Psychiatric and immune factor structure

The current analyses utilized genome-wide association study (GWAS) summary statistics of 11 immune-mediated diseases, 13 psychiatric disorders, and 14 immune markers (Table 1). We began by using Genomic SEM to model the factor structure of the psychiatric disorders and immune diseases based on genetic correlations derived from linkage disequilibrium score regression (LDSC). The psychiatric factor structure reflected a previously established five-factor model [17], now including updated GWAS data for bipolar disorder, major depression, and post-traumatic stress disorder (PTSD) (Method). We found that this five-factor model continued to fit the data well with the updated data (CFI = .97; SRMR = .10). The psychiatric factors could be approximately described as reflecting compulsive, schizophrenia/bipolar, neurodevelopmental, internalizing, and substance use disorders. The immune-mediated disease factor structure consisted of a previously established four-factor model [4] (CFI = .96; SRMR = .08), with the four factors reflecting autoimmune, celiac, mixed immune pattern (denoting a shared involvement of the adaptive and innate immune system), and autoinflammatory diseases (Fig 1).

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Table 1. Sample characteristics of included traits.

https://doi.org/10.1371/journal.pgen.1012328.t001

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Fig 1. Immune-mediated disease and psychiatric disorders correlated factors models and correlations between immune and psychiatric factors.

A) Immune-mediated diseases path diagram with standardized estimates for the correlated factors model used in genomic structural equation modelling (genomic SEM) with four factors of immune-mediated diseases. Latent variables are represented as circles. The genetic component of each phenotype is represented with a circle because the genetic component is a latent variable that is not directly measured but is inferred using linkage disequilibrium score regression (LDSC). Single-headed arrows are factor loadings; double-headed arrows connecting back to the same origin are variances; and double-headed arrows connecting two variables are correlations. Paths labeled 1 are fixed to 1; all estimates are given next to the path with standard errors in parentheses. Disease abbreviations are defined in Table 1. B) Psychiatric disorders path diagram. Disorder abbreviations are defined in Table 1. C) Genetic correlations between factors of immune-mediated diseases and factors of psychiatric disorders. IMMUNE, autoimmune diseases; CEL, celiac disease; MIXED, mixed immune pattern diseases; INFLAMM, inflammatory diseases; COMP, compulsive disorders; SB, schizophrenia/bipolar; NEURO, neurodevelopmental disorders; INT, internalizing disorders; SUD, substance use disorders.

https://doi.org/10.1371/journal.pgen.1012328.g001

The correlations across the psychiatric and immune factors were then estimated. Significance was defined using an FDR corrected threshold. We only considered inter-factor correlations significant when they were not also FDR significant for the Q_Factor heterogeneity statistic, which was used as a quality control test to evaluate whether these factor correlations accurately captured genetic overlap [4]. Non-significant Q_Factor results suggest that the factor correlation appropriately captures risk sharing across these two clusters of disease traits. Conversely, Q_Factor would be expected to be significant if disorders loading on Factor 1 had a mixture of positive and negative genetic correlations with the disorders on Factor 2, such that a single correlation between Factor 1 and 2 is insufficient for describing the cross-disorder patterning of associations. Pruning out Q_Factor significant associations yielded four significant inter-factor associations between immune-mediated and psychiatric diseases (S1 Table). These reflected correlations between autoimmune disease and substance use disorder factors, mixed immune pattern diseases with internalizing and substance use disorders factors, and inflammatory disorders with the schizophrenia/bipolar factor.

