportion (The ratio (α=0.05) on a phenotype. Each scenario was simulated 10 times and results were averaged to assess the mean difference in power (see Methods).Transcripts were simulated with 6% heritability . Howeveion , which itself increased serum calcium levels (–0). Mutations in ANKH have been associated with several rare mineralization disorders  . While blood betaine levels negatively impacted serum creatinine levels (–07), the effect of SLC6A12 expression on creatinine was not significant (–03). This observation is particularly interesting given that betaine acts as a protective renal osmolyte whose plasma and kidney tissue concentration were found to be downregulated in renal ischemia/reperfusion injury , or usage of the search term with a different meaning. To attenuate the latter, we also performed manual review of the retained abstracts for transcript-to-phenotype searches. While flawed, this rough estimate of the amount of existing evidence supporting our findings can be interpreted in combination with other lines of evidence. For instance, among the 90 signals that were also identified through TWMR, 93% showed a directionally concordant effect between the transcript-to-phenotype, transcript-to-metabolite, and metabolite-to-phenotype estimates . In these situations, dissection of causal effects provides clues as to the molecular mechanism through which involved genes modify complex phenotypes. This information is particularly valuable to identify key molecular mediators of highly pleiotropic genetic regions, such as the S2 locus . While tANKH to calcium levels through modulation of citrate and SLC6A12 to serum creatinine levels through regulation of the renal osmolyte betaine. Simulation analyses showed that these signals were likely missed by TWMR due to lack of power, as mediation analysis is better suited to detect associations with a low direct to total effect proportion and stronger transcript-to-metabolite than metabolite-to-phenotype effect. Promisingly, our simulations showed that mediation analysis becomes increasingly powerful over a wider range of parameter settings as the sample size of the mediator QTL study increases, highlighting the importance of generating large and publicly available molQTL datasets that can help to unravel functional gene-to-phenotype mechanisms.Strikingly, 58% of the 216 causal transcript-metabolite-phenotype triplets were missed by TWMR – an approach that only considers gene expression and GWAS data. We highlight two novel but biologically plausible mechanisms linking As illustrated through the selected examples, a large fraction of detected mediations involves genes encoding metabolic enzymes or transporters/channels, with an enrichment for ‘secondary active transmembrane transporter activity’, for example . Matching the finding that the most likely effector genes of mQTLs are enriched for pathway-relevant enzymes and transporters , these rTMEM258/FADS1/FADS2 locus  play a crucial role in mediation. It is to note that in the presence of unmeasured mediators or measured mediators without genetic instruments, our mediation estimates are lower bounds of the total existing mediation. In addition, unmeasured mediators sharing genetic instruments with the measured ones can modify result interpretation as some of the observed mediators may simply be correlates of the true underlying mediators. While this is a limitation of all MR methods, metabolic networks may harbor particularly large number of genetically correlated metabolite species. Similarly, owing to linkage disequilibrium and regulatory variants affecting multiple genes, transcripts from adjacent genes might appear to be involved in the same signals, as exemplified with the S2 locus . While ltrans-eQTL association summary statistics, our method does not investigate reverse causality on metabolites and gene expression, nor the role of metabolites as regulators of gene expression. Metabolites might also integrate the effect of several transcripts  before affecting complex phenotypes , and significant .IVs were selected as autosomal, non-strand ambiguous, independent  is easily violated, leading to inaccurate estimates when horizontal pleiotropy occurs . To testand its variance asNext, the deviation of each SNP was tested using the test statisticWhen p<0.05, the SNP with largest | 2r <0.01, pmQTL<1 × 10–07), the direct effect of gene expression on a phenotype can be estimated using a multivariable regression model , which includes cis-eQTLs  for 19,250 transcripts . mQTL data originate from http://metabolomics.helmholtz-muenchen.de/gwas/). Among these metabolites, 242 were manually annotated with the HMDB identifiers . Protein interactions with metabolites were downloaded from HMDB v5.0 (https://hmdb.ca/downloads/) and were used to annotate transcript-metabolites associations.Expression QTL data originated from the eQTLGen Consortium  . eQTL data originated from the eQTLGen Consortium (https://www.eqtlgen.org) and was published in http://metabolomics.helmholtz-muenchen.de/gwas/). The HMDB was used to annotate metabolites and the v5.0 release from November 9, 2021, of the ‘All proteins’ file was downloaded to extract transcript-metabolite interactions (https://hmdb.ca/downloads). PubMed was used for the automated literature review (https://pubmed.ncbi.nlm.nih.gov). The UCSC Genome Browser (https://genome.ucsc.edu/) was used to visualize the FADS locus, while the GWAS Catalog was used to assess the number of reported GWAS signals in the region (https://www.ebi.ac.uk/gwas/). The STRING database was used for the enrichment analysis (https://string-db.org/). Produced data is available as https://github.com/eleporcu/Gene_Metab_Pheno; (swh:1:rev:c6bff8d094e369ff0d399751fc85fcd5ea250134).All data used in this study are publicly available. GWAS summary statistics for outcome traits measured in the UKB originate from the Neale Lab  large cohorts. public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 2 peer reviewers, including Evan Graehl Williams as Reviewing Editor and Reviewer #1, and the evaluation has been overseen by David James as the Senior Editor.Thank you for submitting your article "Exploiting the mediating role of the metabolome to unravel transcript-to-phenotype associations" for consideration by The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.In brief, besides the reviewer-specific comments, there was a common thread regarding significances of the findings  and description of the method. I also apologize for the delay in the reviews; it was a huge challenge to get reviewers in July and August, and we potentially may consult a third reviewer for the revision.Reviewer #1 (Recommendations for the authors):Auwerx et al. have taken a new (or recent?) approach to mine large existing datasets of intermediary molecular data between GWAS and phenotype, with the aim of uncovering novel insight into the molecular mechanisms which lead a GWAS hit to have a phenotypic effect. The authors show that you can get additional insight by integrating multiple omics layers rather than analyzing only a single molecular type, including a handful of specific examples, e.g. that the effect of SNPs in ANKH on calcium are mediated by citrate. Such additional data is necessary because, as the authors' point out, while we have thousands of SNPs with significant impact on phenotypes of interest, we often don't know at all the mechanism, given that the majority of significant SNPs found through GWAS are in non-coding (and often intergenic) regions.Scientific commentsdesigned a new method or have applied a recently-developed method. I follow that the general approach uses MR across multiple data types and then merges the results. I did look at the Github repo ("Gene_Metab_Pheno") but I'm not enough of a mathematical bioinformatician to really judge the novelty there, as to whether this is a new method or application of relatively recent other methods.