Integrative Mendelian Randomization for Detecting Exposure-by-group Interactions Using Group-Specific and Combined Summary Statistics

Integrative Mendelian Randomization for Detecting Exposure-by-group Interactions Using Group-Specific and Combined Summary Statistics | medRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-P4HH5NV'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search Integrative Mendelian Randomization for Detecting Exposure-by-group Interactions Using Group-Specific and Combined Summary Statistics Ke Xu , Nathaniel Maydanchik , Bowei Kang , Jianhai Chen , Qixiang Chen , Gongyao Xu , Shinya Tasaki , David A. Bennett , Lin S. Chen doi: https://doi.org/10.1101/2025.01.26.25321136 Ke Xu 1 Department of Public Health Sciences, The University of Chicago , Chicago, IL, USA 2 Department of Applied and Computational Mathematics and Statistics, University of Notre Dame , IN, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Nathaniel Maydanchik 1 Department of Public Health Sciences, The University of Chicago , Chicago, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Bowei Kang 1 Department of Public Health Sciences, The University of Chicago , Chicago, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Jianhai Chen 1 Department of Public Health Sciences, The University of Chicago , Chicago, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Qixiang Chen 1 Department of Public Health Sciences, The University of Chicago , Chicago, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Gongyao Xu 1 Department of Public Health Sciences, The University of Chicago , Chicago, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Shinya Tasaki 3 Rush Alzheimer’s Disease Center, Rush University Medical Center , Chicago, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site David A. Bennett 3 Rush Alzheimer’s Disease Center, Rush University Medical Center , Chicago, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Lin S. Chen 1 Department of Public Health Sciences, The University of Chicago , Chicago, IL, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: lchen4{at}bsd.uchicago.edu Abstract Full Text Info/History Metrics Supplementary material Data/Code Preview PDF Abstract Interactions between risk factors and covariate-defined groups are commonly observed in complex diseases. Existing methods for detecting interactions typically require individual-level data. The data availability and the measurements of risk exposures and covariates often limit the power and applicability in assessing interactions. To address these limitations, we propose int2MR, an integrative Mendelian randomization (MR) method that leverages GWAS summary statistics on exposure traits and group-separated and/or combined GWAS statistics on outcome traits. int2MR can assess a broad range of risk exposure effects on diseases and traits, revealing interactions unattainable with incomplete or limited individual-level data. Simulation studies demonstrated that int2MR effectively controls type I error rates under various settings while achieving considerable power gains with the integration of additional group-combined GWAS data. We applied int2MR to two data analyses. First, we identified risk exposures with sex-interaction effects on ADHD, and our results suggested potentially elevated inflammation in males. Second, we detected age-group-specific risk factors for Alzheimer’s disease pathologies in the oldest-old (age 95+), many of which were related to immune and inflammatory processes. Our findings suggest that reduced chronic inflammation may underlie the distinct pathological mechanisms observed in this age group. int2MR is a robust and flexible tool for assessing group-specific or interaction effects, providing insights into disease mechanisms. Introduction Complex diseases often arise from a combination of genetic, environmental, and biological factors, resulting in varied effects of risk factors across different subgroups., 1 , 2 These group-specific risk effects, also known as exposure-by-group interaction effects, play a critical role in disease mechanisms. 3 , 4 For example, genetic variations may influence susceptibility to risk factors such as diet, pollution, or lifestyle within specific populations. 5 – 11 Biological differences, such as age and sex, may lead to different disease pathways across groups. 12 – 21 Additionally, social determinants of health, including access to healthcare and socioeconomic status, may shape exposure-disease relationships differently for various groups. 22 – 24 Understanding these exposure-by-group interaction effects is crucial for advancing research on disease mechanisms and precision medicine. By considering group-specific effects, precision medicine can better address the unique risks of diverse populations and improve health outcomes, especially for vulnerable populations. To assess exposure-by-group interaction effects, a common approach is interaction analysis, which estimates both the effects of risk exposures and their interactions with groups or covariates on disease outcomes. 25 These analyses, though, are often constrained by small sample sizes and the limited availability of risk exposure and covariate measurements within individual studies. Moreover, unmeasured confounding variables can bias the results, complicating causal interpretations. Two-stage least squares (2SLS) methods have been applied to detect interactions while allowing for unmeasured confounding under certain assumptions. 