Multivariate GWAS framework for family trios with parental phenotypes to control dynastic effects

Abstract

Background

Effect size estimates in genome-wide association studies (GWAS) and Mendelian randomization (MR) based on unrelated individuals are often confounded by dynastic effects (DE). Existing family-trio-based methods can mitigate this bias, but they typically discard parental phenotypes and cannot jointly model multiple correlated traits. We propose FT-SEM, a multivariate GWAS framework that uses structural equation modeling for family trio data, with the aim of integrating genotypes and phenotypes from parents and offspring across multiple traits to estimate direct genetic effects on a shared latent factor.

Results

Simulations demonstrated that FT-SEM yields unbiased effect estimates with well-controlled type I error, while improving statistical power over conventional trio-based models by incorporating parental phenotypic information. In a genome-wide scan of 778 UK Biobank family trios, no locus reached genome-wide significance, but the FT-SEM-derived family-corrected summary statistics for a latent obesity factor provided an unbiased outcome base for downstream MR. Two-sample MR analyses revealed that the apparent association between systolic blood pressure and obesity was substantially attenuated after accounting for familial confounding, suggesting that it may be spurious. In contrast, the effect of high-density lipoprotein cholesterol on obesity remained directionally consistent and robust, supporting a genuine causal relationship.

Conclusions

FT-SEM provides a rigorous and efficient multivariate framework that eliminates dynastic bias while maximizing the utility of family-trio data. The resulting summary statistics can be seamlessly integrated into two-sample MR analyses, highlighting the necessity of family-trio-informed multivariate modeling for guarding against spurious causal claims in complex trait genetics.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12859-026-06597-8.

Background

Mendelian randomization (MR) is a robust analytical framework that utilizes genetic variants—typically single nucleotide polymorphisms (SNPs)—as instrumental variables (IVs) to estimate the causal effect of an exposure on an outcome [1–4]. The validity of MR estimates hinges upon three fundamental assumptions: (1) relevance, the instrument must be robustly associated with the exposure; (2) independence, there must be no confounding factors influencing both the instrument and the outcome; and (3) exclusion restriction, the instrument must influence the outcome solely through the exposure. Despite its widespread application using genome-wide association study (GWAS) summary data, conventional MR approaches are increasingly recognized as susceptible to specific biases. Notably, when horizontal pleiotropy or dynastic effects (DE) are ignored, causal estimates may be substantially biased [5–7]. Dynastic effects, as illustrated in Fig. 1, represent a form of confounding specific to the family unit [8, 9]. In a family trio consisting of parents and offspring, DE arises when parental genotypes influence offspring traits through unobserved parental phenotypes or other intergenerational mechanisms. The existence of these pathways (indicated by the paths from parental genotypes to offspring phenotypes) violates the independence assumption. Accounting for parental genotypes effectively blocks these non-causal pathways, thereby yielding unbiased estimates. Furthermore, horizontal pleiotropy—where an IV influences the outcome via pathways independent of the exposure—violates the exclusion restriction. While various robust MR methods have been developed to correct for pleiotropy [7, 10–15], addressing dynastic effects requires the integration of family-level data.

Fig. 1.

Directed acyclic graphs illustrate how dynastic effects (DE) can confound both GWAS and MR analyses. In conventional population-based studies, genetic effect estimates of a single nucleotide polymorphism (SNP) on an exposure or outcome, as well as MR-based causal estimates, are susceptible to bias from unobserved confounders. Specifically, DE induces a persistent confounding structure in the SNP-outcome association through intergenerational pathways. DE can induce a statistically confounding structure in the SNP-outcome association, where F, M and O are respectively the genotypes of the parents and their offspring in a family trio, , and , , and , and , and are respectively the corresponding exposures, outcomes and confounders

To mitigate confounding induced by DE in GWAS and MR analyses, several family-based study designs have been employed [5, 8, 16–19]. These are generally categorized into three frameworks: (1) family trios, comprising genotypes and phenotypes from both parents and a single offspring; (2) mother-offspring pairs, focusing on maternal and offsprings’ data; and (3) sibling pairs, utilizing data from two or more siblings within a family. In the context of family trios, a standard approach fits a general linear model using the offspring’s phenotype as the dependent variable, conditioned on both offspring and parental genotypes [8]. While this effectively controls for DE-related bias, it essentially functions as a structural equation model (SEM) limited to observed variables, notably failing to utilize parental phenotypic information. Consequently, while the resulting summary statistics can be applied to two-sample MR, the statistical power of trio-based methods remains suboptimal. For mother-offspring pairs, existing SEM-based methods treat maternal and offspring phenotypes as observed, while modeling latent variables for ancestral genotypes (e.g., grandmother’s genotype) [17–19]. Although these methods correct for maternal DE and require fewer genotype inputs, they inherently ignore paternal effects and discard offspring genotype data. Thus, their application has been largely confined to specialized areas such as birth-weight research. Alternatively, sibling-pair designs utilize the difference between siblings’ genotypes and phenotypes to negate DE. While widely adopted due to the increasing availability of sibling data in biobanks [20, 21], this “within-sibling” method is inapplicable to trios with an only child. Crucially, none of these existing family-based GWAS frameworks have been extended to multivariate analysis. Previously, SEM has also been utilized for multivariate GWAS using data from independent individuals [22]. The core principle of this approach involves modeling the covariance structure of multiple phenotypes with a common latent factor. For instance, a single latent factor may represent the shared genetic architecture of several related traits, enabling the identification of SNPs that exert a direct effect on this unobserved common factor. There is, therefore, a pressing need for a multivariate GWAS framework—particularly for family trio data—that maximizes data utilization, accounts for DE across multiple traits, and facilitates robust two-sample within-family MR analysis.

To address these challenges, we developed FT-SEM, a structural equation modeling framework designed for family trio data that enables multivariate GWAS while accommodating flexible phenotypic relationships. This framework uniquely integrates genotypes and phenotypes from both parents and offspring within each trio, allowing for the simultaneous estimation of direct offspring, paternal, and maternal genetic effects. Through extensive simulations, we assessed the precision of point and interval estimates for both genetic and causal effects, verifying the validity of our hypothesis testing across various degrees of DE. Furthermore, we demonstrate that the summary statistics derived from FT-SEM can be seamlessly integrated with existing two-sample MR methods to facilitate robust causal inference. Finally, by applying FT-SEM to 778 family trios from the UK Biobank (UKB) and incorporating summary data from 99,998 siblings [20] or 315,133 and 757,601 independent individuals [23, 24], we underscore the necessity of family-based data for validating GWAS and MR findings. While the UKB trio sample is relatively small ( N=778), we utilize it primarily as a ‘gold-standard’ validation set to calibrate effects estimated from larger independent cohorts, effectively mitigating the influence of indirect genetic effects (e.g., DE). Our results highlight the methodological advantages of FT-SEM in maximizing data utility and ensuring the robustness of multivariate genetic analyses.