Associations with immune markers

We next examined the genetic correlations between the 14 immune markers and the five psychiatric and four immune factors. We again used the Q_Factor heterogeneity statistic to evaluate whether genetic correlations with the markers were likely to operate at the factor level. In instances where there were significant Q_Factor results, we evaluated whether the immune marker was significantly associated with any of the individual disorders that defined the psychiatric or immune factor. After pruning out significant Q_Factor results, we identified 20 FDR significant immune marker – immune disease relationships, which included associations of ten markers with three immune-disease factors (all but the celiac factor; S2 Table). Interferon gamma (IFNG) was the strongest associated marker for the inflammatory (r_g = .48, standard error [SE] =.10) and mixed immune pattern factors (r_g = .35, SE = .09), while TNF-α had the largest correlation for the immune factor (r_g = .51, SE = .08). For individual disease associations investigated due to significant Q_Factor results, we observed significant correlations between Crohn’s disease and CRP (r_g = .16, SE = .03) and IL-6 (r_g = .33, SE = .06), along with ulcerative colitis and IL-6 (r_g = .12, SE = .06).

For the psychiatric factors, we identified 27 significant immune marker genetic correlations that included ten markers and four of the five psychiatric disorders factors (all but the schizophrenia/bipolar factor; S3 Table), along with five significant correlations with ADHD. Correlations were all positive, with the exception of large negative genetic correlations (range: -.21 to -.41) for 9 markers and the compulsive factor. Interleukin-1 receptor antagonist (IL-1RA) had the largest point estimate across markers for the compulsive (r_g = -.41, SE = .07) and internalizing factors (r_g = .26, SE = .04) and for ADHD (r_g = .35, SE = .04). C-C motif chemokine 3 (CCL3) had the largest correlation for the neurodevelopmental (r_g = .23, SE = .05) and substance use factors (r_g = .32, SE = .07).

Two pairs of markers, tumor necrosis factor receptor superfamily member 1A and B (TNFR1A & TNFR1B) and tumor necrosis factor (TNF) and C-C motif chemokine 3 (CCL3), displayed highly similar patterns of genetic correlations across psychiatric and immune factors. Both marker pairs additionally consisted of highly genetically correlated (see S1 Fig) and mechanistically related markers in terms of their function within the immune system. TNFR1A and B are both representatives of the same TNF-receptor superfamily and part of the same signaling network that influences the effect of TNF-α on macrophage viability and are closely integrated with pattern recognition receptor regulated signaling systems [43]. Similarly, TNF-α and CCL3 are part of the same signaling pathway, with TNF-α directly promoting CCL3 production [44]. Consequently, these two marker pairs were each modeled as two-indicator factors in subsequent mediation analyses to reflect the joint genetic architecture and previously described biology that they share.

To evaluate whether our immune marker results were robust across datasets, replication analyses were conducted for the four immune markers that had separate, well-powered GWAS available. Due to the limited number of available markers with external GWAS, these results are primarily detailed in the Supplementary Results section of the Online Supplement. We note here that 100% of the associations of psychiatric disorders and immune-mediated diseases with CRP, 67% of associations with IL-1RA, 56% of associations with TNF-α, and 13% of associations with CCL3 replicated in the external dataset in terms of significance and direction of effect. This gradient in overlap closely mirrors the discrepancy in power of the respective markers’ replication dataset with that used in the original analyses.

Multiple regression and Mendelian randomization reveal null effects of CRP

In line with prior work describing links between CRP and psychiatric conditions, significant correlations were found for the compulsive (r_g = -.37, SE = .05), internalizing (r_g = .13, SE = .02) and substance use disorder (r_g = .23, SE = .04) factors and for ADHD (r_g = .30, SE = .02). As IL-6 stimulates CRP production [45], it is unsurprising that IL-6 showed a highly similar pattern of associations, again with the compulsive (r_g = -.35, SE = .08), internalizing (r_g = .23, SE = .04) and substance use disorder (r_g = .29, SE = .07) factors and ADHD (r_g = .34, SE = .05). Since CRP is produced by the liver and not able to cross the blood-brain-barrier (despite altering its permeability) [46], and it is biologically more likely that IL-6 that can cross the blood-brain barrier [47], it is plausible that CRP was merely correlated with psychiatric disorders due to its relationship with IL-6. To investigate this, we fit multiple regression models with CRP and IL-6 as correlated predictors to test the partial effects of each marker on the psychiatric disorders or immune diseases (S2 Fig). These revealed that only IL-6 continued to have significant partial associations (S4 Table). This finding was replicated in multiple regressions including an independent CRP GWAS dataset and the same IL-6 GWAS dataset (due to the lack of a sufficiently powered independent IL-6 GWAS dataset Online Supplement).