26 However, their applicability is also restricted to studies with individual-level data, and the power is constrained by the strength of the instruments in the data. Mendelian randomization (MR) is a powerful tool to evaluate the causal effects of risk exposures on complex disease outcomes, treating genetic variants associated with exposures of interest as instrumental variables (IVs). 27 –30 Two-sample MR, which uses two sets of genome-wide association study (GWAS) summary statistics as input, has achieved many successes in assessing the causal effects of complex traits as exposures on various diseases as outcomes. 31 – 42 Most existing MR methods are designed to assess total effects, with limited focus on detecting exposure-by-group interaction effects. While some recent MR methods were proposed to detect interaction effects, 3 , 4 they require individual-level data on exposure, outcome, and the covariate group variables. The growing availability of GWAS summary statistics highlights the need for two-sample MR methods to detect interactions across covariate-defined groups using summary data. Here we propose an int egrative MR method for detecting int eraction effects (int2MR) between exposures and covariate groups on complex diseases, using only summary statistics as input. The int2MR method integrates group-specific and group-combined GWAS summary statistics from multiple studies and consortia, enhancing the power to detect group-specific effects of risk exposures. Through extensive simulations and method comparisons, we demonstrated the advantages of the proposed int2MR method for detecting interactions and main effects. We applied the proposed int2MR method to two data analyses. In the first analysis, by integrating sex-stratified and sex-combined ADHD GWAS summary statistics from the Psychiatric Genomics Consortium 43 , 44 and other major consortia, we boosted the power for identifying exposures with sexinteraction effects on ADHD. In the second analysis, motivated by the observation that AD pathology peaks around age 95 and then declines, we sought to identify risk factors with age-group-specific effects on AD pathology in the oldest-old (defined as death age 95+) compared to the rest of the population. Using int2MR, we integrated age-groupstratified GWAS summary statistics from ROSMAP (Religious Orders Study and the Rush Memory and Aging Project) 45 with publicly available GWAS summary statistics on a wide range of risk exposures from major consortia. We identified multiple immune and inflammation-related exposures with age group-differential effects on AD pathology in the oldest-old, suggesting reduced inflammation and potentially distinct neuroinflammatory mechanisms in the oldest-old compared with the rest of the population. These analyses demonstrate int2MR’s flexibility in assessing exposure-by-group interactions across diverse traits and groups (e.g., socioeconomic or environmental factors) using GWAS summary statistics. It enhances detection power for main and interaction effects by integrating group-stratified and group-combined GWAS data. Methods We propose the int2MR model to detect exposure-by-group interaction effects. We introduce two variations of the model, as illustrated in Figure 1 . In this section, we will describe the input statistics and then present the model formulation and the estimation algorithms for both variations. Furthermore, the model is flexible and can be extended to integrate IV-to-outcome statistics from mixed groups with varying group compositions (see Supplemental Information for details). Download figure Open in new tab Figure 1: Illustrations of the proposed int2MR framework for detecting interaction effects. (a) The causal diagram of the int2MR model, using summary statistics from two group-specific IV-to-outcome GWASs as input. The model estimates the causal effect β for the reference group (Group 0) and β + β int for the comparison group (Group 1), capturing group-specific effects. (b) int2MR using two sets of group-specific IV-tooutcome GWAS statistics and one set of group-combined GWAS statistics for input. The parameter ρ represents the proportion of samples from the comparison group in the mixed-group study. The IV-to-exposure GWAS statistics in int2MR analyses are all from standard group-combined GWAS analyses. int2MR: An integrative MR for detecting exposure-by-group interaction effects with group-seperated GWAS summary statistics As illustrated in Figure 1(a) , the first variation of int2MR takes the following summary statistics as input: IV-to-exposure statistics: Standard GWAS summary statistics for the exposure trait. Group-specific IV-to-outcome statistics: GWAS summary statistics for the outcome stratified by groups (i.e. reference group and comparison group). For the j -th SNP ( j = 1, 2, · · ·, p ), let denote the observed marginal IV-to-exposure effect and its standard error obtained from a GWAS study for the exposure trait. Similarly, let and denote the observed marginal IV-to-outcome effects and their standard errors for the reference group (denoted by subscript 0) and the comparison group (denoted