Methods

FT-SEM method

In family trios, the genetic effects at a SNP can be partitioned into paternal, maternal and offspring components (respectively denoted by , and ), which is similar to early researches [8, 18]. In this framework, the correlations among multiple phenotypes are assumed to be driven by a common latent factor. Accordingly, the primary objective is to estimate SNP effects on this underlying latent construct, which captures the shared genetic effects across phenotypes, rather than focusing on phenotype-specific effects. Therefore, SEM model (FT-SEM) for family trios can be represented as:

1

where , and are respectively the common latent factor of the father, the mother and the offspring in family  i (), where  n is the number of family trios (i.e. sample size). , and represent the intercept terms for the parents and their offspring, respectively. , , , , , and are the numbers of the genetic variants respectively corresponding to the father, the mother, the offspring and the grandparents of the offspring in family i, even if may not be collected in practice and will be regarded as latent variables in SEM later. Due to the , and are paternal, maternal and offspring effects, respectively., and are p-dimensional vectors representing the confounding variables for the parents and the offspring in family i, respectively. , and are p-dimensional vectors representing the corresponding effects of the confounding variables. represents the residual vector for family i, which follows a multivariate normal distribution, where , , and are respectively the residuals of the father’s, mother’s and offspring’s phenotypes. Here, , and are used to respectively denote the variances of the residuals of the father’s, mother’s and offspring’s phenotypes. Moreover, , and are the covariances of the residuals among the father’s, mother’s, and offspring’s phenotypes, respectively. We assumed that the genetic effects in the parental generation are respectively identical to those in the offspring generation (i.e. sharing the same , and ). This assumption has been mentioned in previous study [17]. The hidden factor is the common latent factor of the several phenotypes (denoted by ), where represents the number of corelated phenotypes. The relationship between the common latent factor and the phenotypes could be shown as .    

To ensure model identification, the latent grandparental genotypes (, , and ), are assumed to have the same variance as the observed parental and offspring genotypes (, , ). This variance, denoted Φ, is freely estimated from the observed genotype data under the assumption of Hardy–Weinberg equilibrium and a homogenous population. With this constraint and the Mendelian transmission paths fixed at 0.5, the latent genotype components of the model are identified. Note that the equality of genotype variances across generations is an identifying constraint rather than a testable assumption; its validity rests on the assumption of a single, randomly mating population with no admixture. Figure 2 presents the path diagram of FT-SEM with three phenotypes, which can be fitted using the maximum likelihood estimation with the OpenMx software package [25]. Hypothesis testing for FT-SEM is conducted using the Wald test. In this model, we simultaneously tested the paternal, maternal and offspring effects (, and ). The results can serve as summary data for various downstream analyses, including two-sample MR analysis. Of particular importance is testing the offspring effect () and to conduct its corresponding two-sample MR analysis. Note that the offspring effect is the primary target for downstream GWAS interpretation and MR analyses because it represents the direct genetic effect on the offspring phenotype. The parental effects provide complementary information regarding DE through parental phenotypes and other familial pathways. Therefore, in this study, paternal and maternal effect estimates primarily serve to characterize and quantify DE, whereas offspring effect summary statistics are the quantities required for downstream causal inference using conventional two-sample MR methods. In addition, some robust two-sample MR methods can be employed to control horizontal pleiotropy [7, 10–14]. Then, in the FT-SEM model, we assumed that there is no additional relationship between parental phenotypes and offspring phenotypes. This assumption is based on the fact that the effects of parental phenotypes on offspring’s phenotypes can be partly explained by parental genotypes, while the remaining effects could be reflected through considering the correlations between the residuals of parental phenotypes and that of offspring’s phenotype (i.e. and ). In fact, this assumption has also been made in previous structural equation models based on mother-offspring pairs [17]. Moreover, we assumed that the correlations among different phenotypes of the same individual are entirely explained by a common latent factor, an assumption that has been mentioned in the GW-SEM 2.0 model [22]. Finally, since the common latent factor is incorporated as a latent variable during model estimation, the effects are not identifiable in practice, although products such as are identifiable. As a genetic variant, the SNP generally does not affect the estimation of even if it is not included in the model. Therefore, to accurately estimate , we pre-fit a null model, FT-SEM-null, which is based on the FT-SEM but excludes all genetic variant components, thereby obtaining the estimates By subsequently fitting the FT-SEM, we can obtain biased estimates of the effects, and the factor loading, After calculating the correction factor , the accurate estimate of can be expressed as .

Fig. 2.

FT-SEM used to estimate paternal, maternal and offspring genetic effects on phenotypes. One-headed arrows represent causal paths and two-headed arrows indicate correlation relationships. The twelve observed variables (in squares) denote the father’s, mother’s and offspring’s genotypes ( F, and  O) and their phenotypes (, , , , , , and ). The latent variables (in circles) represent the genotypes of the grandparents (, , and ) and the father’s, mother’s and offspring’s common hidden factor () which causes the phenotypes. The total variances of the latent genotypes and those of the observed genotypes are set to be Ф and are estimated from the data, because we assume the variance of genotypes of mother, father or offspring are similar. The path coefficients between the offspring and their parents are both set to be 0.5 according to Mendelian inheritance. The path coefficients , and refer to paternal, maternal and offspring effects on offspring’s common latent factor, respectively

For ease of comparison, we extended the general linear model-based approach proposed by Brumpton et al. [8]. to the field of SEM, making it applicable to GWAS analysis of multiple phenotypes using family trio data, and named it PSEM. Furthermore, for independent individual data, we employed the method mentioned in the GW-SEM 2.0 paper [22] and referred to it as IndSEM in this study. The correction factor mentioned above was also applied to these two methods.

