Genome-wide association and MaODR-based multi-locus interaction analyses reveal a susceptibility gene network for newly identified metabolic syndrome

Abstract

Background

Metabolic syndrome involves several lipid-related genes, including apolipoprotein A5 (APOA5), lipoprotein lipase (LPL), and cholesteryl ester transfer protein (CETP). Although individual SNP susceptibility has been reported, gene–gene interactions remain underexplored. To address this gap, we apply many-objective multifactor dimensionality reduction (MaODR)—previously developed by our group—to detect gene‒gene interactions in unbalanced newly identified MetS and non-MetS subjects.

Results

Among 40,773 Taiwan Biobank participants (5,723 newly identified metabolic syndrome cases and 35,050 controls) after excluding smokers and individuals with chronic diseases, genome-wide association analysis identifies 35 significant SNPs. We detect a two-locus SNP-SNP interaction between APOA5 and LPL; the most significant genotype combination is rs331-GG with rs651821-CC (bootstrap odds ratio = 1.76; p = 9.61 × 10⁻²⁰). MaODR also reveals a three-way interaction among APOA5, LPL, and CETP. Furthermore, we find that the LPL, APOA5, BUD13, zinc finger protein 1 (ZPR1), APOC3, CETP, and APOE genes collectively contributed to MetS susceptibility, with SNPs of LPL showing a significant metabolic syndrome-associated effect and interacting with SNPs of the APOA5 and CETP genes. Genes linked to metabolic syndrome are enriched in cholesterol metabolism and the peroxisome proliferator-activated receptor signaling pathway.

Conclusions

MaODR detects epistasis networks through SNP-SNP interactions in newly identified metabolic syndrome, highlighting APOA5–LPL and APOA5–LPL–CETP interaction models.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s13059-026-04114-x.

Background

Metabolic syndrome (MetS) is a collection of metabolic conditions that significantly increase the risk of cardiovascular disease [1], type 2 diabetes (DM), and nonalcoholic fatty liver disease [2]. MetS is characterized by several metabolic abnormalities, including abdominal obesity, elevated blood pressures and glucose levels, high triglyceride (TG) levels, and low high-density lipoprotein cholesterol (HDL-C) levels [3]. However, the international definition of MetS always includes patients with DM, hypertension, and hyperlipidaemia, even those treated with all kinds of medicine [4]. People with newly identified MetS without other chronic diseases need more attention for the prevention of chronic diseases.

Recent advancements have significantly improved our understanding of the determinants of MetS [5]. Of particular interest is the exploration of population-specific genetic risk factors, which shows promise for the early identification of individuals predisposed to MetS, allowing for timely intervention and management strategies. Numerous genes have been implicated in MetS, including the cholesteryl ester transfer protein (CETP) allele (rs2303790), which has been linked to age-related macular degeneration in East Asians and is associated with elevated HDL-C levels [6]. A genome-wide association study (GWAS) of individuals with hypertriglyceridaemia revealed significant associations between common variants in four genetic loci, APOB, LPL, GCKR, and APOA5, and elevated TG levels [7]. Polymorphisms within the LPL gene, such as rs13702, have been associated with differences in lipid levels [8] and nonalcoholic fatty liver disease [9]. Additionally, the SNPs rs10757278 and rs2383206 may be associated with coronary heart disease in the Saudi population [10]. However, more extensive research is needed to explore the potential for SNP‒SNP interactions in MetS.

Various computational methods have been proposed to detect epistasis in numerous association studies [11–24]. Data mining and statistical analysis can be used to overcome computational challenges and identify complex gene‒gene interactions. Detecting statistical interactions between single-nucleotide polymorphisms (SNPs) is a challenging task in genetic research. Several methods have been proposed to detect SNP‒SNP interactions, including multifactor dimensionality reduction (MDR) [25], Bayesian epistasis association mapping (BEAM) [26], AntEpiSeeker [27], and SNPRuler [28]. MDR uses a dimensionality reduction technique to segment the prediction rules into high-risk and low-risk groups. This technique is widely used [25]; however, it has some limitations, such as sensitivity to imbalances in case‒control data (the numbers of cases and controls should be even). To address this, methodological extensions have been proposed. Velez et al. introduced a balanced accuracy function to enhance MDR’s performance in imbalanced datasets [28], while Yang et al. developed MDR-ER to further improve error adjustment and class ratio balancing [29]. These advancements demonstrate the ongoing evolution of MDR to handle more realistic and complex data structures better.

The many-objective multifactor dimensionality reduction (MaODR) version [30] of MDR extends the multiobjective multifactor dimensionality reduction (MOMDR) version [31]. It utilizes measures such as the chi-square value (Chi), F_β-measure (F_β), negative predictive value (NPV) [32], Kappa [33], and SNPRuler [28] to identify SNP‒SNP interactions with weak marginal effects and to reduce confounding variables in the scoring model. MaODR introduces an objective function selection approach to determine the optimal combination of measures for identifying these interactions. The MaODR classifier allows for accurate classification of data and calculation of misclassification errors of multiple SNPs that are either high- or low-risk factors [30].

While GWAS have effectively identified SNP associations with MetS, systematic investigations of SNP–SNP interactions remain scarce. Only a few reports, such as interaction effects within SIDT2 and APOA5 variants in East Asian populations [34, 35], have suggested multilocus contributions to MetS risk. MetS is usually defined based on international criteria like those from the AHA/NHLBI, including individuals with diabetes, hypertension, dyslipidaemia, and those receiving related treatments. While this definition is widely accepted, including such individuals can complicate genetic studies because metabolic traits may be significantly affected by long-term disease progression, medication, or lifestyle changes. These treatment- and disease-related effects can confound associations and hide the true genetic contributions to MetS. To better understand the genetic factors involved in disease onset, the current study focused on newly identified MetS patients without chronic illnesses or medication use. This method reduces variability, improves the accuracy of genetic results, and offers a clearer view of the susceptibility loci and interaction networks responsible for early MetS development, providing insights into preventive measures before the onset of chronic conditions. Previous studies employing MDR-based approaches such as generalized multifactor dimensionality reduction (GMDR) have provided limited insights, particularly as they did not focus on newly identified MetS populations [36, 37]. This represents a critical research gap, as epistatic interactions have been suggested to play an important role in the complex genetic architecture of MetS that single-variant analyses cannot fully explain. Therefore, we applied the MaODR framework to identify potential SNP–SNP interaction networks in newly identified MetS patients, thereby extending beyond the limitations of traditional single-variant approaches. In this study, thirty-five SNPs were selected through a GWAS to investigate SNP‒SNP interactions in MetS and to apply the MaODR model to identify statistically significant SNP–SNP interactions associated with MetS in real-world datasets. We utilized various analyses to evaluate the role and mechanisms of MetS GWAS-associated SNPs and genes. These analyses included SNP conservation and functional annotation, gene ontology (GO) analysis, pathway analysis, and protein‒protein interaction (PPI) analyses.

Results

Characteristics of the study population

The study cohort comprised 40,773 participants from the Taiwan Biobank (TWB), including 5,723 individuals with newly identified MetS and 35,050 without MetS (non-MetS). Table 1 shows the essential characteristics of the MetS and non-MetS groups. Compared with those without MetS, MetS patients were significantly older and had a greater body mass index (BMI), waist circumference, systolic blood pressure (SBP), diastolic blood pressure (DBP), glycated haemoglobin (HbA1c), fasting glucose (FG), TG, and HDL-C. Both groups were female dominated; however, the percentage of males in the MetS group (23%) was significantly greater than that in the non-MetS group. In this study, newly identified MetS refers to participants who met the diagnostic criteria for metabolic syndrome at baseline but had no prior diagnosis or treatment for diabetes, hypertension, or dyslipidaemia.

Table 1.