by subscript 1), respectively. The IV-to-outcome statistics for the two groups are obtained from group-stratified GWAS studies on the outcome trait. Suppose that are the true IV-to-exposure effects, and and are the true IV-to-outcome effects for the reference and comparison groups, respectively. For the j -th SNP as an IV, we jointly model the IV-to-exposure effect and the IV-to-outcome effects in the reference and comparison groups as: The true IV-to-outcome effects in the two groups are: Reference group (Group 0) : Γ j = β · γ j + α 0, j , Comparison group (Group 1) : Γ j = ( β + β int ) · γ j + α 1, j . Here, and represent uncorrelated pleiotropic effects 37 in the reference group and comparison group, respectively. The main effect β captures the causal effect in the reference group, while β int represents the differential effect between the comparison and reference groups, i.e., the interaction effects. This framework allows for estimating and testing any linear combination of β and β int . For example, we can separately test for non-zero group-specific causal effects, β and β + β int , for the reference and comparison groups, respectively. Additionally, we can test for non-zero interaction effects, β int . Note that the off-diagonal elements in the covariance matrices of Model (1) are non-zero if there are sample overlaps among different GWAS studies. Flexible int2MR allowing the integration of group-specific and group-combined GWAS statistics The proposed int2MR model can integrate group-specific and group-combined GWAS statistics for the outcome disease/trait, enhancing the power and flexibility of the analysis. As illustrated in Figure 1(b) , the second variation of int2MR can utilize the following types of summary statistics as inputs: IV-to-exposure statistics: Standard GWAS summary statistics for the exposure trait. Group-specific IV-to-outcome statistics: GWAS summary statistics for the outcome stratified by group, which could be statistics specific to the reference group, the comparison group, or both. Group-combined IV-to-outcome statistics: Standard GWAS summary statistics for the outcome trait derived from mixed-group samples, with a known proportion of group composition, ρ . For the j -th SNP as an IV, we jointly model the IV-to-outcome effect for each input study and the IV-to-exposure effect as follows: Note that the covariate matrices above may have non-zero off-diagonal elements if the input GWAS datasets have overlapping samples. These details were omitted here for clarity in presenting the main model. The true IV-to-outcome effect in each study with varying proportions of comparison group samples is specified as: where ρ k represents the proportion of comparison group samples in the k -th study. For the study with only reference group samples ( k = 0), ρ 0 = 0; for the study with only comparison group samples ( k = 1), ρ 1 = 1; and for the study with group-combined samples ( k = 2), ρ 2 reflects the proportion of the comparison group samples in the study. Here, is the uncorrelated pleiotropic effect for each study. The causal effect of the reference group is β , and the causal effect of the comparison group is β + β int . The interaction effect β int captures the difference in causal effects comparing the comparison group versus the reference group. To obtain the parameter estimates and inference of the above models, we build a Bayesian hierarchical model. We implement a No-U-Turn sampler (NUTS) 46 , a variant of the Hamiltonian Monte Carlo method 47 , to generate posterior samples for inference. By the Bernstein–von Mises theorem, the posterior distribution asymptotically approaches a normal distribution. We estimate the standard errors of β and β int using the observed Fisher information matrix, denoted as , where Θ = ( β, β int , γ, α 0 , α 1 , α 2 ) represents the vector of all model parameters. The observed Fisher information matrix is computed from the Hessian of the negative posterior log-likelihood, yielding and . Further algorithmic details are provided in the Supplemental Information. Model (1) integrates group-separated GWAS statistics on outcome and Model (2) integrates group-separated and combined GWAS statistics on outcome. Additionally, int2MR is generalized to integrate group-combined GWAS statistics on outcomes from two or more studies with varying group compositions. See Supplemental Information for details. For instance, when analyzing causal effects of male and female groups, we can integrate GWAS statistics on outcome from the Million Veteran Program (MVP), 48 , 49 which consists of approximately 91.8% males, with another GWAS with an equal proportion of males and females. This flexibility allows int2MR to efficiently combine data from diverse sources, enhancing statistical power and enabling robust inference. Compared to existing MR methods for detecting interaction effects, 3 , 4 a key innovation and major advantage of our model is that it requires only summary statistics. This approach provides unparalleled flexibility in assessing group-specific effects of risk factors on complex diseases, even when individual-level data on risk exposures are incomplete or unavailable. For example, in our data analysis, we evaluated agegroup-specific risk factors for Alzheimer’s disease (AD), with a focus on the