Simulation settings

Firstly, we performed the simulations to investigate the bias and the root mean squared errors (RMSEs) of the point estimate of the offspring effect , the coverage probabilities (CPs) and the average widths of the corresponding 95% confidence intervals (CIs), and the type I error rate and the test power of FT-SEM in modeling family trios. We generated the genotypes of the grandparents (i.e. , , , and ) based on MAF at a single SNP and assuming that Hardy-Weinberg equilibrium holds, and then simulated the genotypes of the parents and the offspring (i.e.  F, M, and O) according to Mendelian inheritance. Each of the SNP effect sizes and the confounding effects (i.e. and ) was set by using the Phenotypic Variance Explained (PVE) with the equation , where PVE represents the proportion of the variance in the phenotype explained by the SNP, and denotes the variance of the genotype distribution at the SNP. If was used to represent the sum of the PVE values across all the variables, then the three variances of the residuals (i.e. , and ) were assumed to be the same for simplicity and were set by using the (i.e. = = = 1 – ). We used the parameter ρ to control the correlations among the residuals with , and ρ was set to be 0.3. The simulations for GWAS were divided into three scenarios related to the magnitude of the DE: DE = 0%, DE = 0.2%, and DE = 0.4%. To simulate DE, we considered a homogenous population with MAF = 0.3 and assigned nonzero values to the parental effects ( and ). Specifically, when or is nonzero, DE is present. In our simulation study, the magnitude of DE was determined by the values of and . We assumed these two parameters to be equal, which respectively represent the variance of the paternal genetic effect and the maternal genetic effect on the offspring’s phenotype. For instance, in the scenario where DE = 0%, we set , corresponding to the , and in the scenario where DE = 0.2%, we set , corresponding to the . Then, in the scenarios where DE = 0.4%, we set , corresponding to the . For all the three scenarios simulated, the intercept was taken as 0 and we generated the values of the confounding variable  U for the father, the mother and the offspring. These values of U for the parents and the offspring were independent of each other but shared the same , corresponding to identical effects on the phenotypes (i.e. ). Then, we evaluated all the methods under both the null and alternative hypotheses. Under the null hypothesis, we set , corresponding to . Under the alternative hypothesis, we set , corresponding to . After setting the parameters, the phenotypes were generated using Eq. (1). Once the phenotypes were generated, the genotypes of the grandparents and the variables  L and  U were removed and treated as missing values. Furthermore, we considered the relationship between the common latent factor and the phenotypes. The strength of this relationship was determined by the . In all simulation scenarios, we consider three phenotypes and set the to 0.4, 0.5, and 0.6, which correspond to , respectively. Furthermore, we considered the sample sizes ( n) of 1,000, 2,000 and 3,000, and compared the results of three methods (FT-SEM, PSEM and IndSEM). For each simulation setting, we considered 10,000 replicates. On the other hand, to evaluate the robustness of FT-SEM and other methods to the violations of some key modeling assumptions, we performed additional simulations under several model misspecification scenarios. Specifically, we considered (i) misspecification of the latent-factor structure by fitting a one-factor model to the data generated from a two-factor model, (ii) misspecification of cross-generational measurement invariance by assuming equal factor loadings when the true loadings differ across generations, and (iii) correctly specifying generation-specific factor loadings. Finally, for evaluating the practical computational burden of FT-SEM, we recorded the runtimes of FT-SEM and the competing methods under the same simulation setting (DE = 0.4%, was set to 0.4, 0.5, and 0.6) using identical hardware and software environments.      

As mentioned previously, after conducting the GWAS using FT-SEM based on family trios, the GWAS results can be applied to various downstream analyses, including two-sample MR. In this context, robust two-sample MR methods can be employed to consider horizontal pleiotropy. Therefore, we further performed the simulations to investigate the bias and the RMSE of the point estimate of the causal effect of offspring’s exposure on offspring’s outcome, the CP and the average width of the corresponding 95% CI, and the type I error rate and the test power of these two-sample MR methods. For simplicity, we selected the ratio estimation approach as the two-sample MR method, which can be considered as a simplified version of the inverse variance weighting (IVW) method with only one instrumental variable. In the two-sample MR simulation, the exposure and outcome variables (denoted as X and Y, respectively) are simulated separately. Firstly, we set , where represents the PVE of the exposure explained by offspring effect (similar to in the GWAS) and denotes the PVE of the outcome attributed to vertical pleiotropic effect in the absence of horizontal pleiotropy. Then, the generation of the exposure can follow Eq. (1), and the simulation of the outcome is also based on Eq. (1) with an additional term included to represent the causal effect of the exposure on the outcome. For simulating the exposure in all the scenarios, we set (i.e. ) and to be 5% for the exposure (i.e. ), indicating that the SNP is a strong instrumental variable. For simulating the outcome in all the scenarios, we set (i.e. ). Afte that, under the null hypothesis, we set , corresponding to , and we assumed that , corresponding to under the alternative hypothesis. Furthermore, when simulating the outcome, the direct effect between SNP and outcome is set to 0, indicating that there is no horizontal pleiotropy. When simulating the exposure in the scenario of DE = 0%, we considered a homogenous population with MAF = 0.3 and specified , which corresponds to . For simulating the outcome in the presence of DE, we used the same population and set , leading to . When simulating the scenario of DE = 0.2%, the for both simulation of exposure and outcome. Then the for both simulation of exposure and outcome under the scenarios of DE = 0.4%. In all simulation scenarios, we consider three phenotypes and then set the to 0.4, 0.5, and 0.6 for both simulation of exposure and outcome, which correspond to 0.632, 0.707, and 0.775, respectively. After generating the exposure and outcome variables, the samples were randomly divided into two parts of equal sizes. In the first part (the first sample), the outcome variable was removed to investigate the association between the offspring’s genotype and the exposure, while in the second part (the second sample), the exposure variable was deleted to study the association between the offspring’s genotype and the outcome. For each simulation setting, we used the sample sizes of 2,000, 4,000, and 6,000, ensuring that the two samples in the MR analysis had equal sizes of 1,000, 2,000, and 3,000, respectively. Finally, we considered 10,000 replicates, and we compared the results of three methods (FT-SEM, PSEM and IndSEM) with the ratio estimation approach.        

Real data applications

To evaluate the performance of FT-SEM and quantify potential biases arising from DE, we conducted family-based GWAS using the UKB resource. We subsequently integrated these results with existing sibling-based GWAS summary statistics [20] to perform within-family two-sample MR analyses. Kinship within the UKB was characterized based on kinship coefficients and the proportion of zero-state identity-by-state (IBS0) alleles provided in the official “King.n.d” file, following the rigorous filtering criteria established by Manichaikul et al. [26]. To minimize bias from population stratification and ensure compatibility with the exposure GWAS summary statistics (which were also derived from European populations), we restricted our analysis to individuals of European ancestry. All participants belonging to a full trio were selected for the analysis. Genetic data underwent stringent quality control (QC) process, including: (1) genotype call rate > 99%, (2) MAF > 1%, (3) individual call rate > 99%, and (4) Hardy-Weinberg equilibrium p value > . We extracted three anthropometric phenotypes from the UKB: body mass index (BMI), body fat percentage (BFP), and waist-to-hip ratio (WHR). These phenotypes capture complementary aspects of adiposity. BMI reflects overall body size and general adiposity, BFP directly quantifies total body fat content, whereas WHR characterizes body fat distribution, particularly central adiposity [27]. Because these phenotypes are moderately correlated and each reflects a distinct dimension of obesity, jointly modeling them through a common latent factor enables FT-SEM to capture their shared obesity-related genetic architecture while reducing phenotype-specific measurement error and biological heterogeneity. This strategy is consistent with the objective of multivariate SEM, which aims to estimate genetic effects acting on the common variance shared across correlated traits. Prior to analysis, all three phenotypes were standardized. Within the SEM framework, they were modeled jointly to capture the influence of a common obesity-related latent factor, with the goal of identifying SNPs associated with this underlying unobserved determinant of obesity. After excluding trios with missing phenotypic values, 778 complete trios were retained for the primary analysis (detailed in Supplementary Fig. 1). For comparative analysis, the IndSEM method was applied to a subset of 778 independent individuals, selected by randomly sampling one individual from each family to ensure independence.