(1) It's not quite clear to me whether the authors have (2) The sample sizes are huge here since it is a meta-analysis, which means it's not quite clear to me how this method would scale to studies where there are not tens of thousands of individuals measured. It would be good to already have some general idea of what are the requirements in terms of power (sample size/target effect size / etc) for this approach – either added as a figure panel or two in this paper or just as text if the necessary parameters have already been explained elsewhere. I guess this comes back to the p >> n issue. I see for instance that the authors have 21k transcripts but they narrow it down to 7883 with {greater than or equal to} 3 IVs, used against their sample size of n = 7824 patients. Is this just convenient that n ~= p, or were the required parameters tweaked exactly so that you could reduce the number of transcripts down to more or less the sample size? You have a section on "Power Analysis" already which I appreciate, but reading through it again I can't tell what the minimum N would be. Or can I use an N = 500 I just have to use some other way to select only 500 (or whatever) transcripts? The power calculations go up to N = 90'000 which indeed is "state-of-the-art sample sizes" and would be unattainably large for all but the largest of international human cohorts, and perhaps a few large yeast or cell line studies.(3) Related, I wasn't quite clear if the data from TwinsUK and KORA were analyzed separately, or if they were somehow merged.(4) The authors mention "overall, 83% of the involved genes were causally influencing the level of a single metabolite, while TMEM258 and FADS2 affected 12 metabolites". Firstly I would mention that they affect 12 metabolites each just to be clear – although it's clearly annotated in Table S1. Second, and more relevantly, it would be nice to know in this table how many of these hits already are known in the literature. For instance I see the most significant hit is MAF1 with 5-oxoproline which doesn't immediately turn up anything . Hit #7, for SLC22A4 and isovalerylcarnitine does appear to be known in the literature ( http://www.metabolomix.com/rs272889-slc22a4-octn1-with-acylcarnitines/ ). Doing a decent literature analysis on all 257 of these hits in Table S1 might take a while  but even just some cherry-picking and/or (better) systematic analysis of the top 20-50 would be nice to see. It greatly improved my confidence in the findings when I just looked into two of your hits just now and found that one of them appears to be reasonably well known by literature.(5) The authors mention that only 33% of the transcript-metabolite-phenotype triplets were observed by TWMR, but that 91% of those observed by all are in concordant directionality. I guess that means for those with concordant directionality, if no significant association was observed in one layer, there was just no cross-layer comparison? i.e. that the 91% "concordant directionality" are only checking among the 33% of hits by TWMR that were also observed both within and across layer?(6) The authors mention no availability of trans-eQTL data; is that because the sample size is not sufficient to do a proper trans-eQTL analysis, or is it because of data privacy and an inability to get the precomputed trans-eQTLs from the eQTLGen Consortium due to some potential conflict (GDPR?).(7) Back to Table S1: There are 257 hits here, with 191 genes (out of 7883) and 154 metabolites (out of 453), meaning that 299 metabolites didn't even have one significant association?Reviewer #2 (Recommendations for the authors):1. In general, the methodological approach should be explained in more detail. The study presents a novel MR-based approach and thus, the discussion of the method basics should be elaborated. This pertains to the following points:– In the definition of causal effects from molecular traits on the outcome (eq. (1)), the symbol β' is not explained. The method used for standardization of effect sizes is not elaborated.– For the multivariable MR analysis (equation not numbered), no causal effect statistic is specified. As discussed in the public review, no significance testing has been performed, but we strongly urge the authors to do so or give reasons for this lack of testing in the case of causal triplets.– In the description of the simulation analyses, it should be made more clear how the definition of βGWAS as a function of βmQTL is reached.– The authors should include a thorough discussion and a description of the method employed to evaluate the comparison between total and direct transcript-phenotype effects in Figure 2B.2. There is some apparent inconsistency in the interpretation of results from the empirical study: The abstract states that 67 transcript-phenotype effects present within the 206 causal triplets were missed in a TWMR-only analyses, while the paragraph "Power Analysis" states that only 67 triplets showed a significant effect estimated by TWMR. The text relating to Figure 2B states that 79 % (~163) of the triplets were estimated to be due to direct effects by the transcript only. This should be presented in a more consistent and clear manner.3. Plots for the distribution of the number of IVs per transcript/metabolite should be included .4. It would be interesting to discuss potential modes of mediation between transcripts, metabolites and phenotypes. For example, individual metabolites might integrate the effects of several transcripts. This would not result in triplets, but ultimately, networks of mediation as shown for the TMEM258, FADS1, FADS2 case. How would such cases be treated in a statistically sound manner? Reviewer #1 (Recommendations for the authors):Auwerx et al. have taken a new (or recent?) approach to mine large existing datasets of intermediary molecular data between GWAS and phenotype, with the aim of uncovering novel insight into the molecular mechanisms which lead a GWAS hit to have a phenotypic effect. The authors show that you can get additional insight by integrating multiple omics layers rather than analyzing only a single molecular type, including a handful of specific examples, e.g. that the effect of SNPs in ANKH on calcium are mediated by citrate. Such additional data is necessary because, as the authors' point out, while we have thousands of SNPs with significant impact on phenotypes of interest, we often don't know at all the mechanism, given that the majority of significant SNPs found through GWAS are in non-coding (and often intergenic) regions.Scientific comments(1) It's not quite clear to me whether the authors have designed a new method or have applied a recently-developed method. I follow that the general approach uses MR across multiple data types and then merges the results. I did look at the Github repo ("Gene_Metab_Pheno") but I'm not enough of a mathematical bioinformatician to really judge the novelty there, as to whether this is a new method or application of relatively recent other methods.While the core Mendelian randomization (MR) and mediation analysis methodology used in this study is well-established, the novelty of the manuscript lies in (i) the strategy that sequential application of univariable and multivariable MR analyses across the different omics layers  can improve discovery power and (ii) the resulting key message that by incorporating metabolomic data to genetic studies, it becomes possible to gain functional and targetable insights into the pathways linking genetic variation to phenotypic diversity. To clarify this point, we have modified the Introduction of our revised manuscript:“Here, we develop a framework based on established MR methodology that hypothesizes a mediating role of the metabolome in the transcript-to-phenotype axis. Specifically, our integrative MR analysis combines summary-level multi-omics  data to compute the indirect effect of gene expression on complex traits mediated by metabolites in three steps .”