Characteristics of the study population

Variables	Entire population (n = 40,773)
	MetS (n = 5,723)	Non-MetS (n = 35,050)	p values
Sex (male/female)	1316 (23.0%)/4407 (77.0%)	7030 (20.1%)/28020 (79.9%)	< 0.001
Age (years)	48.4 ± 10.8	51.9 ± 10.3	< 0.001
BMI (kg/m2)	27.2 ± 3.6	23.0 ± 3.2	< 0.001
Waistline (cm)	91.1 ± 8.0	79.2 ± 8.8	< 0.001
SBP (mmHg)	129.3 ± 16.8	114.0 ± 15.7	< 0.001
DBP (mmHg)	79.0 ± 10.5	70.2 ± 9.8	< 0.001
HbA1c (%)	6.0 ± 1.0	5.6 ± 0.5	< 0.001
Fasting glucose (mg/dl)	102.4 ± 25.8	90.8 ± 10.4	< 0.001
TG (mg/dl)	182.5 ± 124.1	89.4 ± 51.3	< 0.001
HDL-C (mg/dl)	45.4 ± 9.4	58.9 ± 13.0	< 0.001

Continuous variables are shown as means ± standard deviations. Comparisons between MetS and non-MetS groups were performed using independent-samples t-tests for continuous variables and chi-square tests for categorical variables. Participants with elevated blood pressure but without prior hypertension diagnosis or treatment were included as “newly identified MetS” cases, explaining the higher mean SBP and DBP values in the MetS group

BMI body mass index, SBP systolic blood pressure, DBP diastolic blood pressure, HbA1c glycated haemoglobin, TG triglyceride, HDL-C high-density lipoprotein cholesterol

Single-locus analysis

A GWAS was conducted, and the Manhattan plot (Fig. 1A) illustrates the genetic associations with metabolic syndrome. Significant loci were observed to cluster primarily on chromosomes 8, 11, 16, and 19, highlighting potential regions of interest for further investigation. Based on a structured selection strategy, 35 SNPs were prioritized for further analysis (Table 2). This set included SNPs reaching genome-wide significance (p < 5 × 10^–8) or suggestive significance (p < 1 × 10^–5), as well as representative variants with nominal associations (p < 0.05) located in genes of established relevance to lipid metabolism and metabolic syndrome (e.g., LPL, APOA5, CETP). For the latter category, only one SNP per linkage disequilibrium (LD) block (pairwise r² > 0.8) was retained. These 35 SNPs were then carried forward into multilocus MaODR modeling to explore potential gene–gene interactions.

Fig. 1.

A Manhattan plot of the genome-wide association study for MetS. Each dot represents a SNP plotted by its chromosomal position against –log₁₀(p). The red horizontal line indicates the genome-wide significance threshold (p < 5 × 10^–8), and the grey line marks the suggestive significance threshold (p < 1 × 10^–5). The certain biologically relevant SNPs with p < 0.05 were labeled if they mapped to genes previously implicated in lipid metabolism or MetS (e.g., APOA5, LPL, CETP). These labeled SNPs were prioritized as candidates for multilocus analysis (MaODR). B Quantile‒quantile (Q‒Q) plot for the GWAS of MetS. C Haploview LD display of candidate SNPs associated with MetS

Table 2.

Single-locus analysis of 35 SNPs for the MetS and non-MetS groups

	SNPs	Genotype	Cases	Controls	Odds ratio	95% CI	p value
1	rs295	AA	3754	21,808
		CA	1779	11,609	1.123	(1.057, 1.194)	1.76 × 10–04
		CC	184	1547	1.447	(1.237, 1.693)	4.00 × 10–06
2	rs320	TT	3762	21,865
		GT	1771	11,591	1.126	(1.060, 1.197)	1.29 × 10–04
		GG	181	1533	1.457	(1.244, 1.706)	3.00 × 10–06
3	rs326	AA	3760	21,861
		GA	1771	11,593	1.126	(1.059, 1.196)	1.33 × 10–04
		GG	182	1524	1.440	(1.230, 1.686)	6.00 × 10–06
4	rs331	GG	3779	21,990
		AG	1755	11,494	1.126	(1.059, 1.196)	1.43 × 10–04
		AA	170	1471	1.487	(1.264, 1.749)	2.00 × 10–06
5	rs13702	TT	3775	21,984
		CT	1738	11,408	1.127	(1.060, 1.198)	1.25 × 10–04
		CC	173	1460	1.449	(1.233, 1.703)	7.00 × 10–06
6	rs15285	CC	3799	22,109
		CT	1743	11,411	1.125	(1.058, 1.196)	1.57 × 10–04
		TT	174	1473	1.455	(1.239, 1.708)	5.00 × 10–06
7	rs10105606	CC	3809	22,144
		AC	1732	11,386	1.131	(1.064, 1.202)	8.10 × 10–05
		AA	177	1470	1.429	(1.218, 1.676)	1.20 × 10–05
8	rs2083637	AA	3799	22,121
		GA	1738	11,405	1.127	(1.060, 1.198)	1.26 × 10–04
		GG	177	1468	1.424	(1.214, 1.671)	1.40 × 10–05
9	Affx-31885734	TT	3795	22,094
		GT	1745	11,429	1.125	(1.058, 1.196)	1.55 × 10–04
		GG	178	1470	1.419	(1.210, 1.664)	1.70 × 10–05
10	Affx-31885823	CC	3810	22,299
		AC	1737	11,303	1.112	(1.046, 1.182)	6.72 × 10–04
		AA	174	1423	1.397	(1.189, 1.642)	4.70 × 10–05
11	rs28526159	CC	2735	15,676
		TC	2380	15,201	1.114	(1.050, 1.182)	3.46 × 10–04
		TT	596	4090	1.197	(1.089, 1.317)	2.05 × 10–04
12	rs2367970	GG	2536	16,869
		AG	2517	14,898	0.890	(0.839, 0.944)	1.17 × 10–04
		AA	657	3228	0.739	(0.673, 0.811)	2.00 × 10–10
13	rs7350481	CC	3075	20,894
		TC	2240	12,346	0.811	(0.765, 0.860)	3.00 × 10–12
		TT	406	1799	0.652	(0.582, 0.731)	3.00 × 10–14
14	rs1558861	TT	3384	22,520
		CT	2016	11,091	0.827	(0.779, 0.877)	4.00 × 10–10
		CC	309	1365	0.664	(0.584, 0.755)	4.00 × 10–10
15	rs9326246	GG	3397	22,584
		CG	2012	11,069	0.828	(0.780, 0.878)	5.00 × 10–10
		CC	310	1366	0.663	(0.583, 0.754)	4.00 × 10–10
16	rs11216126	AA	3331	19,133
		CA	2060	13,396	1.132	(1.067, 1.201)	4.00 × 10–05
		CC	320	2481	1.350	(1.195, 1.525)	1.50 × 10–06
17	rs180326	TT	3391	22,579
		GT	2014	11,041	0.823	(0.776, 0.874)	2.00 × 10–10
		GG	307	1346	0.658	(0.579, 0.749)	2.00 × 10–10
18	rs3825041	CC	3422	22,789
		TC	1997	10,933	0.822	(0.774, 0.873)	1.00 × 10–10
		TT	300	1294	0.648	(0.568, 0.738)	7.00 × 10–11
19	rs2160669	TT	3392	22,634
		CT	2018	11,014	0.818	(0.771, 0.868)	4.00 × 10–11
		CC	303	1336	0.661	(0.580, 0.752)	4.00 × 10–10
20	rs964184	CC	3390	22,648
		GC	2022	11,036	0.817	(0.770, 0.867)	3.00 × 10–11
		GG	302	1334	0.661	(0.581, 0.753)	4.00 × 10–10
21	rs2075290	TT	3224	21,595
		CT	2142	11,795	0.822	(0.775, 0.872)	8.00 × 10–11
		CC	346	1582	0.683	(0.604, 0.771)	9.00 × 10–10
22	rs603446	CC	3158	17,937
		TC	2174	14,224	1.152	(1.086, 1.222)	3.00 × 10–06
		TT	385	2845	1.301	(1.162, 1.457)	5.00 × 10–06
23	rs3741298	TT	2713	16,042
		CT	2110	14,497	1.162	(1.093, 1.235)	2.00 × 10–06
		CC	877	4374	0.843	(0.776, 0.917)	6.00 × 10–05
24	rs2266788	AA	3384	22,618
		GA	2029	11,025	0.813	(0.766, 0.863)	1.00 × 10–11
		GG	301	1329	0.661	(0.580, 0.752)	4.00 × 10–10
25	Affx-4282911	CC	4811	30,869
		AC	862	4025	0.728	(0.672, 0.788)	1.00 × 10–13
		AA	45	134	0.464	(0.331, 0.651)	9.00 × 10–06
26	rs7396835	CC	2612	17,211
		TC	2480	14,696	0.899	(0.848, 0.954)	4.00 × 10–04
		TT	619	3068	0.752	(0.684, 0.828)	5.00 × 10–09
27	rs2854117	CC	2792	17,013
		TC	1831	12,113	1.086	(1.019, 1.157)	0.011
		TT	1096	5882	0.881	(0.816, 0.950)	0.001
28	rs2854116	CT	2783	16,966
		TT	1869	12,400	1.088	(1.022, 1.159)	0.008
		CC	1065	5648	0.870	(0.806, 0.939)	4.00 × 10–04
29	rs247616	CC	4115	24,364
		TC	1497	9677	1.092	(1.024, 1.164)	0.007
		TT	108	987	1.544	(1.262, 1.888)	2.00 × 10–05
30	rs17231506	CC	4097	24,264
		TC	1502	9736	1.094	(1.027, 1.166)	0.005
		TT	109	994	1.540	(1.260, 1.882)	2.00 × 10–05
31	rs711752	AG	2735	16,816
		GG	2161	12,410	0.934	(0.879, 0.993)	0.028
		AA	822	5787	1.145	(1.053, 1.245)	0.001
32	rs7499892	CC	3795	24,195
		TC	1720	9823	0.896	(0.842, 0.953)	5.00 × 10–04
		TT	206	975	0.742	(0.636, 0.866)	2.00 × 10–04
33	rs429358	TT	4547	28,526
		CT	995	5361	0.859	(0.797, 0.925)	6.00 × 10–05
		CC	137	961	1.118	(0.932, 1.341)	0.228
34	rs651821	TT	2683	19,040
		CT	2432	13,528	0.784	(0.739, 0.832)	1.00 × 10–13
		CC	589	2316	0.554	(0.502, 0.612)	1.00 × 10–13
35	rs662799	AA	2694	19,135
		GA	2431	13,542	0.784	(0.739, 0.832)	1.00 × 10–13
		GG	592	2323	0.552	(0.500, 0.610)	1.00 × 10–13