We performed family-based GWAS on the UKB dataset using three distinct methodologies: FT-SEM, PSEM, and IndSEM. To ensure robust estimation, we adjusted for specific sets of covariates across these models. In the FT-SEM framework, we incorporated the offspring’s sex, date of birth, and age, alongside the corresponding parental ages and dates of birth. For PSEM, covariates were restricted to the offspring’s sex, date of birth, and age. In the IndSEM model, we accounted for the individual’s sex, date of birth, age, and generational cohort. Furthermore, to mitigate the potential confounding effects of population stratification, the first ten principal components (PCs) derived from all autosomal SNPs were included as fixed effects in all three models.

After the GWAS, we performed two-sample MR analyses to evaluate the causal effects of high-density lipoprotein (HDL) cholesterol and systolic blood pressure (SBP) on obesity. We selected obesity as the primary outcome and evaluated the potential causal effects of two exposure traits with distinct epidemiological profiles (HDL cholesterol and SBP). HDL cholesterol and SBP were chosen as exposures because both are well-established correlates of obesity in observational studies [28], yet their causal relationships remain contentious. A large body of conventional MR studies have reported protective effects of HDL cholesterol and casual effects of SBP on obesity-related outcomes (cardiovascular disease, coronary heart disease, etc.) [29, 30]. However, these estimates of causal effects may be confounded by DE due to shared familial environments, socioeconomic factors, and intergenerational transmission of lifestyle behaviors. By applying our FT-SEM framework to family-trio data from the UKB, we aimed to re-evaluate these causal associations in a within-family design which is robust to such confounding. The GWAS summary statistics generated from FT-SEM, PSEM, and IndSEM served as the outcome data for the downstream MR analyses described below. We assumed that SNP-exposure associations are comparable across the exposure and outcome samples, both of which were derived from European-ancestry populations. Minor differences in effect sizes due to sample characteristics remain a potential source of bias. Notably, the family trios used for our outcome GWAS were identified through stringent kinship-based filtering and comprised complete parent-offspring units; such trios were typically excluded from conventional population-based GWAS and sibling-based analyses which require unrelated individuals or sibling pairs. Consequently, our two-sample MR design involved no sample overlap between the exposure and outcome datasets.

Instrumental variables (IVs) were selected following the stringent filtering pipelines detailed in Supplementary Figs. 2–5. SNP-exposure associations were sourced from sibling-based GWAS summary statistics [20] (for FT-SEM and PSEM) or population-based GWAS data [23, 24] (for IndSEM), while SNP-outcome associations were derived from our internal UKB analyses. To mitigate weak instrument bias, we excluded variants with an F-statistic < 10, in accordance with established guidelines [31]. For the IVW analyses within the FT-SEM and PSEM frameworks, we identified 53 and 17 independent SNPs ( within 10,000 kb) significantly associated with HDL cholesterol and SBP , respectively. These variants were selected by integrating results from sibling-based GWAS (“ieu-b-4844” and “ieu-b-4818”) with our trio-based GWAS results. For the IndSEM analysis, 157 and 359 independent SNPs were selected based on identical criteria from independent GWAS datasets (“ebi-a-GCST90018956” and “ieu-b-38”). Data harmonization and clumping were performed using the TwoSampleMR [32] R package to ensure allele effect consistency across datasets.

Our primary MR analysis relies on the three core assumptions. First, the genetic variants are robustly associated with the exposure (HDL cholesterol or SBP), which we ensured by selecting genome-wide significant SNPs with F-statistics > 10. Then the genetic variants are not associated with confounders of the exposure-outcome relationship. A key feature of our study is the use of within-family GWAS (FT-SEM, and PSEM) and sibling-based exposure data, which specifically aims to satisfy this assumption by controlling for DE. Finally, the genetic variants affect the outcome (obesity) exclusively through the exposure. We assessed the plausibility of this assumption througha suite of robust sensitivity analyses (e.g., MRcML [33], MRBEE [34]) which operate under different pleiotropy assumptions. To ensure the robustness of our findings, we conducted several analyses using IVW, weighted median, weighted mode, and MR-Egger regression [32, 35, 36]. Furthermore, we employed MRcML [33] and MRBEE [34]—advanced methods capable of automated IV selection and pleiotropy adjustment—to maximize statistical power and ensure the reliability of our causal inferences [33, 34].

To evaluate whether the difference between family-based and population-based MR analyses was primarily attributable to difference in instrument selection, we performed an additional sensitivity analysis using a harmonized set of genetic instruments. Specifically, instrumental variables were selected from the sibling-based GWAS, thereby ensuring that the same SNP set was used in both MR analyses. For the exposure, SNP–trait association estimates were obtained from the sibling-based GWAS. For the outcome, SNP–trait association estimates for SBP were derived from the IndSEM-based GWAS, ensuring that both analyses used a common outcome GWAS while differing only in the exposure effect estimates. Two-sample MR analyses were then performed using the harmonized instrument set following the same analytical procedures as described above.

All statistical analyses were performed using R software (version 4.4.1). The FT-SEM model was fitted using the OpenMx package (Version 2.22.11) [25]. Two-sample MR analyses were conducted using the TwoSampleMR packages (Version 0.5.6) [32]. MRcML and MRBEE analyses were conducted using their respective R packages [33, 34]. The study protocol for this analysis was not pre-registered.

Results

Simulations for GWAS

Figure 3 illustrates the simulated biases, RMSE, CP, 95% CI widths, and type I error rates for FT-SEM, PSEM, and IndSEM. Simulations were conducted under the null hypothesis (offspring genetic variance explained = 0) with a residual correlation of 0.3 across three DE scenarios (0%, 0.2%, and 0.4%). Under the baseline scenario of no confounding (DE = 0%), all three methodologies yielded unbiased point estimates and well-controlled type I error rates. Notably, IndSEM achieved the highest statistical efficiency—characterized by the lowest RMSE and narrowest CIs—suggesting that while family-based methods ensure robustness, they involve an inherent trade-off in efficiency when confounding is absent. However, as DE increased to 0.2% and 0.4%, the performance of IndSEM deteriorated, producing increasingly biased estimates and inflated type I error rates. In contrast, both FT-SEM and PSEM maintained unbiased point estimates and CIs with coverage probabilities near the nominal 95% across all DE magnitudes and sample sizes. Critically, FT-SEM consistently outperformed PSEM, exhibiting lower RMSE and narrower CIs. This demonstrates that incorporating parental phenotypes partially recovers the efficiency loss typically associated with within-family designs. Furthermore, the RMSE for FT-SEM decreased as sample sizes increased, consistently remaining lower than those of both IndSEM and PSEM under biased scenarios. While IndSEM’s coverage probability deviated markedly from the nominal level as DE and sample size increased, FT-SEM maintained robust performance. These results underscore the superior capacity of FT-SEM to eliminate DE while maximizing estimation precision and inferential reliability. To evaluate the robustness of FT-SEM to the violations of some key modeling assumptions, we performed additional simulations under three model misspecification scenarios, including misspecification of latent-factor structure and cross-generational measurement invariance. Supplementary Table S1 showed that across all scenarios, the offspring, paternal, and maternal genetic effect estimates remained essentially unbiased. Furthermore, empirical type I error rates were well controlled and the coverage probabilities of the nominal 95% confidence intervals remained close to their expected levels. These findings suggest that FT-SEM is robust to these violations of the modeling assumptions. Besides, the computational performance of FT-SEM and the competing methods is summarized in Supplementary Table S2. As expected, FT-SEM required a longer runtime than existing approaches because the SEM was re-estimated for every SNP. Nevertheless, the computational burden remained manageable for genome-wide analyses on modern computing platforms.