Additionally, bidirectional Mendelian randomization (MR) between CRP and IL-6 supported by Steiger directionality testing, confirmed a highly significant, reciprocal relationship between IL-6 and CRP (p_{Steiger_IL6-CRP} = 2.57e-80; p_{Steiger_CRP-IL6} = 1.01e-39). Notably, this test was much more significant for the IL-6 on CRP direction, despite the much larger sample size of CRP, and the larger number of instruments that was identified for this biomarker (N_{SNP_CRP} = 234; N_{SNP_IL6} = 5). The absolute effects were also larger for IL-6 than for CRP, but inconsistencies in significance across the MR-Egger (β_IL6-CRP = -.69; p_IL6-CRP = 2.11e-02; β_CRP-IL6 = -.34; p_CRP-IL6 = 1.94e-05) and the weighted median method were observed (β_IL6-CRP = -.38; p_IL6-CRP = 3.50e-110; β_CRP-IL6 = .06; p_CRP-IL6 = 1.28e-01). Sensitivity analyses of the bidirectional models additionally revealed significant heterogeneity across instruments (Cochran’s Q p < 0.001) and evidence of directional horizontal pleiotropy via the MR-Egger intercept test (IL-6 intercept p = 0.045; CRP intercept p < 0.001). Consequently, the univariable effect estimates from these bidirectional models may be confounded by shared pathways and should be interpreted as capturing both direct and pleiotropic effects. While outlier removal is a common approach to address such assumption violations, discarding these variants would obscure true biological signal in this context. This observed pleiotropy is expected given the enmeshed nature of the inflammatory cascade, where genetic variants frequently influence multiple highly correlated immune markers simultaneously. Because this correlated pleiotropy violates the exclusion restriction assumptions of univariate MR, it necessitated a structural modeling solution rather than variant exclusion.

Multivariable MR (MVMR) was used to jointly model IL-6 and CRP as predictors of psychiatric outcomes. This produced partial causal effect estimates on the psychiatric outcomes that control for genetic overlap across these immune markers. In the joint genetic model predicting psychiatric disorders, genetically predicted IL-6 retained a significant direct causal effect for internalizing disorders (β_IL6-INT = .04; SE = .02; p = .011) and substance use disorders (β_IL6-SUD = .07; SE = .02; p = .002), whereas the effect of CRP was attenuated for internalizing (β_CRP-INT = .02; SE = .01; p = .057) and for substance use disorders (β_CRP-SUD = .03; SE = .02; p = .04). For ADHD neither marker was significant, although the effect estimate was larger and the p-value smaller for IL-6, indicating that this is likely a power issue. CRP was therefore dropped from all subsequent mediation models in favor of IL-6. Fig 2 shows how previously identified strong and significant effects of CRP on psychiatric disorders can be attenuated and become insignificant when accounting for shared signal with IL-6. Results for the bidirectional analyses and their sensitivity analyses are provided in S24 Table and results for the MVMR analyses and their sensitivity analyses are provided in S25 Table.

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Fig 2C. -Reactive protein regression models.

Regression model of the internalizing disorders factor regressed on CRP in Panel A and a multiple regression model of the internalizing disorders factor regressed on CRP and IL-6 in Panel B. This demonstrates how significant relationships of CRP with psychiatric disorders may be better explained by IL-6. Factor loadings of the internalizing factor differ from those in the correlated factors model (Fig 1) because cross-loadings are dropped for the follow up regression models. Single-headed arrows indicate regression relationships as modelled in genomic SEM and importantly do not imply expected or modeled directional relationships.