ORs were calculated relative to the major genotype, defined as the most frequent genotype in the study population. p-values were obtained from chi-square tests comparing each genotype to the reference category. Reported p-values are unadjusted; statistical significance was defined as p < 0.05

Multilocus analysis – determination of the best model

For the multilocus interaction analysis, we used all 35 SNPs that passed the GWAS screening step as candidate loci. The MaODR framework was then applied to evaluate 2-way and 3-way SNP–SNP interaction models (m = 2 and m = 3). This approach allowed us to systematically assess potential epistatic interactions among the GWAS-identified variants and to determine the most informative multilocus models associated with newly identified MetS. Significant 2-locus SNP‒SNP interactions were detected via the MaODR. The best model was selected according to the model with the highest frequency in cross-validation consistency (CVC), which consisted of the model with the lowest error rate in each cross-validation (CV). Among these models, the average correct classification rate (CCR) in the fivefold CV of the best model was 0.549 for the 2-loci model (rs331 and rs651821), the average normalized mutual information (NMI) was 0.01 on average, and the average likelihood ratio (LR) was 13.673. rs331 and rs651821 located in LPL and APOA5, respectively. Figure 2 summarizes the rs331 and rs651821 genotype combinations associated with newly identified MetS and non-MetS from the MaODR. In Fig. 2B, the label “(Ref)” denotes the reference genotype. Nominal p-values are shown to present the raw test results in a clear and interpretable manner, while statistical significance was determined using Benjamini–Hochberg FDR–adjusted p-values (p < 0.05). Complete lists of nominal p-values and BH-FDR–adjusted p-values are provided in Additional file 1: Table S1. In the 2-locus MaODR models, all eight non-reference genotype combinations remained statistically significant after BH-FDR adjustment. rs331-GG and rs651821-TT were combined as the reference and used to evaluate the other genotype combinations regarding risk and protection effects between cases and controls. The genotype combinations included risk and protection effects, demonstrating the interaction between rs331 and rs651821. rs651821-CC presented three significant risks (odds ratio > 1 and BH-FDR–adjusted p-value < 0.05; Fig. 2B), and rs651821-CT presented two risks and one protection. rs331-GG combined with rs651821-CC was the most significant 2-locus combination (OR = 1.76, BH-FDR–adjusted p-value = 7.69E-19).

Fig. 2.

Two-locus interaction model (rs331 in LPL and rs651821 in APOA5) identified by the MaODR. A Distribution of genotype combinations in MetS and non-MetS groups (rs331-1 = GG, rs331-2 = AG, rs331-3 = AA; rs651821-1 = TT, rs651821-2 = CT, rs651821-3 = CC). For each genotype combination, the left bar represents cases and the right bar represents controls. B ORs and nominal p-values for each genotype combination relative to the major genotype reference (rs331-GG + rs651821-TT), denoted as “(Ref)”. Gray cells indicate risk (OR ≥ 1), and white cells indicate protective effects (OR < 1). Nominal p-values are presented for clarity, while statistical significance was determined using BH-FDR correction (FDR-adjusted p < 0.05). Genotype combinations that remained significant after BH-FDR adjustment are highlighted in bold. Complete details of ORs, nominal p-values, and FDR-adjusted p-values are provided in Additional file 1: Table S1

Figure 3 shows the significant 3-loci SNP‒SNP interactions. The combination of the rs331, rs651821, and rs711752 genotypes was associated with newly identified MetS and non-MetS. The SNP rs711752 is located in CETP, and the SNPs rs331 and rs651821 are in LPL and APOA5, respectively. Figure 3A summarizes the numbers of rs3741298, rs711752, and rs3741298 genotype combinations associated with high and low risks for newly identified MetS from the MaODR. The combination of rs331, rs651821, and rs711752 was associated with newly identified MetS and non-MetS. rs711752 is located in CETP, and rs331 and rs651821 are in LPL and APOA5, respectively. Figure 3A summarizes the distribution of genotype combinations, and Fig. 3B shows the corresponding ORs and nominal p-values relative to the major genotype reference, denoted as “(Ref)”. Full details of ORs, nominal p-values, and BH-FDR–adjusted p-values for all genotype combinations are summarized in Additional file 2: Table S2. In the 3-locus models, 11 of the 26 non-reference genotype combinations achieved statistical significance after BH-FDR adjustment, while the remaining combinations did not pass the adjusted threshold. The genotype combinations included both risk and protective effects, demonstrating the interaction among rs331, rs651821, and rs711752. In the specific subset of rs651821(-CT)–rs331(-GG), all combinations with any rs711752 genotype consistently showed significant risk associations (odds ratio > 1 and BH-FDR–adjusted p-value < 0.05; Fig. 3B), and no protective combinations were observed within these subsets.

Fig. 3.