(2) The sample sizes are huge here since it is a meta-analysis, which means it's not quite clear to me how this method would scale to studies where there are not tens of thousands of individuals measured. It would be good to already have some general idea of what are the requirements in terms of power (sample size/target effect size / etc) for this approach – either added as a figure panel or two in this paper or just as text if the necessary parameters have already been explained elsewhere. I guess this comes back to the p >> n issue. I see for instance that the authors have 21k transcripts but they narrow it down to 7883 with {greater than or equal to} 3 IVs, used against their sample size of n = 7824 patients. Is this just convenient that n ~= p, or were the required parameters tweaked exactly so that you could reduce the number of transcripts down to more or less the sample size?Requiring at least 3 IVs is common practice in the field of MR as it allows to estimate the causal estimate more robustly, as previously described (PMID: 31341166). In general, the more instruments, the less outliers can bias results. If the InSIDE assumption holds the MR estimates are asymptotically unbiased, hence more instruments reduce bias. Finally, more instruments also increase discovery power. Hence, the fact that the number of transcripts is reduced to the sample size of the study is pure coincidence. Of note, while this reduces the multiple testing burden, it also means that we potentially miss out on true causal effects of transcripts that cannot be instrumented properly.You have a section on "Power Analysis" already which I appreciate, but reading through it again I can't tell what the minimum N would be. Or can I use an N = 500 I just have to use some other way to select only 500 (or whatever) transcripts? The power calculations go up to N = 90'000 which indeed is "state-of-the-art sample sizes" and would be unattainably large for all but the largest of international human cohorts, and perhaps a few large yeast or cell line studies.While we are hopeful that in the future, ever larger multi-omics datasets will become available to the research community , we agree that the majority of currently available molecular datasets have smaller sample sizes than the one used in this study. To address this comment, we ran power analyses simulating mQTLs studies performed on 1000, 2000, and 4000 individuals. Following the previously observed trend, the gain in power of mediation analysis over TWMR decreases with decreasing “Repeating the simulations with a mQTL sample size of 90,000, nearing state-of-the-art sample sizes [7], we observe a strong shift in the above-described trends . Specifically, when the effect of the transcript on the phenotype is dominated by the effect mediated by the metabolite ((3) Related, I wasn't quite clear if the data from TwinsUK and KORA were analyzed separately, or if they were somehow merged.et al., 2014 (PMID: 24816252). Specifically, genome-wide association analyses were performed separately in KORA and TwinsUK for all 486 metabolite concentrations present in both studies after quality control steps. Association results were then combined using inverse variance meta-analysis based on effect size estimates and standard errors, adjusting for genomic control. Our study solely uses the publicly available meta-analysis summary statistics provided by Shin et al., 2014 for 453 of these metabolites.Data from KORA and TwinsUK have previously been analyzed, as described in Shin We would also like to highlight that based on comments by Reviewer #1 and #2, the revised manuscript now focuses on a restricted set of 242 metabolites for which we were able to identify a Human Metabolome Database (HMDB) identifier through manual annotation. This approach is motivated by only analyzing metabolites whose potential associations can be followed up.The current version of the manuscript reads as follows:Results: “Summary statistics for cis-eQTLs stem from the eQTLGen Consortium meta-analysis of 19,942 transcripts in 31,684 individuals [3], while summary statistics for mQTLs originate from a meta-analysis of 453 metabolites in 7,824 individuals from two independent European cohorts: TwinsUK  and KORA . After selecting SNPs included in both the eQTL and mQTL studies, our analysis was restricted to 7,884 transcripts with ≥ 3 instrumental variables (IVs)  and 242 metabolites with an identifier in The Human Metabolome Database (HMDB) .”Methods: “mQTL data originate from Shin et al., 2014 which used ultra-high performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) to measure 486 whole blood metabolites in 7,824 European individuals. Association analyses were carried out on ~2.1 million SNPs and are available for 453 metabolites at the Metabolomics GWAS Server (http://metabolomics.helmholtz-muenchen.de/gwas/). Among these metabolites, 242 were manually annotated with Human Metabolome Database (HMDB) identifiers (Supplementary File 1a) and used in this study.”(4) The authors mention "overall, 83% of the involved genes were causally influencing the level of a single metabolite, while TMEM258 and FADS2 affected 12 metabolites". Firstly I would mention that they affect 12 metabolites each just to be clear – although it's clearly annotated in Table S1.This has been clarified in the revised manuscript:“Most involved genes  were causally influencing the level of a single metabolite, with some notable exceptions acting as mQTL hubs, such as TMEM258 and FADS2 both affecting the same 11 metabolites, followed by FADS1 affecting a subset of 6 metabolites.”Second, and more relevantly, it would be nice to know in this table how many of these hits already are known in the literature. For instance I see the most significant hit is MAF1 with 5-oxoproline which doesn't immediately turn up anything . Hit #7, for SLC22A4 and isovalerylcarnitine does appear to be known in the literature (http://www.metabolomix.com/rs272889-slc22a4-octn1-with-acylcarnitines/ ). Doing a decent literature analysis on all 257 of these hits in Table S1 might take a while  but even just some cherry-picking and/or (better) systematic analysis of the top 20-50 would be nice to see. It greatly improved my confidence in the findings when I just looked into two of your hits just now and found that one of them appears to be reasonably well known by literature.This is a great suggestion which led us to conduct a more detailed follow-up investigation. Having a rough estimation of the number of associations that have previously been described in the literature would indeed be of great interest. Due to the large number of identified associations, performing a thorough, manual investigation of each of the identified associations is hardly manageable. As an alternative, we used an automated literature review strategy that we briefly describe below.First, we reduced the number of investigated metabolites to 242 interpretable compounds for which we could identify an HMDB identifier through manual annotation (see reply to scientific comment #3). Second, using this annotation, we identified transcript-to-metabolite effects for which an interaction between the encoded protein and metabolite was reported in the HMDB. In parallel, we performed an automated literature review in PubMed for all identified transcript-to-metabolite effects. Next, for the 37 causal transcript-metabolite-phenotype triplets for which either the HMDB or the PubMed search for the transcript-to-metabolite yielded