https://doi.org/10.1371/journal.pgen.1012328.g002

Immune markers mediate immune-psychiatric associations

We aimed to produce a robust set of findings by only testing mediation models that met three requirements: (i) the marker was significantly associated with an immune disease factor or disorder (often denoted the a – path in a mediation model), (ii) the marker was significantly associated with a psychiatric factor or disorder (b – path), and (iii) the disorders or factors from the a and b paths were themselves significantly associated (the total effect to be mediated, often denoted the c – path). This process resulted in three types of mediation models that tested a marker’s mediation of: a factor-factor relationship, representing an immune-mediated disease factor to psychiatric factor relationship; a factor-trait relationship, representing an immune-mediated disease factor to an individual psychiatric disorder relationship or a psychiatric disorder factor to and individual immune-mediated disease relationship, or finally; a trait-trait relationship that represents an individual immune-mediated disease to an individual psychiatric disorder relationship.

We tested 12 mediation models for six markers that met the inclusion criteria described above (as detailed in Fig 3 with model fit statistics in S5 Table and model outputs in S6–S17 Tables). Of these 12, 11 were significant at an FDR threshold. A graphical representation of the direct, indirect and total effects of each mediation is depicted in Fig 4 and a pie chart of the proportions of these effects for each mediation model can be found in Fig 5. Six of the mediations were for factor-factor relationships, five were for factor-trait relationships. There were no trait-trait relationships that exhibited significant mediation by an immune marker.

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Fig 3. Example mediation model.

Example of a mediation model for the relationship between an immune disease factor with indicators I1-3 and a psychiatric disorder factor with the indicators P1-3. The marker serves as a mediator and the corresponding a, b, and c’-path are tested and with them, the direct, indirect, and total effects are calculated according to the above equations. Single-headed arrows indicate regression relationships as modelled in genomic SEM and importantly do not imply expected or modeled directional relationships.

https://doi.org/10.1371/journal.pgen.1012328.g003

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Fig 4. Significant mediation model effect estimates.

Direct, indirect, and total effect estimates for each of the tested mediation models. Error bars display 1.96 * standard error. All mediation models displayed here were significant, as indicated by the significant indirect effect estimates and additionally, all total effect estimates were significant. Immune, autoimmune diseases; Mixed, mixed immune pattern diseases; Int, internalizing disorders; SUD, substance use disorders; CD, Crohn’s disease; ADHD, attention-deficit/hyperactivity disorder.

https://doi.org/10.1371/journal.pgen.1012328.g004

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Fig 5. Proportions of direct and indirect effects.

Pie charts are displaying the proportions of the direct and indirect effects for each of the mediation models tested. The size of the pie charts represents the size of the total effect. Immune, autoimmune diseases; Mixed, mixed immune pattern diseases; Int, internalizing disorders; SUD, substance use disorders; CD, Crohn’s disease; ADHD, attention-deficit/hyperactivity disorder. A displays all factor-factor relationships and B displays all factor-trait relationships.

https://doi.org/10.1371/journal.pgen.1012328.g005

Four of the six factor-factor models reflected mediation of the association between the mixed immune pattern and the internalizing factors by IL-6, IL-1RA, the combined TNF-α/CCL3 factor, and the TNFR1A/TNFR1B factor. The largest mediating effect was by IL-6, where the direct effect was attenuated to only.01 (SE = .03), and the indirect effect was.09 (SE = .02, p_FDR = 2.98e-04), such that IL-6 mediated ~92% of the total effect. The largest effect across models was for TNF-α/CCL3, which mediated 100% of the association between a substance use and autoimmune factor, wherein the direct effect was estimated at 0 (SE = .07), and the indirect effect at.13 (SE = .05, p_FDR = 1.96e-02).