Three-locus interaction model (rs331 in LPL, rs651821 in APOA5, and rs711752 in CETP) identified by the MaODR. A Distribution of genotype combinations in MetS and non-MetS groups (rs331-1 = GG, rs331-2 = AG, rs331-3 = AA; rs651821-1 = TT, rs651821-2 = CT, rs651821-3 = CC; rs711752-1 = AG, rs711752-2 = GG, rs711752-3 = AA). For each genotype combination, the left bar represents cases and the right bar represents controls. B ORs and nominal p-values for each genotype combination relative to the major genotype reference (rs331-GG + rs651821-TT + rs711752-AG), denoted as “(Ref)”. Gray cells indicate risk (OR ≥ 1), and white cells indicate protective effects (OR < 1). Nominal p-values are presented for clarity, while statistical significance was determined using BH-FDR correction (q < 0.05). Genotype combinations that remained significant after BH-FDR adjustment are highlighted in bold. Complete details of ORs, nominal p-values, and FDR-adjusted p-values are provided in Additional file 2 Table S2

GO and pathway analyses of newly identified MetS GWAS-associated loci

The results revealed that approximately 14% of the participants included in the study presented newly identified MetS. GWAS identified 35 SNPs significantly associated with newly identified MetS. These variants were subsequently mapped to protein-coding or annotated genes, including LPL (rs295, rs320, rs326, rs331, rs13702, rs15285, rs10105606, rs2083637, rs28526159, Affx31885734 (rs2083636), Affx31885823 (rs35237252)), APOA5 (rs651821, rs662799, rs2367970, rs2266788, Affx4282911(rs2075291)), APOA4 (rs7350481), BUD13 (rs1558861, rs9326246, rs11216126, rs180326, rs3825041), ZPR1(rs2160669, rs964184, rs2075290, rs603446, rs3741298), LOC124902762 (rs7396835), APOC3 (rs2854117, rs2854116), CETP (rs247616, rs17231506, rs711752, rs7499892), APOE (rs429358)) on chromosomes 8, 11, 16, and 19. For downstream enrichment analysis, we restricted the analysis to mapped protein-coding genes with valid GO annotations in the PANTHER database. APOC3 was classified as “no PANTHER category assigned (unclassified),” while LOC124902762 was returned as an “Unmapped ID.” Consequently, both genes were excluded from the GO term categorization presented in Fig. 4. The results of the GO enrichment analysis, based on the remaining mapped genes, are illustrated in Fig. 4. The mapped genes were annotated to the following biological process categories (Fig. 4A): biological regulation (3 genes, 13.6%), cellular process (4 genes, 18.2%), developmental process (1 gene, 4.5%), homeostatic process (3 genes, 13.6%), localization (3 genes, 13.6%), metabolic process (5 genes, 22.7%), and multicellular organismal process (3 genes, 13.6%). With respect to molecular function (Fig. 4B), the mapped genes were annotated to binding (6 genes, 50.0%), catalytic activity (1 gene, 8.3%), molecular function regulator activity (2 genes, 16.7%), and transporter activity (3 genes, 25.0%). For cellular component categories (Fig. 4C), the mapped genes were annotated to cellular, anatomical entity (6 genes, 60.0%) and a protein-containing complex (4 genes, 40.0%) (Fig. 4C). Because individual genes can be annotated to multiple GO categories and terms, the summed counts across categories exceed the number of unique genes analyzed. The detailed mapping of each GWAS-mapped gene to its corresponding GO categories, including excluded genes (APOC3 and LOC124902762), is provided in Additional file 3: Table S3.

Fig. 4.

GO enrichment of mapped genes from GWAS-significant loci. Seven mapped protein-coding genes with available GO annotations were analyzed (two loci lacked eligible annotations and were excluded). APOC3 (no PANTHER category assigned) and LOC124902762 (Unmapped ID) were excluded. Pie charts illustrate the proportion of mapped genes annotated to each GO category: A Biological Process, B Molecular Function, and C Cellular Component. Because individual genes can be annotated to multiple GO terms, the summed counts across categories may exceed the number of unique genes. A detailed list of all nine mapped genes and their GO annotations is provided in Additional file 3: Table S3

Protein‒protein interaction network

Figure 5 shows the significant protein‒protein interaction network (PPI enrichment p value < 1.0e-16) according to the "evidence view" from STRING. The proteins with strong connections were CETP, APOE, APOA4, LPL, APOA5, ZPR1, and BUD13, and some of these proteins were involved in cholesterol metabolism (CETP, APOE, APOA4, LPL) and the PPAR signalling pathway (APOA5 and LPL). We further analysed the potential PPI network using STRING; APOF, APOC4, APOC1, APOC2, and LPA were the potential proteins with strong connections with CETP, APOE, APOA4, LPL, APOA5, ZPR1, and BUD13. These proteins were influenced by cholesterol metabolism (CETP, APOE, APOA4, and LPL) and the PPAR signalling pathway (APOA5 and LPL).

Fig. 5.

Protein–protein interaction (PPI) networks derived from GWAS-mapped genes associated with newly identified MetS. A Core PPI network generated in STRING from protein-coding genes mapped from GWAS-significant loci with valid functional annotations. B Expanded PPI network including predicted functional partners identified by STRING’s network expansion feature. Nodes shown in black font represent proteins encoded by GWAS-mapped genes, while nodes shown in blue font denote proteins added by STRING as potential functional interactors. Nodes represent proteins (gene products), and edges represent predicted or known interactions. Edge colors denote the source of supporting evidence: green (neighborhood), red (gene fusion), mustard (text mining), black (co-expression), purple (experimental data), and blue (co-occurrence)

Discussion

In this study, we utilized data from the TWB to delineate the composition of newly identified MetS patients and identify SNPs and genomic regions associated with MetS in the Taiwanese population. Patients with DM, hypertension, hyperlipidaemia, current smoking and a history of smoking were excluded. Our results indicated that gene‒gene interactions of APOA5 rs651821, LPL rs331, and CETP rs711752 might contribute to the pathophysiology of MetS. MaODR is an analytic approach for gene‒gene interactions that detects nonlinear multigene interactions. This study showed that the unbalanced function-based MaODR was effective in detecting multi-locus interaction signals (APOA5–LPL–CETP) within an imbalanced cohort. The findings, the details of the computational processes, and the SNP‒SNP interaction networks were further validated via single SNP‒to‒single SNP interaction analyses for the best 2‒3-locus models regarding OR values. Our objective was both to establish statistical associations and to clarify the functional implications of the identified SNPs. Variants detected by MaODR were mapped to their corresponding genes and analyzed within the STRING PPI network. In this network (Fig. 5), nodes represent the proteins encoded by the genes of interest, and edges indicate predicted or known functional associations among these proteins, based on integrated evidence channels including experimental data, curated pathway databases, co-expression data, and text mining. This systems-level perspective provides biological context for the observed genetic interactions. We limited our multilocus search to 2- and 3-way interactions. Although higher-order models are theoretically possible, contemporary reviews and methods papers highlight a persistent combinatorial explosion, with the number of candidate interactions increasing exponentially with interaction order, resulting in prohibitive computational cost. Moreover, higher-order models have been reported to exhibit reduced statistical reliability and limited interpretability, particularly in large-scale genomic settings [38, 39]. These considerations support focusing on lower-order epistasis in practice, where the balance between computational feasibility and biological interpretability can be more appropriately maintained.

A comparison of our findings with those of other studies highlights a considerable overlap of gene associations with MetS, underscoring their significance across diverse populations and contexts [40–42]. LPL is instrumental in lipoprotein metabolism and the use of fatty acids. It functions by hydrolysing triglycerides present in circulating lipoproteins. Dysregulation or malfunction of LPL can disrupt lipid processing, potentially contributing to MetS [43]. In this study, polymorphisms rs295, rs320, rs326, rs331, rs13702, and rs15285 in the LPL gene were associated with MetS based on a GWAS. The rs331 polymorphism has been studied for its potential association with MetS components, particularly lipid abnormalities [44]. Furthermore, when the rs331 GG type was combined with the rs651821 CC type (in the APOA5 gene), the OR for MetS increased to 1.76 (p = 9.61E-20) relative to the designated reference genotype, according to our MaODR analysis.

APOA5 plays a pivotal role in lipid metabolism [41], and mutations in this gene have been associated with abnormal lipid levels and increased cardiovascular risk. One of our findings was the identification of a common polymorphism within the APOA5 gene (rs651821, rs662799, rs2266788, and rs2075291 [Affx4282911 probe ID]), which were associated with MetS. APOA5 is a crucial regulator of lipid metabolism, particularly triglyceride metabolism. This relation was especially apparent with a two combined model: rs651821 and rs331 combined, as well as a 3 combined model: rs651821, rs331 with the addition of rs711752 (a SNP in the cholesteryl ester transfer protein-encoding gene, CETP).