Fig. 3.

Simulated biases and RMSEs, CPs and average widths of the corresponding 95% CIs and type I error rates of offspring effect estimates for FT-SEM, PSEM and IndSEM with MAF of 0.3 when the sample size is fixed at 1,000, 2,000 and 3,000, with the PVE of offspring’s phenotype explained by offspring’s genotype being set to be 0, and the residual correlation being set to be 0.3 under Dynastic effect (DE) = 0%, DE = 0.2% and DE = 0.4%. a-c Biases of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. d-f RMSEs of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. g-i CPs of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. j-l Average widths of offspring effect estimate for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. m-o Type I error rates of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively

Figure 4 presents the simulated biases, RMSEs, CPs, and statistical power for FT-SEM, PSEM, and IndSEM under the alternative hypothesis. In these scenarios, the PVE by the offspring’s genotype was fixed at 0.4% (corresponding to an effect size of 0.098). The point and interval estimation results under the alternative hypothesis were consistent with those observed under the null. As expected, the statistical power of all methods increased with larger sample sizes. In the presence of confounding (DE = 0.2% and 0.4%), FT-SEM demonstrated substantially higher power than PSEM. While IndSEM exhibited the highest nominal power, this “gain” is spurious as the method fails to maintain a calibrated type I error rate under these conditions. Conversely, under the baseline scenario (DE = 0%), FT-SEM was slightly less powerful than IndSEM but significantly outperformed PSEM. The superior power of FT-SEM relative to PSEM stems from its strategic integration of parental phenotypic data, which remains unexploited in the PSEM framework. These findings further reinforce the principle that while rigorous bias control often necessitates a trade-off in statistical efficiency, FT-SEM effectively minimizes this loss by maximizing the utility of family-trio information.

Fig. 4.

Simulated biases and RMSEs, CPs and average widths of the corresponding 95% CIs and powers of offspring effect estimates for FT-SEM, PSEM and IndSEM with MAF of 0.3 when the sample size is fixed at 1,000, 2,000 and 3,000, with the PVE of offspring’s phenotype explained by offspring’s genotype being set to be 0.4%, and the residual correlation being set to be 0.3 under Dynastic effect (DE) = 0%, DE = 0.2% and DE = 0.4%. a-c Biases of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. d-f RMSEs of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. g-i CPs of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. j-l Average widths of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. m-o Test power of offspring effect estimates for FT-SEM, PSEM and IndSEM under DE = 0%, DE = 0.2% and DE = 0.4%, respectively

Simulations for two-sample MR

Figure 5 illustrates the simulated biases, RMSEs, CPs, and type I error rates for causal effect estimates across the three methodologies. To ensure a robust instrumental variable, the PVE in the offspring’s exposure by their genotype was set to 5% (offspring effect = 0.345), thereby minimizing weak instrument bias. Under the null hypothesis (true causal effect = 0), the PVE in the offspring’s outcome attributed to their genotype was set to 0%. Consistent with the GWAS simulations, IndSEM exhibited superior efficiency only in the absence of confounding (DE = 0), characterized by the lowest RMSE and narrowest CIs. This performance advantage stems from the fact that IndSEM does not implement bias-control mechanisms, thus avoiding the efficiency loss inherent to within-family designs. However, when DE was introduced (DE ≠ 0), IndSEM demonstrated substantial bias, suboptimal CPs, and severely inflated type I error rates. Conversely, FT-SEM maintained unbiased point estimates and nominal type I error rates regardless of the DE magnitude. Notably, FT-SEM achieved the lowest RMSE and the narrowest CIs among the three methods when DE was present, outperforming PSEM in both precision and statistical power. These results indicate that the integration of parental phenotypes in FT-SEM significantly recovers the statistical efficiency lost in traditional trio-based designs.

Fig. 5.

Simulated biases and RMSEs, CPs and average widths of the corresponding 95% CIs and type I error rates of causal effect estimates of offspring’s exposure on offspring’s outcome for FT-SEM, PSEM and IndSEM with MAF of 0.3 and the residual correlation of 0.3 under the null hypothesis when the sample size is fixed to be 2,000, 4,000 and 6,000. a-c Biases of causal effect estimates for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. d-f RMSEs of causal effect estimates for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. g-i CPs of causal effect estimates for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. j-l Average widths of causal effect estimate for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. m-o Type I error rates of causal effect estimates for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively

Figure 6 summarizes the simulation results under the alternative hypothesis, where the PVE in the offspring’s exposure by their genotype was maintained at 5%, and the PVE in the offspring’s outcome was fixed at 0.4% (corresponding to a true causal effect of 0.283). Mirroring the trends observed in the GWAS simulations, FT-SEM consistently achieved the lowest RMSE and provided unbiased point estimates in the presence of dynastic effects (DE ≠ 0). Furthermore, it maintained CPs near the nominal 95% level and produced the most precise (narrowest) confidence intervals among the methods tested. Notably, FT-SEM exhibited substantially higher statistical power than PSEM, demonstrating the benefit of incorporating parental phenotypes. Conversely, while IndSEM appeared efficient under the null, it suffered from severely inflated type I error rates and compromised power when DE was present. Collectively, these findings reinforce the conclusion that IndSEM is only optimal in the specialized case where DE is entirely absent (DE = 0); once DE is introduced, FT-SEM becomes the superior choice for ensuring reliable and efficient causal inference.

Fig. 6.

Simulated biases and RMSEs, CPs and average widths of the corresponding 95% CIs and powers of causal effect estimates of offspring’s exposure on offspring’s outcome for FT-SEM, PSEM and IndSEM with MAF of 0.3 and the residual correlation of 0.3 under the alternative hypothesis when the sample size is fixed to be 2,000, 4,000 and 6,000. a-c Biases of causal effect estimates for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. d-f RMSEs of causal effect estimates for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. g-i CPs of causal effect estimates for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. j-l Average widths of causal effect estimate for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively. m-o Test power of causal effect estimates for FT-SEM, PSEM and IndSEM using the ratio method under DE = 0%, DE = 0.2% and DE = 0.4%, respectively

Real data applications

Initially, we performed a GWAS utilizing the UKB. Biological families were identified by calculating pairwise kinship coefficients, followed by a stringent filtering process to retain only complete family trios. After this multi-step screening and rigorous QC protocol, a final cohort of 778 complete trios was established. This dataset served as the basis for the subsequent comparative analyses using the FT-SEM, PSEM, and IndSEM frameworks.