oldest-old (death-age 95+). Using the ROSMAP study, we obtained age-group-separated GWAS statistics on AD for the oldest-old and those for all samples in ROSMAP as groupspecific and combined IV-to-outcome statistics, respectively. Publicly available GWAS statistics for various complex traits, sourced from other GWAS consortia, served as IV-to-exposure statistics. Notably, many of these risk exposures are not directly measured in the ROSMAP data. Yet, our method can assess their interaction effects and age-group-specific contributions to AD and pathologies. Allowing correlated SNPs as IVs by accounting for linkage disequilibrium (LD) We extend the int2MR model to allow moderately correlated SNPs as IVs by modeling the LD structure: where and γ = ( γ 1 , γ 2 , · · ·, γ p ) are the vectors of estimated and true marginal IV-to-exposure effects, respectively. and Γ k = (Γ k ,1 , Γ k ,2 , · · ·, Γ k,p ) ? are the vectors of estimated and true marginal IV-tooutcome effects in the k -th GWAS sample ( k ∈ {0, 1, 2}). and are the corresponding diagonal matrices of standard errors; and R is the estimated correlation matrix among all selected IVs, which could be estimated using an independent reference panel data. This framework allows for weak to moderate correlations among IVs by accounting for their correlation structures. However, the application of int2MR may not be suited when IVs are highly correlated. Results Simulations to evaluate the performance of int2MR in detecting interaction and main effects We evaluated the performance of our proposed summary-statistics-based MR method, int2MR, by comparing it with existing methods that utilize either individual-level data or summary statistics. We simulated individual-level genotype data for GWASs of both the exposure and the outcome traits. For the outcome GWAS, we simulated GWAS datasets with group-specific effects, and generated both group-specific and group-combined GWAS summary statistics. In each simulation, we generated 300 SNPs as IVs. For the group-specific GWAS, we simulated 1,000 individuals for the comparison group and 2,000 for the reference group, and each group has group-specific effects. We calculated group-combined GWAS summary statistics by combining data from both the reference group and the comparison group. The total sample size for the mixed group was varied to investigate its effects on method performance, in particular power. In the group-combined GWAS data, individuals from the reference and comparison groups were represented in equal proportions. From the simulated datasets, we obtained the IV-to-exposure GWAS summary statistics, as well as group-separated and group-combined GWAS summary statistics for the outcome. These summary statistics were used as inputs for our int2MR analyses. We selected the appropriate input data type, either individual-level data or summary statistics, for specific comparison method (See Supplemental Information for additional simulation details). We evaluated the type I error rates and power using a p -value threshold of 0.05. Table 1(a) compares the type I error rates of int2MR using group-separated GWASs with int2MR +20k integrating an additional group-combined GWAS consisting of 20,000 mixed-group samples. Additionally, we compared with the 2SLS method for interactions 26 and standard interaction tests based on ordinary least squares (OLS) regression. We simulated various settings with and without horizontal pleiotropy and with varying strengths of confounding effects. In all settings, the proposed int2MR approach, using both group-separated and group-combined GWAS statistics for outcomes, controlled type I error rates. In contrast, the 2SLS method for interactions failed to control type I error rates in the presence of pleiotropy, and the OLS-based interaction test failed to control type I error rates in the presence of confounding. Table 1(b) compares type I error rates for testing non-zero total effects for int2MR and other existing MR methods under group-specific pleiotropy and confounding. For int2MR and int2MR+20k, the null hypothesis H 0 : β = β int = 0 was tested. For competing MR methods, IVW, 31 MR-Egger, 32 MR-Median, 50 MR-RAPS, 33 and MR-cML 36 , we tested for total effects since these methods do not assess interactions. The proposed int2MR methods consistently controlled type I error rates, whereas some competing methods showed slight inflation in type I error rates under group-specific pleiotropy or confounding. View this table: View inline View popup Download powerpoint Table 1: Simulation results comparing the type I error rates of different methods in different settings: with and without horizontal pleiotropy effects ( α ) and in the presence of confounders ( U ). For int2MR, we integrated group-separated GWASs for reference and comparison groups on outcome. In int2MR +N , the subscript “+N” represents the additional sample size from the group-combined GWAS. Among the competing methods, individual-level data-based approaches, such as 2SLS and OLSbased interaction tests, can test for interaction effects, while summary-statistics-based MR methods are limited to testing total effects. (a) Type I error rate comparisons for testing interaction effects ( β int ), in the presence of (group-specific) confounding and pleiotropy. (b) Type I error rate