CETP facilitates the transfer of cholesterol esters and triglycerides between lipoproteins, significantly influencing cholesterol metabolism and the lipid balance [45]. The transfer of cholesteryl esters, exchange of lipids, regulation of HDL-C levels, and influence on cardiovascular health are the primary functions of the CETP gene [46]. Research has shown that this polymorphism is significantly related to low HDL-C levels, a component of MetS [47]. This finding suggests a genetic influence of CETP variations on the risk and development of MetS [45, 48]. We reported that the polymorphisms rs17231506, rs711752, and rs7499892 in the CETP gene were associated with MetS. In addition, the combination of the rs331 GG + rs651821 CC type and the rs711752 GG type increased the OR for MetS to 1.87 (p = 2.51E-10), relative to the designated reference genotype.

The LPL gene encodes the enzyme lipoprotein lipase, which plays a crucial role in lipid metabolism. The main functions of the LPL gene and its enzyme products include hydrolysis of triglycerides, lipid uptake, regulation of plasma lipid levels, and influence on metabolic health [49]. A previous study has indicated that aerobic exercise improved metabolic syndrome outcomes in Taiwanese adults with the rs3779788 CC/CT genotype relative to those with the TT genotype [50]. Other findings suggest that the LPL rs301 genotype may offer protection against MetS in Taiwanese adults who consume coffee compared with those who do not drink coffee [51]. In line with our results, Ho et al. reported that the LPL polymorphism was associated with MetS [48].

The ZPR1 gene is involved in various cellular processes. ZPR1 has been implicated in mRNA transport and localization, DNA damage repair, and cell proliferation and apoptosis regulation. ZPR1 interacts with other proteins and nucleic acids to carry out its functions, although its exact mechanisms and roles in different cellular contexts may still be under investigation. Previous research investigating the association of rs3741298 with health outcomes has yielded mixed results. Some studies have reported associations between this SNP and various metabolic traits, including lipid levels [52] and the risk of cardiovascular diseases [53, 54]. For example, certain studies have reported associations between rs3741298 and plasma lipid levels, such as triglyceride and LDL cholesterol levels [55]. Our investigation also revealed associations between MetS and specific SNPs within the ZPR1 gene, including rs2160669, rs964184, rs2075290, rs603446, rs3741298, and rs2266788.

In addition to statistical significance, the potential biological mechanism under the interaction models was our concern. Therefore, we investigated the functional relevance of the interactive effects of APOA5, LPL, and CEPT on MetS via the MaODR. The BUD13, ZPR1, and APOA5 genes encode three proteins within the APOA5 protein pathway located in the 11q23.3 chromosomal region. One of our more interesting findings was the identification of gene‒gene interactions, polymorphisms within the APOA5 gene (rs651821), and the LPL gene (rs331), which were associated with MetS. Aung et al. used GMDR analyses to identify potential gene‒gene interactions between the BUD13 and ZPR1 genes, which influence the risk of hypercholesterolemia and hypertriglyceridaemia in Chinese subjects [36]. A three-way model including BUD13 rs623908, CETP rs820299, and LIPA rs1412444 (p = 0.001), as well as a four-way model involving APOA5 rs662799, BUD13 rs623908, CETP rs820299, and LIPA rs1412444 (p = 0.012), were identified, indicating potential gene–gene interactions among APOA5, BUD13, CETP, and LIPA in relation to MetS using the GMDR method [37]. Notably, several of these loci, such as APOA5 and CETP, were also highlighted in our MaODR-based interaction models, while ZPR1 emerged as an associated locus in both studies. This convergence across studies employing distinct analytical frameworks reinforces the biological relevance of these genes to MetS susceptibility. During the 14-year follow-up period, 1270 subjects developed MetS, and five SNPs in four genes—BUD13 rs10790162, ZPR1 rs2075290, APOA5 rs2266788, APOA5 rs2075291, and MKL1 rs4507196—were significantly correlated with susceptibility to MetS (p < 0.00005) [56]. We further investigated the combination of three SNPs from a group of 35 candidate SNPs. The findings revealed that SNPs in the APOA5 gene (rs651821), the LPL gene (rs331), and the CETP gene (rs711752) demonstrated the most significant associations with MetS. Studies have shown that the rs651821 T allele is associated with increased plasma triglyceride levels [57]. This effect is believed to be due to reduced expression of the APOA5 gene, leading to slower breakdown of triglycerides and their accumulation in the blood. The rs331 polymorphism in the LPL gene affects lipid metabolism by influencing CETP activity, which plays a critical role in transferring cholesteryl esters and triglycerides between lipoproteins. The rs331 polymorphism may interact with other genetic variants, such as those in the CETP gene, influencing overall lipid metabolism and contributing to the complexity of MetS [58]. To further interpret these findings in a systems-level context, we analyzed the GWAS-mapped genes within STRING PPI networks. The expanded STRING network (Fig. 5B) highlights potential functional interactions among the genes mapped by GWAS. These predicted associations are integrated from multiple evidence sources and should be regarded as hypothesis-generating rather than confirmatory [59]. Nevertheless, the enrichment of lipid and cholesterol metabolism pathways within these interaction clusters underscores the biological relevance of the GWAS findings and helps prioritize candidate genes for further investigation.

To improve the interpretation of our GWAS results, we compared the lead SNPs identified in our analysis with nearby variants previously reported to be associated with MetS or lipid-related traits (see Additional file 4: Table S4). Several key loci—such as APOA5 rs651821, LPL rs331, and CETP rs711752—reside in genomic regions that also harbor other variants (e.g., APOA5 rs662799 and rs2266788, LPL rs13702 and rs320, CETP rs247616 and rs17231506) repeatedly implicated in independent studies across different populations. Available evidence suggests that these variants often fall within the same haplotype blocks, indicating potential LD. Although precise pairwise LD (r²) values should ideally be calculated using the Taiwan Biobank or the 1000 Genomes East Asian panel, the reported effect directions appear broadly consistent. In particular, alleles linked to elevated triglyceride levels or reduced HDL-C concentrations are generally associated with increased MetS risk, reinforcing the biological relevance of these loci. The concordance between our GWAS findings and prior research highlights APOA5, LPL, and CETP as important contributors to MetS susceptibility and underscores the need for locus-wide analyses to better capture the full spectrum of genetic variation in these regions.

There are several limitations associated with multiple factors, including genetic background, environmental factors, and gene‒environment interactions, which likely influence the effects of gene‒gene interactions on health. The genetic homogeneity of the TWB cohort reduces the risk of population stratification; however, it also limits the applicability of findings to populations with different allele frequencies or LD patterns. Furthermore, rare variants and structural variants not well captured by genotyping arrays may have been missed. Environmental and lifestyle factors—such as dietary habits, physical activity, tobacco use, alcohol consumption, and socioeconomic status—were not fully integrated into the analyses due to issues with data completeness and variability, leaving potential for residual confounding. Although the MaODR framework was used for gene–gene interaction analyses, it could be adapted to include categorical environmental variables, enabling gene–gene–environment (G × G × E) interaction studies. Finally, despite excluding participants with previous diagnoses or treatments for diabetes, hypertension, or hyperlipidemia, the presence of undiagnosed conditions at baseline cannot be completely excluded. Nevertheless, the comprehensive health assessments conducted within the TWB help mitigate this concern. Another limitation of our study is that the TWB does not provide detailed information on the specific drug names or classes used (e.g., ACE inhibitors, statins, or metformin). While this approach allowed us to exclude individuals whose laboratory measures may have been modified by pharmacological treatment, the lack of drug-specific data limits the reproducibility and granularity of our exclusion criteria. Further research, including larger-scale genome-wide association, linking with prescription databases or electronic health records, and functional studies, is needed to fully elucidate the health effects of suspected genes and their role in human health and disease.

Conclusions

In this study, we used data from the TWB to describe the composition of relatively pure MetS and identify SNPs and genomic regions associated with newly identified MetS in the nonsmoking Taiwanese population. Our analysis revealed that approximately 14% of the participants were newly identified with MetS without DM, hypertension, or hyperlipidaemia. The GWAS analysis identified 35 SNPs that were significantly associated with MetS. These SNPs were located on or near the LPL, APOA5, BUD13, ZPR1, APOC3, CETP, and APOE genes on chromosomes 8, 11, 16, and 19. Our results also suggested that gene‒gene interactions among APOA5 rs651821, LPL rs331, and CETP rs711752 might contribute to the pathophysiology of MetS. Further studies of multiple factors, including genetic background, environmental factors, and gene‒environment interactions, are necessary to elucidate the health effects of suspected genes and their role in human health and metabolic diseases.