Within the factor-trait mediation models, we found that IL-6 mediated ~60% of the relationship between the internalizing factor and Crohn’s disease, with a direct effect of.05 (SE = .02) and indirect effect of.09 (SE = .02, p_FDR = 2.98e-04). Similar to the large number of mediation between mixed immune pattern diseases and internalizing disorders, three factor-trait mediation models were identified for the mixed immune pattern factor and ADHD, with the markers reflecting IL-1RA, TNFR1A/TNFR1B, and IL-6. The marker that again accounted for the largest proportion of the total effect was IL-6, with a direct effect of only.02 (SE = .05) and an indirect effect of.12 (SE = .03, p_FDR = 7.97e-04) that accounted for ~88% of the total effect.

Multiple mediator models

The relationships between mixed immune pattern diseases and both internalizing disorders and ADHD were significantly mediated by the genetic liability for several immune markers, which together accounted for more than 100% of the total effect. This, along with the fact that these markers were themselves highly genetically correlated (S1 Fig), indicated that the mediating markers were tapping into interrelated biological pathways. This prompted running multiple mediator models that included the set of identified markers as correlated mediators (Fig 6). For the mixed immune pattern disease and the internalizing factor, the set of markers (IL-6, IL-1RA, TNF-α/CCL3, TNFR1A/B) collectively mediated 100% of the relationship, with a direct effect estimated at 0 (SE = .03, p_FDR = 9.56e-01) and a significant collective indirect effect of all markers combined of.10 (SE = .02, p_FDR = 2.79e-05). Only the individual mediating effect of IL-1RA remained significant with an indirect effect of.05 (SE = .02, p_FDR = 1.75e-02). The multiple mediator model for ADHD by IL-1RA, IL-6, and TNFR1A/B revealed a non-significant direct effect (.01; SE = .05, p_FDR = 8.84e-01) and a significant cumulative indirect effect of all markers combined of.13 (SE = .03, p_FDR = 5.44e-06) that accounted for ~94% of the total effect. We were not sufficiently powered to detect significant partial mediating effects of any markers.

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Fig 6. Multiple mediator model results.

Pie charts are displaying the proportions of the direct and indirect effects, with the total indirect effect broken down into the effects of the individual markers in a multiple mediation framework. Immune, autoimmune diseases; Mixed, mixed immune pattern diseases; Int, internalizing disorders; SUD, substance use disorders; CD, Crohn’s disease; ADHD, attention-deficit/hyperactivity disorder. A Multiple mediation results for the mixed immune pattern disease and internalizing disorder relationship. B Multiple mediation results for the mixed immune pattern disease and ADHD relationship.

https://doi.org/10.1371/journal.pgen.1012328.g006

Phenotype selection and quality control

Recent studies of markers of the immune system associated with psychiatric disorders were referenced to compile an initial list of immune markers. The literature across psychiatric disorders commonly linked to immune markers was referenced [59,60,78,79], and cross referenced with the list of available circulating metabolites (https://olink.com/products/olink-explore-3072-384). This approach was chosen over a more comprehensive approach to narrow down the large number of immune and inflammatory markers to avoid excessive multiple testing correction. This ensured that meaningful biological pathways in the context of immune mediated diseases and psychiatric disorders could be identified. Immune markers that were identified as important in the context of psychiatric disorders but do not have an associated GWAS due to their relatively invasive assessment and therefore small sample sizes (such as translocator protein, which is assessed through Positron Emission Tomography (PET) scans) were excluded. The initial list of immune markers was then filtered based on availability of sufficiently powered (reflected by a SNP-based heritability () Z-statistic > 4) [80], publicly available genome-wide association study (GWAS) summary statistics (excluding for example Interleukin-2 due to low power). For each phenotype, we chose the most well-powered, publicly available GWAS conducted on unrelated individuals of European-like genetic ancestry. We excluded traits with GWAS summary statistics that had low genomic coverage (fewer than 850,000 SNPs), which led to a final selection of 14 immune markers. For psychiatric and immune-mediated disease traits, the same GWAS summary statistics of 13 disorders [17] and 11 immune mediated diseases [4] from their previously established factor structures were used respectively. In the case of the psychiatric disorders, the factor structure from the original paper was retained, while GWAS summary statistics that had a more recent version with larger sample sizes since the publication, were updated in the model. These included PTSD that increased in the total sample size (including cases and controls) from 9,537–1,254,808, bipolar disorder that increased from 413,466–840,309, and MDD with a sample size increase from 500,199–2,009,702. All GWAS summary statistics were subjected to a standardized quality control procedure using the “munge” function from the GenomicSEM R package. This function limits the data to HapMap3 SNPs, standardizes the reference alleles across all GWAS summary statistics, and applies filters for a minor allele frequency greater than 1% and imputation quality above 0.9, where available. All GWAS summary statistics and their sample characteristics are presented in Table 1.