comparisons for testing total effects, in the presence of (group-specific) confounding and pleiotropy. Figure 2(a) compares the power of different methods for detecting interaction effects. While 2SLS and OLS require individual-level data, int2MR demonstrated comparable power to the OLS-based interaction test with 2,000 samples from the reference group and 1,000 from the comparison group. When additional group-combined GWAS statistics with larger sample sizes (10k, 20k, and 50k) were integrated, int2MR showed a substantial power improvement. Figure 2(b) compares the power for detecting both main and interaction effects. For 2SLS, OLS, and int2MR, we tested non-zero main and interaction effects, while for other summary-based MR methods, we tested total effects. int2MR improved power by jointly testing for main and interaction effects. Download figure Open in new tab Figure 2: Simulation results comparing the power of int2MR with competing methods. (a) Power comparison for detecting interaction effects. The method int2MR +N integrates group-separated GWAS data with a group-combined GWAS dataset, where the subscript N represents the sample size of the group-combined GWAS. Comparison methods are 2SLS and OLS-based interaction test, both requiring individual-level data. (b) Power comparison for detecting non-zero causal effects. We test for non-zero main or interaction effects for 2SLS, OLS-based interaction, and int2MR. For existing MR methods (colored green), we test for total effects. In summary, the simulations showed that int2MR effectively controls type I error rates in the presence of pleiotropy and confounding. In addition, int2MR demonstrated strong power in detecting interaction effects and group-specific causal effects. The integration of group-combined and group-separated GWASs on outcomes further enhanced its power. Data Analysis: Identifying Risk Factors with Sex-Biased Effects on ADHD Attention-deficit/hyperactivity disorder (ADHD) is a sex-biased condition, with males significantly more likely to be diagnosed than females. 51 – 53 These observed sex differences suggest that certain risk factors may have varying causal effects depending on sex. Identifying and understanding these sex-specific effects and their mechanisms are crucial for improving diagnosis and developing targeted interventions for both sexes. In this analysis, we leverage existing GWAS summary statistics to systematically identify potential risk factors with sex-biased effects on ADHD. We applied the proposed int2MR method to evaluate the interaction effects between risk exposures and sex groups on ADHD. The IV-to-exposure statistics were obtained from publicly available GWASs for 33 complex traits and diseases related to immunology, metabolism, gastrointestinal health, cardiovascular health, dermatological conditions, and brain function. The IV-to-outcome GWAS statistics on ADHD were obtained from the Psychiatric Genomics Consortium (PGC), including two sexstratified ADHD GWAS datasets as well as a sex-combined dataset. The male-only GWAS included 32,102 individuals of European ancestry, while the female-only GWAS included 21,191 individuals. 54 Additionally, we used a larger sex-combined GWAS dataset consisting of 224,534 individuals, approximately 49.61% females 43 . We first applied int2MR using only sex-stratified ADHD GWAS statistics as the IV-to-outcome statistics. Additionally, we expanded the int2MR analysis by integrating sex-stratified GWAS statistics with a larger sex-combined GWAS to enhance the power for detecting interaction effects. For each exposure, SNPs significantly associated with the exposure ( p -values ≤ 5 × 10 −8 ) were selected as IVs, followed by LD clumping with an r 2 threshold of 0.05. At a false discovery rate (FDR) threshold of 0.1, we identified 10 traits with significant sex-biased effects on ADHD by integrating of the large sex-combined GWAS. In comparison, int2MR using only sex-stratified GWASs identified 8 of these exposures. See Table 2 for the list of ten exposures with significant sex-interaction effects on ADHD. Overall, we observed more significant p -values for the exposures when integrating the sex-combined GWAS. The results demonstrate improved power in detecting interaction effects by integrating sex-combined GWAS summary statistics. View this table: View inline View popup Download powerpoint Table 2: Results on ten risk exposures with significant sex-interaction effects on ADHD (FDR ≤ 10%) identified using int2MR. The left panel shows the results based on integrating sex-stratified with sex-combined GWAS statistics. Right shows the results based on int2MR using sex-stratified GWAS statistics only. View this table: View inline View popup Download powerpoint Table 3: Risk exposures and their age-group interaction effect estimates on three AD pathologies obtained in the int2MR analysis. The three AD pathologies analyzed are Amyloid Pathology (amyloid), Global AD Pathology Burden (gpath), and Tangles Pathology (tangles). Significant exposure-by-age-group interactions were identified at a 5% FDR threshold. Figure 3 highlights several immune-related traits with sex-biased effects on ADHD, including white blood cell count, reticulocyte count, and granulocyte count, all of which showed larger effects (in absolute value) in males compared to females. These findings are consistent with previous reports on immune-related risk factors for ADHD, 55 –57 suggesting that immune system activity may play a more significant role in ADHD development among males. Prior studies have also shown that males are more prone to increased inflammatory responses, potentially driven by hormonal influences such as testosterone, which promotes a pro-inflammatory state. 