at least one results, we (i) added a third term to the PubMed search relating to the associated phenotype and (ii) replaced the metabolite term by the phenotype term to determine whether the transcript-to-phenotype analysis had previously been reported. Owing to the low specificity of the phenotype search term , we manually reviewed the abstracts of retained publications, excluding findings in which the search terms were used in an unintended way. We describe the methods and results of these analyses in detail in the revised manuscript – along with a discussion of the limitations of our approach – and provide the PMIDs of our automated search in the Supplementary File 1b:Methods:“Omics and traits summary statistics[…] mQTL data originate from Shin et al. 2014, which used ultra-high performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) to measure 486 whole blood metabolites in 7,824 European individuals. Association analyses were carried out on ~2.1 million SNPs and are available for 453 metabolites at the Metabolomics GWAS Server (http://metabolomics.helmholtz-muenchen.de/gwas/). Among these metabolites, 242 were manually annotated with Human Metabolome Database (HMDB) identifiers (Supplementary File 1a) and used in this study. GWAS summary statistics for 28 outcome traits measured in the UK Biobank (UKB) originate from the Neale Lab . Protein interactions with metabolites were downloaded from HMDB v5.0 (https://hmdb.ca/downloads/hmdb_proteins.xml) and were used to annotate transcript-metabolites associations.Automated literature reviewAn automated literature review of all transcript-metabolites associations (Supplementary File 1b) was conducted in PubMed (20/09/2022) following the scheme:For transcript-metabolite associations involved in a causal triplet and for which the transcript-metabolites returned at least one publication (Supplementary File 1f), the search was extend by (i) adding a further search term for the trait  of the 133 associations were reported in HMDB, an automated literature review (see Methods) identified a match for 22 (16.5%) of the identified transcript-metabolite pairs (Supplementary File 1b).Mapping metabolome-mediated effects of the transcriptome onto complex phenotypes[…] Among the 37 triplets for which the transcript and metabolite had previously been linked through automated literature review, none remained after incorporating a third term for the phenotype in the search and manually removing abstracts for which the search terms were used in an erroneous context. Relaxing the search criteria by omitting the metabolite term, 13/37 (35%) triplets returned at least one match for the gene-trait association.”Discussion:“Our automated literature review indicates that while some detected associations were previously reported, a large fraction, especially among the triplets, appears to be novel. It should be noted that the number of previously reported associations is likely underestimated as our approach does not account for all synonyms of a given feature and requires the terms to appear in the title or abstract of the publication. This makes it more likely for hypothesis-driven studies, inherently biased towards well-studied genes and metabolites, to be identified. Conversely, high-throughput, hypothesis-free studies that report the given association in a supplemental table are likely to be missed. Furthermore, due to its automated nature, our search is context-blind, so that some of the identified studies might report negative results, associations only under specific conditions , or usage of the search term with a different meaning. To attenuate the latter, we also performed manual review of the retained abstracts for transcript-to-phenotype searches. While flawed, this rough estimate of the amount of existing evidence supporting our findings can be interpreted in combination with other lines of evidence. For instance, […].”(5) The authors mention that only 33% of the transcript-metabolite-phenotype triplets were observed by TWMR, but that 91% of those observed by all are in concordant directionality. I guess that means for those with concordant directionality, if no significant association was observed in one layer, there was just no cross-layer comparison? i.e. that the 91% "concordant directionality" are only checking among the 33% of hits by TWMR that were also observed both within and across layer?In response to Reviewer #2’s comments, the current version of the manuscript uses more stringent significant thresholds. At FDR 5%, we now observe 216 transcript-metabolite-phenotype triplets. Among these 216 triplets, 90 (42%) had a significant transcript-to-phenotype TWMR effect. Among these 90 triplets, 84 (93%) showed a directionally concordant effect between the transcript-to-phenotype, transcript-to-metabolite, and metabolite-to-phenotype estimates, meaning that the sign of the product of the transcript-to-metabolite and metabolite-to-phenotype effects equals the sign of the transcript-to-phenotype effect. This is now clarified in the Discussion:“[…] among the 90 signals that were also identified through TWMR, 93% showed a directionally concordant effect between the transcript-to-phenotype, transcript-to-metabolite, and metabolite-to-phenotype estimates .”(6) The authors mention no availability of trans-eQTL data; is that because the sample size is not sufficient to do a proper trans-eQTL analysis, or is it because of data privacy and an inability to get the precomputed trans-eQTLs from the eQTLGen Consortium due to some potential conflict (GDPR?).The trans-eQTLs data from eQTLGen Consortium are restricted to ~10,000 SNPs reported to be associated with complex traits in GWAS catalog due to the massive size of this type of data. There are current efforts within the eQTLGen Consortium to meta-analyse trans-eQTL summary statistics genome-wide, but these data will not be available before Q3 of 2023. Currently available data is unfortunately not sufficient to investigate reverse causality on metabolites and gene expression, as specified in the manuscript’s Discussion:“Due to the lack of genome-wide trans-eQTL association summary statistics, our method does not investigate reverse causality on metabolites and gene expression […].”(7) Back to Table S1: There are 257 hits here, with 191 genes (out of 7883) and 154 metabolites (out of 453), meaning that 299 metabolites didn't even have one significant association?This is correct. In the current version of the manuscript and as explained in the reply to previous points, we restricted our analysis to 242 metabolites manually annotated with HMDB identifiers. In Supplementary File 1b, we report 133 significant (FDR < 5%) transcript-to-metabolite effects involving 75 unique metabolites, so that in case of 167 metabolites we do not have evidence for them being impacted by any of the 7,824 tested genes. It is interesting to notice that despite changes in our analysis , the proportion of metabolites that are not affected by any transcripts remains similar . One potential explanation is lack of power, given the relatively small sample size of the mQTL dataset , as compared to GWASs for other complex traits (> hundreds of thousands), that prevents detection of associations for a large fraction of metabolites. Alternatively, these metabolites might be influenced by transcripts that cannot be instrumented, making it impossible to detect association.Reviewer #2 (Recommendations for the authors):1. In general, the methodological approach should be explained in more detail. The study presents a novel MR-based approach and thus, the discussion of the method basics should be elaborated. This pertains to the following points:– In the definition of causal effects from molecular traits on the outcome (equation (1)), the symbol β' is not explained. The method used for standardization of effect sizes is not elaborated.We clarified this in the current version of the manuscript, which now reads as follows:“Here, – For the multivariable MR analysis (equation not numbered), no causal effect statistic is specified. As discussed in the public review, no significance testing has been performed, but we strongly urge the authors to do so or give reasons for this lack of testing in the case of causal triplets.The equation has now been labeled (6). As specified in the Methods, we used multivariable MR (MVMR) only to estimate the direct effect of gene expression on the phenotype. We do not test the significance of this estimate as we only compare it with the total effect estimated by TWMR regardless its significance. Regarding significance testing for other sections of the manuscript, please see extensive reply to major concern #1 and #2.