LD-score regression

We performed multivariable Linkage Disequilibrium (LD)-score regression (LDSC) [80] using LD scores calculated from the European-like genetic ancestry subset of the 1000 Genomes Phase 3 project. The MHC region was excluded due to its complex LD structure, which could bias the results [67]. Multivariable LDSC generates two matrices: (i) a genetic covariance matrix with SNP-based heritabilities on the diagonal and genetic covariances on the off-diagonal, and (ii) a sampling covariance matrix with squared standard errors of the estimates and sampling dependencies representing participant sample overlap on the diagonal and off-diagonal, respectively. For binary traits, such as disease or disorder status, the LDSC estimates were converted to a more interpretable liability scale, which accounts for the continuous distribution of genetic risk (liability) and corrects for sample ascertainment. The conversion to the liability scale was based on population prevalence from the corresponding GWAS paper or a representative prevalence for the study sample. Additionally, we used the sum of effective sample sizes from the contributing cohorts for the ascertainment correction, to produce the accurate estimates of the heritability on the liability-scale [81]. For these analyses, we entered a sample prevalence of 0.5 in LDSC [81], as the sample ascertainment had already been corrected through the effective sample size calculation. For continuous traits, such as the immune markers, the total continuous sample sizes were used, and no corrections were necessary.

Genomic SEM

We utilized genomic SEM to model the genetic overlap across immune markers and subsequently conduct mediation analyses with the genetic liability for immune markers mediating the genetic relationships between immune-mediated diseases and psychiatric disorders. Genomic SEM takes as input the output from multivariable LDSC along with a user specified SEM [82]. Good model fit was established based on the comparative fit index (CFI ≥ .9) and the standardized root mean squared residual (SRMR ≤ .1). To account for varying levels of sample overlap and differing sample sizes and therefore precision of our included traits, we utilized genomic SEM’s default diagonally weighted least squares estimator.

To determine the genetic factor structure of immune markers, we ran exploratory factor analyses (EFA) utilizing genomic E-SEM [83]. We used this to specify a confirmatory factor analysis where markers loaded on a factor when they had a standardized factor loading > .4. This cutoff is flexible and on the higher end of cutoffs commonly used [84], reflecting the fact that higher loadings might be expected given the biologically proximate nature of a set of immune markers. The best fitting model was a three-factor solution that fit the data well (CFI = .959, SRMR = .071); however, this model excluded four of the markers that did not load onto any of the factors, and among the remaining 10 markers, the identified model was overly complex with many markers cross-loading on multiple factors. To facilitate interpretation, individual markers of the immune system were therefore used as mediators of the relationships between immune disease and psychiatric disorders. However, rather than clustering markers purely on their genetic overlap with each other, we also adopted a more outcome-oriented approach for markers within the same theoretical immune pathways. Because there were clear patterns in how certain markers relate to the immune diseases and psychiatric disorders in the following a- and b-path analyses, TNF-α/CCL3 and TNFR1A/B were combined into two-indicator factors. This strategy allowed us to account for shared biological mechanisms while maintaining interpretable association patterns with the outcomes.