Methods

Study population

The research utilized data from the TWB (https://www.twbiobank.org.tw/) [60], a comprehensive community research database initiated in 2005, to serve as a central repository for biomedical research, collecting data from 43 recruitment stations across Taiwan Island, which serves as a general population-based research database. The primary objective of the TWB is to establish a collection of biological samples and associated health data to facilitate continuous monitoring of the Taiwanese population. The TWB enrolled a diverse group of participants aged 30 − 70 years from different regions in Taiwan via structured questionnaires, interviews, and thorough clinical assessments. This comprehensive approach meticulously recorded detailed demographic data, health status, and lifestyle factors. A total of 122,608 participants meeting the quality control criteria for measures of waist circumference, questionnaires, and clinical assessments were recruited for the study, with all participants providing informed consent for TWB before enrolment. Strict adherence to data-sharing protocols and guidelines was maintained throughout, and the protocol was endorsed by the Ethics Committee of Kaohsiung Medical University Hospital (approval number: KMUHIRB-G(II)−20,200,007, approval date: 2020/04/28). Table 1 summarizes demographic and clinical characteristics by MetS status. Continuous variables (BMI, waist circumference, SBP/DBP, fasting glucose, HbA1c, triglycerides, HDL-C) are reported as mean ± SD; categorical variables (e.g., sex) as counts (percentages). BMI was calculated as weight (kg)/height (m²). Records with missing values for a given variable were excluded listwise for that variable; no additional outlier filtering was applied. Between-group comparisons used chi-square tests for categorical variables and two-sample (independent-samples) t-tests for continuous variables. Reported p-values are nominal (unadjusted), as Table 1 is intended for descriptive comparison rather than formal inference. Differences between groups were assessed using independent t-tests for continuous variables and chi-squared tests for categorical variables. A two-sided p < 0.05 was considered statistically significant.

Metabolic syndrome (MetS)

The diagnostic criteria for MetS in both men and women were based on the guidelines set forth by the U.S. American Heart Association/National Heart Lung and Blood Institute [61]. A participant was classified as having MetS if three or more of the following five conditions were met: (1) waist circumference ≥ 90 cm in men or ≥ 80 cm in women; (2) triglycerides ≥ 150 mg/dL or use of lipid-lowering medication; (3) HDL-C < 40 mg/dL in men or < 50 mg/dL in women, or use of medication; (4) systolic blood pressure ≥ 130 mmHg, diastolic blood pressure ≥ 85 mmHg, or use of antihypertensive medication; and (5) fasting plasma glucose ≥ 100 mg/dL or use of antidiabetic medication. TWB data sources used for this classification included directly measured anthropometric parameters (waist circumference, blood pressure), laboratory tests (triglycerides, HDL-C, fasting plasma glucose), and self-reported medical history.

To examine a treatment-naive phenotype of MetS, individuals with a history of smoking, a prior physician diagnosis of diabetes, hypertension, or hyperlipidemia, or current use of related medications were excluded. Accordingly, the analysis focused on newly identified MetS cases defined solely by baseline anthropometric and laboratory criteria, free of prior diagnosis or treatment, and on nonsmoking participants. Medication use for diabetes, hypertension, or hyperlipidemia was defined based on self-reported physician diagnoses together with a binary “yes/no” response on current medication, with indirect biomarker evidence considered supportive when values appeared pharmacologically controlled. Figure 6 shows the flowchart of the participants included in the study. For descriptive comparisons between the MetS and non-MetS groups, categorical variables were tested using the chi-square test, while continuous variables were compared using independent-samples t-tests.

Fig. 6.

Flowchart of the participants included in the study

Genotyping and quality control for GWAS

All TWB study participants were genotyped using the Affymetrix TWB 2.0 SNP chip, a platform comprising approximately 750,000 SNPs. The TWB chips were developed in collaboration with Thermo Fisher Scientific in the United States (Waltham, MA, USA) and at the national center for genome medicine (NCGM) in Taiwan. These chips feature state-of-the-art technology and were designed explicitly for the Taiwanese Han population. They included a carefully curated selection of 750,000 SNPs from diverse origins, including the Axiom genome-wide CHB (Han Chinese in Beijing, China) array. The data can be accessed via the following website: https://www.biobank.org.tw/english.php.

Data processing of the Affymetrix microarray and quality control (QC) were performed using PLINK 1.9 [62]. Sample-level QC removed individuals with ambiguous sex assignment, call rate < 95%, heterozygosity deviating >  ± 3 SD from the mean, and pairwise relatedness (PI-hat > 0.1875; one individual retained per related pair). Marker-level QC excluded SNPs with call rate < 95%, Hardy–Weinberg equilibrium p < 1 × 10⁻5, or minor allele frequency < 0.05. Associations between candidate SNPs and MetS were examined using a primary logistic regression framework under an additive genetic model, with sex included as an adjustment covariate to reduce potential confounding. In Tables 1 and 2, p-values are presented as nominal (unadjusted) values from descriptive statistics and locus-specific genotype comparisons. For GWAS single-SNP associations, genome-wide significance was defined as p < 5 × 10⁻⁸ and suggestive significance as p < 1 × 10⁻5. To ensure sample independence, we assessed pairwise relatedness using the kinship coefficient. Individuals with a coefficient > 0.1875, corresponding to first- or second-degree relationships, were classified as related. For each related pair, one sample was excluded to preserve independence, prioritizing the individual with more complete phenotype and genotype data. When data quality was comparable, the case sample was preferentially retained. This procedure minimized potential inflation of association statistics arising from familial correlations.

For multilocus analyses, a candidate SNP panel was compiled through a structured selection process. First, all loci exceeding the genome-wide or suggestive thresholds were retained. Second, additional nominally significant SNPs (p < 0.05) were included if located in genes with established relevance to lipid metabolism or metabolic syndrome (e.g., APOA5, LPL, CETP). To minimize redundancy while preserving representative signals, LD pruning was applied, retaining a single SNP per LD block defined by pairwise r² > 0.8 in East Asian populations. This procedure yielded representative SNPs for input into the multilocus MaODR analysis. SNP-to-gene mapping was performed using ANNOVAR and Ensembl VEP, based on physical proximity within ± 50 kb, and annotations were restricted to protein-coding genes for downstream GO and STRING enrichment analyses. For multilocus genotype comparisons derived from MaODR models, multiple testing was addressed using the BH-FDR, with p < 0.05 considered statistically significant.

MaODR

In 2023, Yang et al. introduced the MaODR for detecting gene‒gene interactions [30], and the corresponding source code is publicly available on GitHub [63]. This method uses a decision vector X composed of genetic loci and an objective function SSI to quantify the strength of the interaction. When dealing with an many-objective maximization problem, multiple measures can be employed by expressing the maximization problem as O = [f₁(X), …, f_p(X)], where p represents the total number of measures. A vector X^* = (X₁, X₂, …, X_j) can be defined to represent a set of possible combinations of genetic loci, with j being the total number of possible combinations. A solution X₁ is said to dominate another solution X₂ if f(X₁) ≥ f(X₂) and f ∈ O for all selected objective functions. Any other solution does not dominate a Pareto optimal solution. Within the Pareto set, all vectors X ∈ X^* are not dominated by any other vector. To maximize the objective function, several measures of SSI can be formulated.

$$\text{maximize}\left\{\begin{array}{c}{f}_1(X)\\ f_2\left(X\right)\\ ⋮\\ f_p(X)\end{array}\right)$$ 1

The MaODR process introduces the concept of nondominated sorting of the Pareto set filter operator to assess the quality of an m-locus combination. This operator uses multiple measures simultaneously. K subpopulations are obtained through K-fold CV, after which all the subpopulations are merged to obtain the SSI candidates. Following the original MaODR framework [30], we implemented stratified random k-fold cross-validation, which maintains the case–control ratio within each fold and helps mitigate bias in imbalanced datasets. The cross-classified SSIs are utilized to calculate the CVC of the SSIs in the merged population, with the optimal SSIs selected on the basis of the highest CVC. In summary, the MaODR process involves the following:

1. K-fold stratified random cross-validation to create K subpopulations.

2. Creation of possible combinations of m genetic loci.

3. Determination of the ratio of cases to controls within each combination of multiple genetic loci.

4. Generation of a two-way contingency table on the basis of multiple genetic loci combinations.

5. Evaluation of the combinations using three measures.

6. Update of the subpopulations using the non-dominated sorting of the Pareto set filter operator.

7. Computation of the cross-validated consistency and selection of the optimal subpopulation sampling intervals.

Step 1. Utilize K-fold stratified random cross-validation to create K subpopulations

To ensure the accuracy and reliability of our results, we implemented a K-fold stratified CV process using a fivefold CV method. This process involves dividing the dataset into K subsets, with four subsets for identifying potential SSI cases and one subset for evaluating the selected SSIs. By utilizing this approach, we can effectively detect and assess SSIs while mitigating the risk of bias or error in our analysis.