– In the description of the simulation analyses, it should be made more clear how the definition of βGWAS as a function of βmQTL is reached.As described in the Methods, to estimate the effect of the metabolite on the phenotype, we considered a metabolite with heritability – The authors should include a thorough discussion and a description of the method employed to evaluate the comparison between total and direct transcript-phenotype effects in Figure 2B.We have now added a description of the comparison of the direct and total effects in the Methods:“The proportion of direct effect It is crucial that due to lack of power, we do not compare individual direct-vs-total effects but only assess overall direct-vs-total effects across all transcript-phenotype pairs. The central message of the paper is not the difference between the two, but the difference in detection power between the two strategies, as we do illustrate in Figure 4.2. There is some apparent inconsistency in the interpretation of results from the empirical study: The abstract states that 67 transcript-phenotype effects present within the 206 causal triplets were missed in a TWMR-only analyses, while the paragraph "Power Analysis" states that only 67 triplets showed a significant effect estimated by TWMR.We apologize for this inconsistency, which has been clarified. The revised sections now read:Abstract: “We identified 216 transcript-metabolite-trait causal triplets involving 26 medically relevant phenotypes. Among these associations, 58% were missed by classical transcriptome-wide MR […].”Results: “Importantly, only 42% (90/216) of the causal triplets showed a significant total transcript-to-phenotype effect , suggesting that the method lacks power under current settings.”The text relating to Figure 2B states that 79 % (~163) of the triplets were estimated to be due to direct effects by the transcript only. This should be presented in a more consistent and clear manner.In Figure 2B, we plot the direct .We now include Figure 1 —figure supplement 1 to illustrate this.We furthermore refer to these plots in the Results section:“Mapping the transcriptome onto the metabolome[…] After selecting SNPs included in both the eQTL and mQTL studies, our analysis was restricted to 7,884 transcripts with ≥ 3 instrumental variables (IVs)  […].Mapping the metabolome onto complex phenotypesUnivariable metabolome-wide MR  was used to identify causal relationships between 48 metabolites with ≥ 3 IVs and 28 complex phenotypes . […]Mapping the transcriptome onto complex phenotypesWe applied univariable transcriptome-wide MR  to identify associations between expression levels of 10,435 transcripts from the eQTLGen Consortium with ≥ 3 IVs  measured in both exposure and outcome datasets and the same 28 UKB phenotypes described in the previous section (Supplementary File 1c)[…].”4. It would be interesting to discuss potential modes of mediation between transcripts, metabolites and phenotypes. For example, individual metabolites might integrate the effects of several transcripts. This would not result in triplets, but ultimately, networks of mediation as shown for the TMEM258, FADS1, FADS2 case. How would such cases be treated in a statistically sound manner?This is a very interesting idea and we believe that the field is increasingly interested in modelling such complex biological network. The situation where a single metabolite mediates the effect of multiple transcripts only needs a systematic search for metabolites repeatedly occurring in triplets. We identified 12 such metabolites (see Table integrated in revised manuscript as Supplementary File 1g). Nine out of 12 metabolites integrate effect of multiple transcripts to in turn affects multiple phenotypes, as illustrated in the last column of the Table. Of note 8/12 cases, the metabolites integrate the effect of transcript whose genes are in close genomic proximity (shown as bold transcripts in the same color). We already made this observation in the original manuscript and discussed this limitation:“Owing to linkage disequilibrium and regulatory variants affecting multiple genes, transcripts from adjacent genes might appear to be involved in the same signals, as exemplified with the TMEM258/FADS1/FADS2 locus . While literature supports the role of the FADS genes, one cannot exclude a role for TMEM258, nor disentangle the specific function of FADS1 and FADS2.”Investigating more complex scenarios where multiple correlated metabolites mediate the effect of a single transcript would require more advanced modelling techniques that go beyond the scope of this study. We strengthened the Discussion on the topic in the revised manuscript which now reads as follows:“Another consideration is that complex phenotypes can have a stronger impact on gene expression than the opposite [15]. Due to the lack of genome-wide trans-eQTL association summary statistics, our method does not investigate reverse causality on metabolites and gene expression, nor the role of metabolites as regulators of gene expression. Metabolites might also integrate the effect of several transcripts  before affecting complex phenotypes (Supplementary File 1g) or multiple metabolites may jointly mediate the impact of a single transcript. Modelling the latter phenomenon, which is beyond the scope of our current work, requires the development of Structural Equation Models accounting for such effects and will eventually lead to a more comprehensive modelling of causal relations in complex biological networks, nuancing the interpretation of the molecular mechanisms shaping complex traits.”


Interest in the study of gene–environment interaction has recently grown due to the sudden availability of molecular genetic data—in particular, polygenic scores—in many long-running longitudinal studies. Identifying and estimating statistical interactions comes with several analytic and inferential challenges; these challenges are heightened when used to integrate observational genomic and social science data. We articulate some of these key challenges, provide new perspectives on the study of gene–environment interactions, and end by offering some practical guidance for conducting research in this area. Given the sudden availability of well-powered polygenic scores, we anticipate a substantial increase in research testing for interaction between such scores and environments. The issues we discuss, if not properly addressed, may impact the enduring scientific value of gene–environment interaction studies. Although PGS are neither pure  nor uni factors ) measure2 For example, in the twin study literature, there has been substantial interest in whether decompositions of observed variation in a phenotype into genetic and environmental components differ by socioeconomic context or age  environmental exposure, E. We generically describe this data-generating model asϒ may have a Bernoulli distribution). We supplement this simple model with a few crucial assumptions. We assume that we have reasonable proxies available for G and E and some identifiable approximation to f . We comment on each of these assumptions below.We consider some outcome, G, we assume that we can characterize genetic influence on the trait as a PGS,N) of alleles  that an individual i has for each single nucleotide polymorphism (SNP) j is weighted by the effect, βj, identified via GWAS. We note a few assumptions implicit in the above. We are focusing on traits that have a genetic architecture appropriately characterized by effects that are additive with respect to one another  and dispersed over many loci. We view the assumption of additivity as an acceptable simplification given both the success of additive GWAS and the relative lack of strong empirical support for dominance or epistasis  models (With respect to ) models .