58 Additionally, hypertension has been identified as a common comorbidity in adults with ADHD. 59 We observed consistent effect estimates across the two int2MR analyses, with or without the integration of sex-combined GWAS data. By leveraging existing GWAS summary statistics for risk exposure traits and outcome traits from multiple data sources and studies, int2MR enables an efficient evaluation of interaction effects across a wide range of exposures. This is particularly valuable for assessing interactions of risk exposures that are not measured in the studies of outcome traits, making int2MR a powerful and versatile tool for addressing research questions that would be infeasible to study using interaction analysis methods requiring individual-level data. Download figure Open in new tab Figure 3: A forest plot of causal effects for risk factors with significant sex-biased effects, stratified by sex (female vs. male). Many of these risk factors are immunerelated traits. Blue points represent male-specific effects, while red points represent female-specific effects. Data Analysis: Identifying Age-Group-Specific Risk Factors for Alzheimer’s Disease in the Oldest-Old AD and related dementias (ADRD) present a significant public health challenge, particularly as life expectancy continues to rise. Age is the primary risk factor for ADRD. A recent analysis of data from the Religious Orders Study and Rush Memory and Aging Project (ROSMAP), 45 , 60 , 61 involving 1,420 autopsied individuals, found that the probability of Alzheimer’s dementia and cognitive impairment increases with age. Interestingly, a nonlinear relationship was observed for AD pathology, which peaks around age 95 and then slightly declines. 62 This pattern was evident in several AD pathology measures, including global AD pathology burden (gpath), amyloid, and PHF tau tangle density (tangle). In contrast, non-AD pathologies, except for TDP-43, continue to increase beyond age 95 in severity. Survival bias is unlikely, as the nonlinear trajectory with age is observed only for AD pathologies, while non-AD pathologies increase linearly with age. These findings highlight the need to understand the unique biology and mechanisms of neuropathologies in the oldest-old (death-age 95+) to develop effective prevention and treatment strategies for this rapidly growing age group. To identify risk factors with age-group-specific effects on AD and pathologies in the oldest-old compared to the rest, we applied the int2MR method. We examined 35 complex traits and diseases as exposures. We obtained the GWAS summary statistics for clinically diagnosed AD, three AD pathologies (gpath, amyloid, tangle), and three non-AD pathologies including TDP-43, 63 – 67 hippocampal sclerosis (hspath), 67 – 69 and cortical Lewy body (dlbany), 70 – 72 from the ROSMAP study. The ROSMAP GWAS data included 2,587 individuals, 408 of whom were 95 years or older at the time of death. We also obtained the GWAS summary statistics for only the oldest-old (N=408). For each exposure, SNPs with a p -value ≤ 10 −8 were selected as IVs, followed by LD clumping with an r 2 threshold of 0.05. The analysis was restricted to 51 exposures with at least 50 IVs after IV selection. Figure 4 presents a heatmap showing the significance of age-group-interaction effects of selected exposures (FDR≤ 0.05) on AD pathologies (bottom panel) versus non-AD pathologies (top panel). The heatmap showed that several inflammationand immune-related traits and diseases have significant age-group-interaction effects comparing the oldest-old to the others (95+ vs. 95-). Traits such as lymphocyte and eosinophil counts showed stronger associations with AD pathologies in younger individuals (below 95). However, these associations weaken or even reverse in the oldest-old, suggesting diminished immune responses in the oldest-old. In contrast, these risk factors do not have significant age-group interaction effects on non-AD pathologies. While immune-related exposures are strongly associated with non-AD pathologies, their associations are relatively consistent across age groups (95+ vs. 95-). Download figure Open in new tab Figure 4: A heatmap showing age-group interaction effects on AD pathologies (bottom panel) and non-AD pathologies (top panel), comparing the oldest-old to younger age groups (95+ vs. 95-). Significant interaction effects were observed for several immune-related traits on AD pathologies. In contrast, these risk exposures showed less differences in effects comparing the two age groups, i.e., weaker age-group interactions for non-AD pathologies. These findings underscore distinct pathological mechanisms in the oldest-old compared to the rest. The role of neuroinflammation in AD progression has been welldocumented, with inflammation and immune responses driving the accumulation of AD pathology. 