Step 2. Create possible combinations of m genetic loci

All possible combinations of SNPs are generated to assess the number of combinations and evaluate SSIs on the basis of the m-locus model. For example, with a dataset of three SNPs {SNP₁, SNP₂, SNP₃}, the feasible decision vectors with two-locus combinations result in three SSIs {ssi₁ = {SNP₁, SNP₂}; ssi₂ = {SNP₁, SNP₃}; ssi₃ = {SNP₂, SNP₃}}, where ssi denotes an SSI. The process considers haplotype diversity and LD goals in collecting the input dataset for MaODR, as it is based on the MDR approach and does not explicitly account for LD [64].

Step 3. Determine the ratio of cases to controls within each combination of multiple genetic loci

Step 3–1

For each possible m-locus combination, a contingency table containing 3 ^m multilocus genotype cells is constructed. In the training dataset, samples are assigned to cells according to their multilocus genotypes, and the number of cases and controls in each cell is tallied. For example, in a two-locus combination {SNP₂, SNP₃}, the table consists of nine genotype cells. The genotypes for SNP₂ are coded as AA, Aa, and aa, while those for SNP₃ are coded as BB, Bb, and bb, resulting in the 3 × 3 table of multilocus genotypes.

Step 3–2

Evaluation of the case‒control ratio of the multilocus genotype using the following:

$${\theta }_a=\frac{n_{+0}\times n_{a1}}{n_{+1}\times n_{a0}}$$ 2

where n_a0 and n_a1 are the samples in the bath multilocus genotype in the control and case groups, and n₊₀ and n₊₁ are the total samples in the control and case groups, respectively. The high- and low-risk groups of multilocus genotypes are subsequently determined in X. Determination of high- and low-risk groups is based on the value of θ_a, with a multilocus genotype categorized as high risk if θ_a is greater than or equal to one and low risk otherwise.

Step 4. Generate a two-way contingency table on the basis of multiple genetic loci combinations

The two-way contingency table is derived from the 3 ^m labelled multilocus genotypes categorized on the basis of their labelled grouping (high- and low-risk groups) and outcome (case and control groups). The table's true-positive (TP), false-positive (FP), false-negative (FN), and true-negative (TN) values are computed on the basis of the sample counts in the respective groups and outcomes using formula (3).

$$\left\{\begin{array}{c}TP={\sum }_{a\in \left\{{\theta }_{a,},{\theta }_a,\ge ,1\right\}}{t}_{a1}\\ FP={\sum }_{a\in \left\{{\theta }_{a,},{\theta }_a,\ge ,1\right\}}{t}_{a0}\\ FN={\sum }_{a\in \left\{{\theta }_{a,},{\theta }_a,<,1\right\}}{t}_{a1}\\ TN={\sum }_{a\in \left\{{\theta }_{a,},{\theta }_a,<,1\right\}}{t}_{a0}\end{array},,\right)$$ 3

where t_ab represents the individuals matched to the a-th multilocus genotype in outcome status b, b = 1 denotes the case group and b = 0 denotes the control group. TP and FP denote the number of case and control samples classified in the high-risk group, respectively. FN and TN denote the number of case and control samples classified in the low-risk group, respectively.

Step 5. Evaluate the combinations using three measures

The objective function of the m-locus combination X is calculated. In the original MaODR framework, ten alternative objective functions were introduced for model evaluation. Based on prior benchmarking, however, the combined use of balanced CCR, NMI, and LR was shown to be the most effective, and thus only these three objectives were applied in the current study.

Primary objective function

The balanced CCR can manage unbalanced datasets to calculate the proportion of appropriately classified individuals [29, 65]. The balanced CCR is calculated as the TP ratio for cases and the TN ratio for controls as follows:

$$CCR=0.5\times \left(\frac{\mathit{TP}}{TP+FN},+,\frac{\mathit{TN}}{FP+TN}\right),$$ 4

where TP, FP, FN, and TN are calculated in (3) from Step 4. A balanced CCR value is within an interval of 0 to 1, with 1 representing the optimal solution.

Objective function

In addition to the balanced CCR, the objective function of the m-locus combination X can be selected from the alternative contingency table measures, including the normalized mutual information (NMI) and likelihood ratio (LR).

NMI measures the reduction in uncertainty about the true class labels provided by predicted classifications, based on Shannon entropy [32]. In a 2 × 2 contingency table, the row entropy H(x), column entropy H(y), and conditional entropy H(y|x) are defined as:

$$H\left(x\right)=-\sum _i{p}_i{\text{log}}_2{p}_i$$

$$H\left(y\right)=-\sum _j{p}_j{\text{log}}_2{p}_j$$

$$H\left(y,|,x\right)=\sum _i{p}_i\left[-,\sum _j,\frac{p_{\mathit{ij}}}{p_i},{\mathit{log}}_2,\frac{p_{\mathit{ij}}}{p_i}\right]$$

where p_i and p_j are the frequencies of the predicted and true class states, respectively, p_ij is the joint probability, i = {1, 2}, and j = {1, 2}. We let PN = TP + FP + FN + TN, P = TP + FP, N = TN + FN, TPN = TP + FN, and TNP = TN + FP. The NMI function is expressed as follow:

$$\begin{array}{cc}\hfill \mathit{NMI}& =\frac{H\left(y\right)-H\left(y,|,x\right)}{H(y)}\hfill \\ \hfill & =\frac{2\left\{\begin{array}{c}PN{\mathit{log}}_{2}PN+TP{\mathit{log}}_{2}TP+FN{\mathit{log}}_{2}FN\\ +TN{\mathit{log}}_{2}TN+FP{\mathit{log}}_{2}FP-P{\mathit{log}}_{2}P\\ -TPN{\mathit{log}}_{2}TPN-TNP{\mathit{log}}_{2}TNP-N{\mathit{log}}_{2}N\end{array}\right\}}{2\left\{\begin{array}{c}PN{\mathit{log}}_{2}PN-TPN{\mathit{log}}_{2}TPN-TNP{\mathit{log}}_{2}TNP\end{array}\right\}}\hfill \end{array}$$ 5

Likelihood Ratio (LR)

The LR compares the likelihood of the observed data under the unrestricted model (observed frequencies) with the likelihood under the null hypothesis of no association (expected frequencies) [32]. LR is calculated as:

$$\begin{array}{cc}\hfill \text{LR}& =2\sum \text{Observed log}\left[\frac{\text{Observed}}{\text{Expected}}\right]\hfill \\ \hfill & =2\left[T,P,\times ,\text{log},\left(\frac{\mathit{TP}}{A_{}^{\ast }}\right),+,F,P,\times ,\text{log},\left(\frac{\mathit{FP}}{B_{}^{\ast }}\right),+,F,N,\times ,\text{log},\left(\frac{\mathit{FN}}{C_{}^{\ast }}\right),+,T,N,\times ,\text{log},\left(\frac{\mathit{TN}}{D_{}^{\ast }}\right)\right]\hfill \\ \hfill & \text{s}.\text{t}.\left\{\begin{array}{c}\begin{array}{c}A_{}^{\ast }=\frac{(TP+FN)(TP+FP)}{TP+FP+FN+TN}\\ B_{}^{\ast }=\frac{(FP+TN)(TP+FP)}{TP+FP+FN+TN}\\ C_{}^{\ast }=\frac{(TP+FN)(FN+TN)}{TP+FP+FN+TN}\end{array}\\ D_{}^{\ast }=\frac{(FP+TN)(FN+TN)}{TP+FP+FN+TN}\end{array}\right)\hfill \end{array}$$ 6

Step 6. Update the subpopulations via the nondominated sorting of the Pareto set filter operator

The Pareto operation, with its systematic approach, involves the use of a Pareto set filter operator to gather candidates (X_j^* = [X₁, …, X_l]) into a Pareto set indexed by j, where j ∈ {1,…, K} and l is the total number of possible m-locus combinations on the basis of the CCR, LR, and NMI values. In the jth Pareto set, nondominated sorting selects candidates through the following two steps:

1. Comparison of an m-locus combination X with all the candidates of the jth Pareto set. If the jth Pareto set is empty, X is added; otherwise, X is considered a candidate and added to the jth Pareto set if no candidate dominates it.