βj) for SNPs that are not relevant to the phenotype of interest will go toward zero; thus, a summative approach can still potentially be used in such cases. Moreover, much of our discussion still applies when using genetic predictors constructed from a smaller number of variants or even using a single variant allele count  are themselves potentially a function of both trait-specific biology and contextual features of the data used to derive them: for example, the social and policy landscape governing behavior of participants in the GWAS, selection issues associated with being a part of GWAS sample, et cetera. .We also note that GWAS results . This limitation may act as a strict limiting factor when it comes to identifying GxE with polygenic scores. A related issue is that, if the environmental context of the participants in the GWAS sample used to construct the PGS is similar to that in the test sample used to estimate GxE, then it is unlikely to include SNPs that demonstrate lens-type patterns, as the main effects of these SNPs will be close to zero.We can also understand the difference between a dimmer and a lens in terms of their effect on the rank ordering of outcomes. All else being equal, a dimmer is order-preserving; that is, it preserves the order of the genotypes at different levels of the environment. Variation in the dimmer serves to vary the distance, in the outcome metric, between different levels of the PGS but never changes the rank orderings of the levels. In contrast, a lens reverses the order of genotypes; a PGS that predicts an outcome near the top of the distribution at one level of environmental exposure will predict an outcome near the bottom at another level of environmental exposure. Our dimmer/lens typology is similar in many respects to the ordinal/disordinal typology previously suggested  but may Conceptually, researchers will benefit from being attentive as to the form of GxE they expect; for example, is the candidate environment expected to operate as a lens, as a dimmer, or according to some more complex functional form? In our experience, GxE researchers will tend to observe that environments with large main effects on a phenotype act as dimmers. Such environments will moderate the magnitude of the effect of the polygenic score on the outcome without changing its sign. Although these observations may be of value, they need to be distinguished from the more dramatic patterns of sign reversal of PGS effects in different environments that have received a great deal of conceptual attention. In studies seeking to identify lens-type patterns , both thAnalytically, we offer several suggestions that might be of interest in future work. We first emphasize the potential for analyses that take advantage of environmental variation without identifying a specific environmental feature of interest. In situations wherein individuals cluster into some unit, researchers may first want to consider the level of empirical support for GxE based on relatively omnibus measures of the environment. For example, one might test for variation observed in the relationship between phenotype and polygenic score across environmental units ; see Yet another approach that researchers might want to consider involves analyses of heritability and genetic correlation as captured by genomic techniques . PolygenWe also note the increase in methodologies focused on identifying genetic variants that are associated with the amount of variation in the outcome rather than strictly the level . Such apϒ may have crucial implications for conducting GxE studies. When ϒ is a discrete outcome coarsened from an underlying continuous variable, researchers encounter an opportunity to mis-interpret affirmative findings of GxE. For simplicity of exposition, we focus on the simplest case where ϒ is dichotomous . Suppose a dichotomous outcome ϒ is a coarsened version of some continuously varying latent indicator ϒ* . For example, ϒ might be obesity or college completion . Suppose we estimate ϒ* instead of ϒ and yield a nonzero and statistically significant b3. How should we interpret such a finding? One possibility is that a finding of GxE suggests differences in the slope of association between G and ϒ*. This, we argue, is what researchers generally have in mind when conducting studies testing for GxE. However, a second possibility is that a purely environmental shock may shift the intercept of the association line between G and Y*, thus resulting in a GxE finding  with different interpretation.Characteristics of the distribution of ϒ* in ϒ in b3) but they may suffer from low power  due to low variability in the dichotomized outcome at some regions of the environmental measure. This problem may be even more severe when gene–environment correlation results in a large shift in the distributions of the PGS along the range of the environmental measure.We illustrate the basic problem in ϒ* is of less interest than the dichotomized ϒ  or when ϒ* is latent. However, we also need not confuse matters by misunderstanding the nature of the associations in question. If findings are driven by differences in intercepts and relatively consistent slopes, as in 5Findings such as those in When research uses coarsened outcome variables due to substantive interest in the coarsened outcome themselves , sensitivity analyses that probe the issue considered here based on the underlying (noncoarsened) variable are essential. Such analyses will help to better contextualize findings from coarsened variables. In analysis of binary outcomes for which no underlying continuous variable is available , utilization of multiple methods, such as both logistic and linear probability models, may be used to probe for sensitivity of the results to the functional form of the model. This will be especially important when the environment is itself nontrivially correlated with the outcome under study.Although we do not focus here on coarsened outcomes that are nonbinary , we note that many of the concerns raised here would be of relevance in those cases as well. At a minimum, sensitivity analyses probing the persistence of findings across a range of model specifications may be valuable. For example, in an analysis of the highest math course taken by high schools students , a varieG, which results from imprecise estimates of the GWAS betas used to construct the PGS, has received some attention .Measurement error acts both to bias associated parameter estimates toward zero  and to dttention . However6 We assume that we measure both the PGS and the target environmental variable with error. We focus on variation in the reliability of the environmental measure (the x axis) and choose two levels of reliability  of 0.25 (on left) and 0.5 (on right) for the PGS; we view these reliabilities as representative of relatively weak and relatively strong polygenic scores given existing GWAS. The main