73 – 75 However, the reduced association between immune traits and AD in the oldest-old suggests a decline in immune response and neuroinflammatory activity, potentially explaining the plateau in AD pathology accumulation in this age group. This may be due to an age-related decline in the immune system’s ability to mount an inflammatory response, along with the brain’s compensatory mechanisms. 76 – 81 In contrast, non-AD pathologies continue to increase with age, 62 , 82 which may result from a continuous and escalating inflammatory response that persists or intensifies with aging. 83 – 88 The underlying risk factors and molecular mechanisms driving these patterns in the oldest-old remain largely unexplored. Understanding the biology of AD and related pathologies is critical for developing targeted strategies for prevention, progression, and treatment. The proposed int2MR method demonstrates its advantage by leveraging age-group-specific GWAS statistics from ROSMAP, even with a limited sample size (N=408), and integrating them with publicly available GWAS data on diverse exposures. It enables the comprehensive evaluation of age-group interaction effects across a wide range of risk exposures, many of which are not directly measured in the ROSMAP dataset. Such evaluations would be infeasible with traditional interaction tests. Discussion In this study, we introduced int2MR, an integrative MR method for detecting exposureby-group interaction effects by leveraging GWAS summary statistics. int2MR combines group-separated and group-combined GWAS statistics on outcomes with GWAS statistics on exposures. The ability to use only summary statistics provides unparalleled flexibility, enabling the evaluation of group-specific effects of risk factors on complex diseases when individual-level data are incomplete or unavailable. Our simulation studies demonstrated the high power and robustness of int2MR. The method consistently controlled type I error rates in various settings. In terms of power, int2MR showed reasonable performance when using group-separated GWAS summary statistics, comparable to analyses based on individual-level data. When integrating additional group-combined GWAS data on outcomes, int2MR had substantial power improvements. We applied int2MR to identify exposure-by-sex interaction effects for ADHD, a sex-biased disorder. The analysis revealed multiple risk factors suggesting increased inflammatory responses in males. These findings are consistent with prior studies linking inflammation and immune dysregulation to ADHD. Importantly, the integration of sex-combined GWAS data improved the power to detect interaction effects, demonstrating the method’s ability to leverage additional data to improve power. We further applied int2MR to identify age-group-specific risk factors for AD pathologies, with a focus on the oldest-old. This analysis identified multiple inflammation and immune-related risk factors, suggesting that chronic inflammation is reduced in the oldest old. This may reflect an age-related decline in the immune system’s ability to mount inflammatory responses, coupled with compensatory mechanisms in the brain. In both analyses, int2MR integrated group-separated GWAS statistics on outcomes with GWAS statistics on exposures from various sources. This capability is a major advantage over existing methods that require individual-level data, allowing for the broad assessment of interactions and group-specific effects of risk factors for complex diseases. Despite its strengths, int2MR has several challenges that present opportunities for future research. First, the current MR model assumes that IVs are not associated with unmeasured confounders, an assumption relaxed by some recent MR methods for total effects. Future work could explore model extensions in this direction. Second, int2MR currently supports only binary group variables. Expanding the framework to interactions with continuous or multi-category variables would significantly broaden its utility. Another opportunity is the application of int2MR in transcriptome-wide MR analyses, enabling the detection of genetically regulated genes and molecular risk factors with interaction effects across various cellular contexts. int2MR is a flexible, robust, and scalable tool for detecting exposure-by-group interaction effects. Its ability to integrate diverse GWAS summary statistics opens new avenues for understanding the complex interplay between risk factors and group-specific disease mechanisms. Data Availability All data produced in the present study are available upon reasonable request to the authors. https://pgc.unc.edu/for-researchers/download-results/ https://adknowledgeportal.synapse.org/Explore/Studies/DetailsPage/StudyDetails?Study_Name=(ROSMAP) Data and code availability All the summary statistics used in this paper are publicly available. They can be accessed via the corresponding references. The code for int2MR is available at https://github.com/Likeli-Ke/int2MR . Our implementation of algorithms depends on rstan (available on https://CRAN.R-project.org/package=rstan ). 89 Author contributions L.S.C. conceived the project. L.S.C. and K.X developed the methods and wrote the manuscript. K.X. developed the algorithm, and conducted the simulations. K.X. and N.M analyzed the data. 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