2. Comparison of X_p and X_q (where p ≠ q) in the jth Pareto set. If X_p dominates X_q, then X_q is removed from the set.

All the candidates in the Pareto set can be visually represented as a Pareto frontier.

Step 7. Compute the cross-validated consistency and choose the optimal subpopulation sampling intervals

In multiobjective optimization with differential evolution, the jth Pareto set is constructed by selecting candidates (i.e., m-locus combinations) via j-fold CV training data, where j ranges from 1 to K and K represents the number of CV partitions. Each CV partition is subsequently utilized to identify the significant candidates, i.e., the Pareto set, through steps 2 to 5 using the training data. A standard method for determining the optimal SSI involves selection of the optimal model with a high CVC. When the CVC reaches the number of CVs, these SSIs are likely optimal in another dataset. During the CVC process, the m-locus combination with the highest number of occurrences in the K Pareto sets emerges as the optimal solution. If multiple m-locus combinations occur with the same frequency, they are deemed optimal SSIs. Steps 3 to 5 are iterated K times to assess the fitness values of the selected objective functions (CCR, LR, and NMI) for the optimal SSI using the K test data. The average fitness value, calculated as the sum of the fitness values divided by K, is then derived for the objective function associated with the optimal SSI. MaODR analyses were performed using the software package released by the method developers (available at https://github.com/DarrenYDLin/MaODR.git).

GO and pathway analysis

Gene Ontology (GO, https://geneontology.org/) is a widely recognized resource for functional annotations, encompassing biological processes, molecular functions, and cellular components [66, 67]. GO enrichment analysis was performed using the PANTHER database (http://www.pantherdb.org), with enrichment evaluated via hypergeometric statistics and p-values adjusted for multiple testing using the Benjamini–Hochberg false discovery rate (BH-FDR) method. The Kyoto Encyclopedia of Genes and Genomes (KEGG, https://www.genome.jp/kegg/pathway.html) was used to interpret curated pathway information. KEGG pathway enrichment and PPI network analyses were performed in STRING (version 12.0, https://string-db.org/) [68]. We performed enrichment analyses to identify functional categories and pathways associated with genes mapped from GWAS-significant SNPs in newly identified MetS. For GO analyses, enrichment was tested using hypergeometric statistics, and p-values were adjusted for multiple comparisons using the BH-FDR procedure. Genes lacking valid GO annotations in the PANTHER database (e.g., classified as “unclassified” or returned as “Unmapped ID”) were automatically excluded from downstream GO analyses. For STRING-based analyses, Fisher’s exact test with BH-FDR correction was applied, and categories with FDR-adjusted p-values < 0.05 were considered statistically significant.

Protein‒protein interaction analysis

PPI networks were constructed and analyzed using STRING (version 12.0, https://string-db.org/) [68]. The initial network was derived from GWAS-mapped protein-coding genes that possess valid functional annotations. To delve deeper into their biological relevance, we utilized STRING's network expansion feature, limiting the expansion to a single shell depth with a high-confidence cutoff (combined score ≥ 0.70). The evidence sources for the interactions included experimental data, curated pathway databases, co-expression data, and text mining; no expansions beyond one shell depth were conducted. This expanded network served as a hypothesis-generating framework to position GWAS-mapped genes within broader biological interaction contexts [59]. We assessed the functional enrichment of the PPI networks for GO terms and KEGG pathways using Fisher’s exact test, applying BH-FDR. Categories exhibiting BH-FDR-adjusted p-values < 0.05 were deemed statistically significant.

Post-hoc inference for ORs

For each MaODR-identified m-locus model, we estimated ORs for all multilocus genotype combinations relative to the major genotype reference cell using contingency-table chi-square tests; Fisher’s exact test was used when an expected count < 5. To account for multiple post-hoc comparisons within a given m-locus panel, p-values were adjusted using the BH-FDR procedure. For 2-locus (3 × 3) tables this yields up to 8 tests (excluding the reference), and for 3-locus (3 × 3 × 3) tables up to 26 tests after excluding the reference and any sparse cells. Statistical significance was defined as p < 0.05 for BH-FDR-adjusted results; nominal p-values are reported alongside for transparency.

Software and computational resources

All statistical and computational analyses were performed on institutional workstations running Windows 10 (64-bit), equipped with Intel Core i7-7700 CPUs and 32 GB RAM. Genotype quality control and preprocessing for GWAS were carried out using PLINK 1.9, which was also used to generate Manhattan and Q–Q plots. R (version 4.5.1) was employed to compute descriptive statistics and summary tables. MaODR analyses were conducted with the official implementation provided by the developers (https://github.com/DarrenYDLin/MaODR.git) [30]. GO enrichment was analyzed using PANTHER, whereas KEGG pathway enrichment and PPI analyses were performed with STRING (version 12.0). Multilocus OR plots were manually prepared in Microsoft PowerPoint, and all figures were finalized in Adobe Illustrator.

Authors’ contributions

Conceptualization, Y.-D. L., H.-Y. C., and C.-H. Y.; methodology, K.-H. L., Y.-D. L., H.-Y. C., and C.-H. Y.; software, K.-H. L., Y.-D. L. and C.-H. Y.; validation, L.-Y. C.; formal analysis, K.-H. L., Y.-D. L., H.-Y. C., and C.-H. Y.; investigation, Y.-D. L., K.-H. L., L.-Y. C., H.-Y. C., and C.-H. Y.; resources, H.-Y. C., and C.-H. Y.; data curation, K.-H. L., and H.-Y. C.; writing—original draft preparation, Y.-D. L. and K.-H. L.; writing—review and editing, H.-Y. C. and L.-Y. C.; visualization, L.-Y. C. and Y.-D. L.; supervision, C.-H. Y. and H.-Y. C.; project administration, H.-Y. C. and Y.-D. L.; funding acquisition, C.-H. Y. and H.-Y. C. All the authors have read and agreed with the published version of the manuscript.

Funding

This study was supported by grants from the National Science and Technology Council, Taiwan (NSTC 112–2221-E-992–105-MY3, NSTC 111–2314-B-037–038-MY2, NSTC 111–2221-E-165–002-MY3, NSTC 114–2314-B-037–060, and NSTC 114–2221-E-165–001), Kaohsiung Medical University Hospital (KMUH114-4R85), and Kaohsiung Medical University (110KK037). This work was also supported partially by the Research Center for Precision Environmental Medicine, Kaohsiung Medical University, Kaohsiung, Taiwan, from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan and by a Kaohsiung Medical University Research Center Grant (KMU-TC114A01).

Data availability

The data can be accessed via the following website: (https://www.biobank.org.tw/english.php). MaODR analyses were performed using the software package released by the method developers (available at https://github.com/DarrenYDLin/MaODR.git) [30]. The MaODR source code used in this study is publicly available on GitHub [63].

Declarations

Ethics approval and consent to participate

The protocol was endorsed by the Ethics Committee of Kaohsiung Medical University Hospital (approval number: KMUHIRB-G(II)-20200007, approval date: 2020/04/28).

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.