takeaway is that ignoring measurement error with respect to the environment inevitably leads to inflated power calculations.N = 10,000 will suffer from power limitations when the environment is also measured with substantial error. These calculations are based upon a toy model that might not be relevant in all cases, but given that interaction studies are power-hungry even without considering measurement error  in the case where we have 1,000 respondents. We first assume that there is no error in our environmental measure (region emphasized in gray rectangle). In such a case, power is below standard levels of acceptability (power = 0.8). As the reliability of our environmental measure declines, however, power becomes increasingly poor. Even when the environment is measured with decent reliability , power is greatly reduced (power = 0.4). In the case where the PGS is of lower reliability, power is even worse . When the PGS is measured with substantial error , even relatively large samples (when considering population-based studies) of nt error , our modWe recommend that power analyses be the norm (and not the exception) in GxE research. Traditional power analyses are used to inform key design features, such as the sample size, prior to the implementation of a study. In contrast, power analyses of the type considered here offer information about the power of a study design given existing data  and key assumptions about the relevant parameters. In particular, power analyses specifically designed to offer insights into the level of power available given measurement error in both the polygenic score and the environment would be valuable additions when planning analyses of data that are already available. As Selection processes complicate inference in observational settings in a number of ways, and studies of GxE are no exception. An often-underappreciated point is that sample selection issues threaten both external and internal validity. We discuss several  types of selection that are particularly relevant for GxE research. These sample selection processes limit the population to which GxE findings can be generalized and may lead to spurious results via collider bias . NotablyWe begin with mortality selection. Such selection occurs when a nonrandom subset is lost to mortality and therefore not observed. In studies of older respondents , mortality selection tends to make the resulting sample “healthier, wealthier, and wiser” . MortaliA second issue is that demographic factors play a role in who gets included in genetic studies. This, in turn, has implications with respect to the populations to which results using genetic subsamples may generalize. Of particular note is the massive overrepresentation of European-descent individuals in both GWAS  and PGS These selection problems offer both internal and external validity threats to GxE studies that are important to consider carefully. An additional concern is that nonrandom selection into the analytic samples used in empirical studies may lead to reduced environmental variation further challenging attempts to make accurate inferences regarding GxE. As an illustration, we consider two key adolescent environments—the socioeconomic circumstances of home  and the Issues concerning selection require careful attention. Second, on the analytic side, attempts to model the relevant selection processes may lead to direct insights into the degree of generalizability of patterns. For example, researchers may examine how results change when using formal techniques that correct for selection . Even lGxE characterizes both the environmental contingency of genetically linked processes and the genetic contingency of environmentally linked processes. In our view, GxE studies involving human behavior and polygenic scores may offer valuable insights but are also at risk of repeating many of the mistakes made by previous eras of research . Our goal has been to emphasize the need for careful thinking about the rationale and methods underlying investigations of GxE.In particular, we highlighted four issues—selection of the relevant environment, analysis of coarsened outcomes, the role of measurement error, and issues of sample selection—that deserve additional scrutiny in future research. We also attempted to offer recommendations for beginning to address each problem. We readily acknowledge that ours are a relatively modest set of recommendations that will not fully resolve the vast range of analytic and inferential challenges associated with GxE research with PGSs.useful models of human behavior. In our view, useful models avoid unnecessary complexity when accounting for messy data. At its best, GxE research can help inform the construction of such models by parsimoniously showcasing complexities from empirical reality that need to be accounted for. For instance, GxE research can help reveal important heterogeneity in developmental processes, treatment responses, and policy effects. To be informative, however, we must exercise care. Otherwise, GxE research threatens to introduce confusion into the already challenging landscape of social and behavioral science research.An overarching goal of research examining the combined genetic and environmental contributions to human behavior is to help construct Exactly how predictive a PGS is of a given trait depends on both on the trait’s heritability and the sample size of the GWAS used to derive the effect size estimates; see We note that one could alternatively discuss environmental effects differing as a function of genetics; we utilize the original formulation in this article but note that the latter may occasionally be the more germane.In practice, polygenic scores may contain information on correlated nongenetic factors  in addition to true genetic risk .Specifically, convex lenses have such image-inverting properties. Here we use “lens” as shorthand for convex lens but note that concave lenses do not have this property.https://twitter.com/Joni_Coleman/status/1220332653599186946?s=20.For a similar observation in a different context, see https://gist.github.com/ben-domingue/6f14e3c4532ecb62df5f6e0c44c60411.Code available here:


Globally, sorghum is the fifth most important crop, which is used for food, feed and fuel. However, its production and productivity are severely limited by various stresses, including drought. Hence, this study aimed to determine the responses of different drought-tolerance related traits in the Ethiopian sorghum germplasm through multi-environment field trials, thereby identifying novel sources of germplasm that can be used for breeding the crop for drought-tolerance. Three hundred twenty sorghum landraces and four improved varieties were grown at three sites within drought-prone areas  in Ethiopia. The targeted traits were chlorophyll content at flowering (CHLF), chlorophyll content at maturity (CHLM), green leaf number at flowering (GLNF), stay-green (SG), flag leaf area (FLA), peduncle length (PDL), and panicle exertion (PAE). Multi-variate analyses of the collected data revealed the presence of high phenotypic variation in all traits. The combined and AMMI Analysis of variance showed that phenotypic variation due to the genotypes was higher for SG, CHLM, CHLF and GLNF and lower for FLA, PE and PDL in comparison with variation due to the environments or genotype by environment interactions. High broad sense heritability was observed for CHLF, CHLM, SG, GLNF, FLA, and PDL, whereas PAE showed moderate heritability. Due to the high heritability of chlorophyll content and the relatively small effect of environmental factors on it, it could serve as a criterion for selecting desirable genotypes for drought-tolerant breeding in sorghum. It has been found that chlorophyll content has a significant positive correlation