We systematically compared the performance of FT-SEM, PSEM, and IndSEM using the curated UK Biobank dataset. FT-SEM and PSEM were applied to the complete cohort of 778 family trios. In contrast, IndSEM was restricted to 778 independent offspring—selected by sampling a single individual per trio—to serve as a independent-individual-based comparator. Notably, FT-SEM and PSEM allow for the simultaneous estimation of direct offspring effects alongside paternal and maternal genetic effects; the detection of significant parental effects serves as a diagnostic indicator of potential DE. Conversely, IndSEM estimates the offspring effect in isolation, potentially yielding biased results if intergenerational confounding remains unaddressed. The estimated factor loadings between the latent obesity factor and the three obesity-related phenotypes are all statistically significant (Supplementary Table S3), supporting the interpretation that BMI, BFP, and WHR capture a common underlying obesity-related latent construct. While a sample size of 778 trios lacks the statistical power to achieve genome-wide significance for complex latent factors such as obesity, the resulting association estimates remain highly informative. Crucially, these estimates provide valid, family-corrected summary statistics for use as the “outcome” component in two-sample MR analyses. This highlights the utility of the FT-SEM framework: it facilitates robust causal inference even in specialized datasets where the discovery of novel loci is constrained by sample size.

Following our GWAS of the UKB dataset, we performed two-sample MR analyses to evaluate the causal effects of HDL cholesterol and SBP on obesity. For the exposure traits (Sample 1), we utilized high-powered GWAS summary statistics: sibling-based data () were used for the within-family MR analyses, while independent-individual-based data ( and ) served as the exposure sample for the IndSEM comparison. For the outcome trait (Sample 2), we employed the offspring-effect summary statistics derived from our FT-SEM, PSEM, and IndSEM analyses of the UKB cohort. The IVW method was employed as the primary analytical approach, supplemented by a suite of robust MR estimators. We defined three distinct MR frameworks based on the source of the summary data: (1) FT-SEM and (2) PSEM, which integrate sibling-based exposure data with our corresponding trio-based outcome results to ensure a strictly within-family causal estimate; and (3) IndSEM, which pairs independent-individual-based exposure data with our IndSEM outcome results. This structured approach allows for a direct comparison between conventional independent-individual-based MR and our family-corrected multivariate framework, facilitating the identification of biases induced by intergenerational confounding.

Table 1 summarizes the two-sample MR estimates for the causal effect of HDL cholesterol on obesity. Using the IndSEM framework, we detected significant causal associations across the weighted median, IVW, and MRcML methodologies (, respectively). Although the within-family FT-SEM and PSEM methods did not find statistically significant results—likely due to the limited sample size of the trio cohort—the effect directions were consistent with the population-level estimates. In contrast, Table 2 details the causal effect of SBP on obesity. While the IndSEM approach identified a significant association using the MR-Egger method (), this finding was not replicated by the family-based methods. Notably, FT-SEM and PSEM not only failed to achieve significance but also resulted in causal estimates which were substantially attenuated toward the zero. This divergence between independent-individual-based and family-based estimates indicates that the association between SBP and obesity observed in conventional studies is likely a false-positive result, primarily driven by familial confounding such as DE. These findings underscore the importance of within-family MR in distinguishing true biological causality from environmental and genetic confounding.

Table 1.

Point estimates and p values for the causal effects of offspring’s HDL cholesterol on offspring’s obesity

Method	MR Method	nsnp	Casual effect	SE	95% LCL	95% UCL	P value
FT-SEM	MR Egger	53	0.011	0.110	− 0.205	0.227	0.921
FT-SEM	Weighted median	53	0.050	0.099	− 0.144	0.244	0.616
FT-SEM	Inverse variance weighted	53	0.093	0.065	− 0.034	0.220	0.153
FT-SEM	Simple mode	53	0.073	0.189	− 0.297	0.443	0.701
FT-SEM	Weighted mode	53	0.049	0.093	− 0.133	0.231	0.597
FT-SEM	MRcML	53	0.074	0.061	− 0.046	0.194	0.220
FT-SEM	MRBEE	53	0.075	0.059	− 0.041	0.191	0.202
PSEM	MR Egger	53	− 0.025	0.151	− 0.321	0.271	0.870
PSEM	Weighted median	53	− 0.034	0.133	− 0.295	0.227	0.797
PSEM	Inverse variance weighted	53	0.085	0.088	− 0.087	0.257	0.333
PSEM	Simple mode	53	0.169	0.240	− 0.301	0.639	0.485
PSEM	Weighted mode	53	0.086	0.129	− 0.167	0.339	0.509
PSEM	MRcML	53	0.094	0.082	− 0.067	0.255	0.255
PSEM	MRBEE	53	0.095	0.084	− 0.070	0.260	0.260
IndSEM	MR Egger	157	0.129	0.080	− 0.028	0.286	0.108
IndSEM	Weighted median	157	0.188	0.092	0.008	0.368	0.042
IndSEM	Inverse variance weighted	157	0.113	0.055	0.005	0.221	0.041
IndSEM	Simple mode	157	0.002	0.178	− 0.347	0.351	0.989
IndSEM	Weighted mode	157	0.159	0.081	0.000	0.318	0.050
IndSEM	MRcML	157	0.113	0.055	0.005	0.221	0.041
IndSEM	MRBEE	157	0.113	0.062	− 0.009	0.235	0.069

“Method” denotes the GWAS approach used for the summary data of the outcome, while “MR Method” represents the method employed for MR analysis, and “nsnp” indicates the number of instrumental variables used. “Causal effect” denotes the point estimate of the causal effect, “SE” stands for the standard error of the causal effect, and “95% LCL” and “95% UCL” refer to the lower and upper bounds of the 95% confidence interval for the causal effect, respectively. “P value” represents the p value of the hypothesis testing for the causal effect. Specifically, for the FT-SEM and PSEM methods, the summary data used for the exposure was “ieu-b-4844” [20], whereas for the IndSEM method, the summary data was identified by the ID “ebi-a-GCST90018956” [24]. The values in bold mean that the p values are less than 0.05

Table 2.

Point estimates and p values for the causal effects of offspring’s systolic blood pressure on offspring’s obesity