with stay-green and grain yield, indicating that high chlorophyll content contributes to increasing grain yield by delaying the process of leaf senescence. The analyses of AMMI, GGE biplot, and genotype selection index revealed that several sorghum landraces outperformed the improved varieties with respect to CHLF, CHLM, and SG. Such landraces could serve as novel sources of germplasm for improving drought tolerance through breeding. Sorghum bicolor (L.) Moench] ranks fifth among the most important cereal crops in the world, after maize, rice, wheat, and barley (−1) of average productivity . On each plot, the seeds were sown in a single 3 m long row and planting was done manually followed by thinning to 0.20 m space between plants. The recommended amount of 100 kg ha-1 DAP fertilizer was applied during planting and 50 kg ha-1 of urea was side dressed 40 days after planting. The recommended field management practices were followed for sorghum field experiments.The 324 sorghum genotypes were evaluated during the main crop-growing season in 2019 at three commonly used testing sites for moisture-stress research: Melkassa (MK), Mehoni (MH), and Mieso (MS). The sites are within moisture stress areas in Ethiopia where smallholder farmers predominantly grow sorghum. The detail descriptions of the sites are presented in All phenotypic data were collected from five randomly selected and tagged plants in each plot. Chlorophyll content of the flag leaves of sorghum plants was measured at flowering (CHLF) and maturity (CHLM) stages using SPAD chlorophyll meter. Green leaf number was recorded by counting the number of green leaves of each plant at a flowering stage (GLNF). Based on via the application of cor.test function in R software. The scatter plots and histograms were generated by applying the chart.Correlation function within the Performance Analytics package (2) of all traits was calculated by META-R software  was carried out using the mixed linear model in R software . The gen package . The brosoftware .2 with a mean value of 218.9 cm2. The mean values of panicle exertion (PE) and peduncle length (PDL) were 6.0 cm and 31.8 cm with individual values ranging from 0.0 to 23.2 cm and 16.3 to 62.5 cm, respectively  as well as the stay-green genotype (B35) in terms of chlorophyll content at the flowering stage Table 2.P < 0.001). These two traits showed highly significant positive correlations with SG (P < 0.001). On the other hand, GLNF was negatively correlated (P < 0.001) with FLA (r = -0.23), PAE (r = -0.25) and PDL (r = -0.40). GY showed significant positive correlations with CHLF (r = 0.16), CHLM (r = 0.16), and GLNF (r = 0.48) and significant negative correlations with FLA (r = -0.12), PAE (r = -016), and PDL (-0.30). PAE showed a highly significant positive correlation with PDL . PAE also showed significant positive correlation with CHLF (r = 0.15), CHLM (r = 0.16), and SG (r = 0.21)  for all traits studied . In the case of FLA, the environmental variance accounted for 43.7% of the total variance whereas genotype and G×E interaction contributed 21.4% and 15.6% to the total variance, respectively. The proportion of the total variance explained by genotype, environment, and G×E interaction for PAE was 30.0%, 3.9%, and 33.4%, respectively. For PDL, environment effects accounted for 81.6% of the total variance whereas genotype and G×E interaction contributed 11.4% and 4.3% to the total variance, respectively  of 0.09, 0.10, and 0.11 were the lowest Table 3,The interaction pattern between genotypes and environments and the best performing genotypes were visualized through the Which-Won-Where polygon view of the GGE biplot Figure 4In “which-won-where” GGE biplot, lines from the origin divide the biplot into different sectors and create different mega environments (MGEs) . In thisThe rank of mean performance and stability of genotypes were evaluated in ranking biplot through the average environment coordinate (AEC) as described in . The aveIn the ranking biplot, the length of the vectors (green dotted lines in the graph) between the genotype positions and the AEA indicates the stability levels of the genotypes Figure 5This study revealed that there exists substantial phenotypic variation within the Ethiopian sorghum gene pool for the drought-tolerance related traits studied across three locations. The observed phenotypic variation in this study and previous studies on Ethiopian sorghum  suggestsThe significant positive correlation observed among the chlorophyll content and grain yield is in agreement with previous studies in sorghum  and otheThe present study confirmed that genotype, environment and G×E interaction have significant effects on the drought-tolerance related traits . This highlights the significance of multi-environment field trials for genotype evaluations aimed at the identification of stable genotypes with a high mean performance for the studied traits. The phenotypic variation due to genotype was high for SG, CHLM, CHLF and GLNF, indicating that genotypes played a larger role in phenotypic variation than environments. The effects of environment and G × E interaction were higher for FLA, PE and PDL, indicating that the effects of genotypes on the phenotypic variation in these traits were lower.High genetic variation exists in the Ethiopian sorghum gene pool , which hIn AMMI analysis, low values of the stability parameters, ASV, EV, SIPC, WAAS and ZA indicate high stability of genotypes and low G×E interaction . In thisThe best performing genotypes could be selected through interpreting the G×E interaction, MGE clustering, and Which-Won-Where GGE biplot that show a particular adaptation of genotypes . In the GGE ranking biplot are commonly used to select top ranking and stable genotypes across environments through based on AEC . In thisPhenotypic evaluation is vital for efficient selection of crop germplasm for conservation and use in plant breeding programs. In this regard, the landrace accessions remain a vital source of novel alleles for traits of interest. Ethiopian sorghum landrace accessions possess significant phenotypic variation for all drought-tolerance related traits  targeted in the present study. This suggests the high possibility of identifying novel drought-tolerant sorghum genotypes within the Ethiopian sorghum gene pool, which consists of a large collection of sorghum germplasm in the national gene bank, which has not yet been evaluated for drought tolerance. High broad-sense heritability observed for the studied traits suggests a strong genetic control, which is a favorable opportunity for improving the traits through crossbreeding and selection. The analysis of variance confirmed that genotype, environment, and G×E interaction have significant effects on the studied traits. Hence, multi-environment field trials should be conducted for reliable identification of top performing and stable genotypes in terms of drought tolerance. Overall, G222, G53, G239, G48, G66, and G175 for CHLF, and G53, G308, G54, G118, G114, and G321 for CHLM were identified as stable genotypes with high mean performance, and could be prioritized for use in sorghum breeding programs. The landrace accessions identified as having a better mean performance than the improved varieties with respect to their chlorophyll content could be potential sources of novel alleles for drought tolerance. Hence, they should be further investigated through methods such as genome-wide association studies.The original contributions presented in the study are included in the article/All authors conceived and designed the experiment. ME conducted the experiment, analyzed the data and wrote the draft manuscript. MG, TF, AC, CH, KT and AS reviewed the manuscript. All authors contributed to the article and approved the submitted version.