Method	MR Method	nsnp	Casual effect	SE	95% LCL	95% UCL	P value
FT-SEM	MR Egger	17	− 0.068	0.100	− 0.264	0.128	0.508
FT-SEM	Weighted median	17	0.010	0.029	− 0.047	0.067	0.739
FT-SEM	Inverse variance weighted	17	− 0.004	0.020	− 0.043	0.035	0.825
FT-SEM	Simple mode	17	0.020	0.047	− 0.072	0.112	0.679
FT-SEM	Weighted mode	17	0.012	0.039	− 0.064	0.088	0.766
FT-SEM	MRcML	17	− 0.009	0.018	− 0.044	0.026	0.626
FT-SEM	MRBEE	17	− 0.005	0.019	− 0.042	0.032	0.810
PSEM	MR Egger	17	− 0.068	0.100	− 0.264	0.128	0.508
PSEM	Weighted median	17	0.010	0.027	− 0.043	0.063	0.724
PSEM	Inverse variance weighted	17	− 0.004	0.020	− 0.043	0.035	0.825
PSEM	Simple mode	17	0.020	0.044	− 0.066	0.106	0.660
PSEM	Weighted mode	17	0.012	0.039	− 0.064	0.088	0.768
PSEM	MRcML	17	− 0.002	0.024	− 0.049	0.045	0.925
PSEM	MRBEE	17	0.012	0.025	− 0.037	0.061	0.644
IndSEM	MR Egger	359	− 0.028	0.012	− 0.052	− 0.004	0.026
IndSEM	Weighted median	359	− 0.011	0.009	− 0.029	0.007	0.211
IndSEM	Inverse variance weighted	359	− 0.001	0.006	− 0.013	0.011	0.834
IndSEM	Simple mode	359	0.003	0.022	− 0.040	0.046	0.885
IndSEM	Weighted mode	359	− 0.018	0.013	− 0.043	0.007	0.189
IndSEM	MRcML	359	− 0.001	0.005	− 0.011	0.009	0.855
IndSEM	MRBEE	359	− 0.001	0.006	− 0.013	0.011	0.871

“Method” denotes the GWAS approach used for the summary data of the outcome, while “MR Method” represents the method employed for MR analysis, and “nsnp” indicates the number of instrumental variables used. “Causal effect” denotes the point estimate of the causal effect, “SE” stands for the standard error of the causal effect, and “95% LCL” and “95% UCL” refer to the lower and upper bounds of the 95% confidence interval for the causal effect, respectively. “P value” represents the p value of the hypothesis testing for the causal effect. Specifically, for the FT-SEM and PSEM methods, the summary data used for the exposure was “ieu-b-4818” [20], whereas for the IndSEM method, the summary data was identified by the ID “ie-b-38” [23]. The values in bold mean that the p values are less than 0.05

Sensitivity analysis using harmonized genetic instruments

The results of the harmonized MR analysis are summarized in Supplementary Table S4. Using the sibling-based GWAS to define a common set of instrumental variables, none of the MR methods detected a statistically significant association between SBP and the latent obesity factor. This finding should be interpreted with caution. Compared with conventional population-based GWAS, sibling-based GWAS generally have substantially smaller effective sample sizes, resulting in weaker instrumental variables and reduced statistical power. Therefore, the attenuation observed in the primary analyses cannot be attributed solely to differences in dynastic effects, and reduced statistical power associated with the sibling-based instruments is also likely to have contributed to the observed results.

Discussion

In this study, we introduced FT-SEM, a robust and statistically powerful SEM framework for multivariate GWAS using family trio data. We further demonstrated the utility of FT-SEM-derived summary statistics in facilitating within-family two-sample MR analyses. By integrating parental genotypes and phenotypes alongside offspring data, FT-SEM maximizes information recovery, significantly enhancing estimation precision and statistical power compared to traditional family-based designs. Our theoretical and simulation-based evaluations elucidate how DE introduce substantial confounding in independent-individual-based GWAS and MR studies. We demonstrate that while conventional methods (e.g., IndSEM) yield biased estimates and inflated type I error rates in the presence of DE, trio-based frameworks—specifically FT-SEM and PSEM—provide unbiased point estimates and maintain nominal coverage probabilities. Notably, FT-SEM consistently outperforms PSEM by exhibiting lower RMSEs and superior statistical power, a direct result of its ability to leverage maternal and paternal phenotypic information. Additional simulation studies further demonstrated that FT-SEM is robust to the violations of the assumed latent-factor structure and cross-generational measurement invariance. Under all the examined scenarios, genetic effect estimates remained essentially unbiased, and empirical type I error and coverage probability of confidence interval remained well controlled. In addition, compared with conventional univariate or multivariate GWAS methods, FT-SEM incurs additional computational cost because it uses a more complex structure of SEM. Even though this increased computational burden, FT-SEM can derive the precise estimation of offspring, paternal, and maternal genetic effects on a latent phenotype. As modern computing resources continue to improve and parallel computing is readily available for genome-wide analyses, we believe that the current computational cost is acceptable for practical applications. Future work could further improve computational efficiency through optimized numerical algorithms or approximate estimation procedures.

Applying these methods to the UKB, we re-evaluated the causal influence of metabolic traits on obesity. Our findings reveal that the previously reported association between SBP and obesity is effectively attenuated to the null after accounting for intergenerational confounding, suggesting that prior independent-individual-level MR findings may have been spurious. Conversely, our analysis of HDL cholesterol and obesity showed consistent effect directions across all methods, providing robust supportive evidence for a genuine biological relationship despite the lower power inherent in family-based cohorts. Collectively, FT-SEM offers a rigorous and efficient approach for multivariate genetic analysis, serving as a critical tool for validating causal inferences in the presence of complex familial confounding like DE. As an additional sensitivity analysis, we repeated the two-sample MR analyses using a harmonized set of SNP instruments selected from the sibling-based GWAS. Although no statistically significant association between SBP and the obesity was observed, these findings should be interpreted with caution. Compared with conventional population-based GWAS, sibling-based GWAS generally have substantially smaller effective sample sizes and consequently identify fewer genome-wide significant variants, resulting in weaker instrumental variables and reduced statistical power. Meanwhile, sibling-based GWAS are expected to provide less biased estimates of offspring effect by reducing confounding from DE and other familial processes. Therefore, the attenuation observed in the harmonized analyses may reflect a combination of reduced statistical power and diminished familial bias. Notably, although the harmonized analysis resulted in wider confidence intervals and loss of statistical significance, the overall pattern of the point estimates remained comparable to that observed in the primary analyses. This observation suggests that harmonizing the instrument set mainly reduced estimation precision because of weaker sibling-based instruments, rather than indicating that difference in instrument selection alone accounted for the attenuation of the estimated causal effect. Future studies based on substantially larger family-based GWAS datasets will be essential to improve instrument strength, distinguish these possibilities, and more precisely quantify the causal relationship between SBP and obesity.

The proposed FT-SEM framework can be conceptualized as a significant extension of SEM-based mother-offspring designs [17], adapted to the full family-trio architecture. For example, by constraining the paternal effect to zero, our model effectively collapses into a mother-offspring SEM, demonstrating its inherent compatibility with simpler family units. While the current study specifically examines a single common latent factor influencing three phenotypes, the structural flexibility of the SEM framework permits the customization of diverse relationship structures among an arbitrary number of phenotypes. Provided that the hypothesized model accurately reflects the underlying biological or causal architecture, FT-SEM offers a versatile and robust analytical tool applicable across various domains of complex trait genetics. An important feature of FT-SEM is that it simultaneously estimates offspring, paternal, and maternal genetic effects within a unified framework. Although the present study primarily focuses on offspring effect because it constitutes the direct genetic component required for downstream MR analyses, the estimated parental effects are themselves biologically informative. Significant paternal or maternal effects may reflect DE mediated through parental phenotypes, family environment, or other intergenerational mechanisms. These estimates therefore provide a useful tool for investigating the genetic architecture of DE. Exploring the biological implications of parental genetic effects is an important direction for future applications of FT-SEM.

In practice, the sample sizes available for family-based GWAS and within-family MR analyses are typically smaller than those utilized in independent-individual-based studies. Consequently, estimates derived from FT-SEM should be interpreted as robust but statistically less efficient relative to their population-level counterparts. Nevertheless, when discrepancies arise between independent-individual-based and family-based estimates, the latter are generally preferred due to their resilience against intergenerational confounding and their unbiased nature. While the FT-SEM framework effectively eliminates the bias induced by DE in both GWAS and downstream MR applications, it remains susceptible to the challenges of horizontal pleiotropy. This limitation, however, can be mitigated by integrating robust two-sample MR estimators designed to explicitly model or correct for pleiotropic effects [7, 10–14, 33, 34]. By combining the family-based rigor of FT-SEM with established pleiotropy-robust methodologies, researchers can achieve highly reliable causal inferences that are safeguarded against both familial and pleiotropic confounding (e.g. DE and horizontal pleiotropy).

While FT-SEM provides a robust framework for multivariate genetic analysis, six potential limitations warrant consideration. (1) Distributional and Functional Assumptions: FT-SEM assumes multivariate normality among observed variables and a linear relationship between genotypes and phenotypes. In cases of significant non-normality, appropriate data transformations—such as rank-based inverse normal transformations—may be employed to satisfy these underlying assumptions [37]. (2) Genetic Model Constraints: Our model assumes additive genetic effects and a constant genetic architecture across generations. While these assumptions are largely consistent with biological observations for complex traits, deviations (e.g., dominance or epistasis) could introduce modest estimation biases. (3) Sample Size Constraints: After stringent quality control, only 778 complete family trios were retained for the primary analysis. This sample size is grossly underpowered to detect genome-wide significant loci for any complex trait, let alone for a multivariate latent factor. For FT-SEM to transition from a robust statistical framework to a genuinely useful discovery instrument, trio-based biobanks with larger sample sizes are indispensable. (4) Computational Complexity: Compared to standard linear models, FT-SEM requires more intensive computational resources. However, as SEM is inherently conducive to parallelization and multi-threading, this computational burden can be effectively mitigated for large-scale genomic datasets. (5) Pedigree Structure: The current iteration of FT-SEM is designed specifically for family trios with a single offspring. To accommodate families with multiple siblings, the model would require extension into a multi-level or pedigree-based SEM framework. (6) Interaction Effects: Finally, the current model focuses exclusively on the main effects of genotypes and phenotypes, without accounting for gene-environment or gene-gene interactions.

In summary, we have presented FT-SEM, a novel structural equation modeling framework designed for family-trio-based GWAS, and demonstrated its application in conducting rigorous two-sample MR analyses. By strategically leveraging phenotypic and genotypic data from the complete trio unit, FT-SEM yields more precise effect estimates and enhanced statistical power compared to traditional family-based methodologies, all while maintaining the robustness inherent in within-family designs. Looking ahead, several avenues for further development remain. The SEM framework also provides a natural foundation for extending FT-SEM beyond parent-offspring trios. Future developments may incorporate arbitrary pedigree structures through pedigree-based covariance modeling, allowing simultaneous estimation of direct and DE across multiple generations and relatives. Such extensions would facilitate pedigree-wide GWAS and within-pedigree MR analyses, enabling more comprehensive dissection of direct genetic effects, dynastic effects, assortative mating, and other intergenerational mechanisms.

Conclusion

In this study, we developed and validated FT-SEM, a novel multivariate GWAS framework based on SEM specifically designed for family trio data. FT-SEM successfully integrates both genotypes and phenotypes from parents and offspring across multiple traits, allowing for the simultaneous estimation of direct genetic effects on a common latent factor. Simulation studies demonstrated that FT-SEM effectively mitigates biases arising from DE, maintaining unbiased point estimates and strictly controlled type I error rates where traditional population-based methods fail. By strategically incorporating parental phenotypic information—which is often neglected in existing trio-based methods—FT-SEM significantly enhances estimation precision and statistical power, partially recovering the efficiency loss typically associated with within-family designs. Application to UK Biobank data revealed that the association between SBP and obesity is largely driven by DE, whereas the causal effect of HDL cholesterol on obesity remains robust. As MR gains popularity, the susceptibility of conventional MR to DE has become a critical concern. FT-SEM provides a rigorous solution by blocking non-causal intergenerational pathways, thereby ensuring more reliable causal inferences in complex trait genetics. Unlike previous family-based frameworks that were either limited to single variables or ignored parental phenotypes, FT-SEM maximizes the informative value of available family-trio data. The framework produces summary statistics that can be seamlessly integrated with existing two-sample MR methods, making it a powerful tool for validating findings from large-scale independent cohorts. In summary, FT-SEM represents a critical step forward in addressing the challenges of confounding in genetic studies, providing a robust approach for multivariate analysis in family-based designs.

Supplementary Information

Below is the link to the electronic supplementary material.

Abbreviations

BFP

Body fat percentage

BMI

Body mass index

CI

Confidence interval

CP

Coverage probabilities

DE

Dynastic effects

GWAS

Genome-wide association studies

HDL

High-density lipoprotein

IVs

Instrumental variables

MR

Mendelian randomization

RMSE

Root mean square error

PVE

Phenotypic Variance Explained

SBP

Systolic blood pressure

SE

Standard error

SEM

Structural equation model

SNPs

Single nucleotide polymorphisms

UKB

UK Biobank

WHR

Waist-to-hip ratio

Author contributions

S.Z. and J.-H.M developed the methods, performed the simulation, conducted real data analysis, and wrote the manuscript. Z.Q., Q.-W.Z., J.-Y.Z. validated the models and the results. Z.Q., Q.-W.Z., Y.-S.L., X.-B.W. and J.-Y.Z. reviewed and edited the manuscript. X.-B.W., J.-Y.Z. administrated the project and supervised the research. All authors contributed to the article and approved the submitted version.

Funding

This work was supported by the National Natural Science Foundation of China (grant number 82574202) and the Hainan Province Science and Technology Special Fund (grant number ZDYF2025SHFZ046).

Data availability

UK Biobank data are available in a public, open access repository. This research has been conducted using the UKB resource under approved application number 55794. The UK Biobank data are available on application to the UK Biobank (https://www.ukbiobank.ac.uk/). The summary data from within-sibship GWAS are available at https://gwas.mrcieu.ac.uk/datasets/ieu-b-4844/ and https://gwas.mrcieu.ac.uk/datasets/ieu-b-4818/. The summary data from independent GWAS are available at https://gwas.mrcieu.ac.uk/datasets/ebi-a-GCST90018956/ and https://gwas.mrcieu.ac.uk/datasets/ieu-b-38/.

Declarations

Ethics approval and consent to participate

This study used publicly available, de-identified data from previously published studies. No new individual-level human or animal data were collected. Therefore, additional ethical approval and consent to participate were not required for this study.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Clinical trial number

Not applicable.