Before running the mediation models, we first tested whether the individual associations within the mediation model, denoted the a, b, and c path, were significant. The a, b, and c paths represent the immune-mediated disease factor to marker relationship, the psychiatric disorder to marker relationship, and the immune-mediated disease to psychiatric disorder relationship respectively. This filtering step was implemented to reduce false positives and increase power to identify true biological signal after multiple testing correction. While this approach might miss significant mediation where the indirect effect masks a significant direct effect (yielding a nonsignificant total effect), it ensures that our analysis isolates viable biological signals and identifies meaningful biological pathways. The psychiatric-immune factor correlations (i.e., the c paths) were estimated in Genomic SEMs that included the full set of psychiatric and immune factors and multiple testing correction was applied to evaluate significance (model specification given in Online Supplement). Next, the five psychiatric and four immune disease factors were specified to correlate with all immune markers in two separate models. This was set up similar to the immune-psychiatric factor relationships with the model for the a-path specifying correlations between the markers and the immune diseases and the model for the b-path specifying correlations between the markers and the psychiatric disorders (model specifications given in Online Supplement). Significant correlations between immune disease factors and the genetic liability for immune markers as well as between the genetic liability for immune markers and psychiatric disorders factors denote significant a and b paths of the mediation model respectively. The a and b paths were considered as being significant if they surpassed the FDR-corrected significance threshold of 14x5 and 14x4 trait-marker combinations and if those relationships did not at the same time become Q_Factor significant. Q_Factor is a measure of local model misfit, specific to a pair of factors, that captures inter-factor correlations which fail to accurately reflect the genetic relationships between the indicators (in our case psychiatric disorders or immune mediated diseases) that define these factors [4]. When the correlation is significant and Q_Factor is non-significant, it suggests that the factor correlation appropriately captures the broad pathways of risk sharing across these two clusters of disease traits. When Q_Factor became significant for either the a, or the b path, we subsequently re-tested the other paths for all individual indicators on the factor to see which of the indicators on the tested factors remained significantly associated with markers and psychiatric disorders or immune-mediated diseases. Only mediation models for indicators with significant a, b, and c paths were then carried forward from the Q_Factor significant factors.

This three-step process thus resulted in mediation models that tested a marker’s mediation of (i) an immune-mediated disease factor to psychiatric factor relationship (from here on denoted as factor-factor relationship), (ii) an immune-mediated disease factor to an individual psychiatric disorder relationship or a psychiatric disorder factor to and individual immune-mediated disease relationship (from here on denoted as factor-trait relationship), (iii) an individual immune-mediated disease to an individual psychiatric disorder relationship (from here on denoted as trait-trait relationship). Mediation models were set up and tested in genomic SEM by specifying “defined” parameters within the lavaan syntax for the total and indirect effect of the mediation, which has the advantage of providing standard error on the effects. Total effects were calculated as Total = a b + c’ and the indirect effects were calculated as Indirect = a b. An example of this framework as written in lavaan syntax is given in the Online Supplement.

Multiple regression

While several immune marker pairs exhibited high intercorrelations, our downstream statistical modeling was specifically tailored to their distinct biological relationships. Notably, formal partial-effect testing via multiple regression was applied exclusively to IL-6 and CRP. This decision was driven by biological plausibility rather than statistical redundancy or power constraints. Specifically, IL-6 and CRP function within a consecutive biological cascade, where IL-6 acts upstream to stimulate CRP production and is (unlike CRP) also able to cross the blood-brain barrier [46,47,85]. Testing their partial effects simultaneously allowed us to evaluate the conditional relationships between these biologically intertwined markers and psychiatric outcomes. In contrast, other highly correlated pairs—specifically TNFR1A/TNFR1B and TNF-α/CCL3—represent complementary indicators of parallel immune processes, rather than a sequential cascade. Consequently, these pairs were deemed better suited for joint latent modeling rather than partial-effect testing. Partial effects were estimated for IL-6 and CRP using a multiple regression model in genomic SEM with IL-6 and CRP as two correlated predictors (model specification given in the Online Supplement). The path diagram for these multiple regressions is given in S2 Fig.

In the case of one marker in a pair consistently exhibiting significant partial effects while the other one did not, we only proceeded to use the significant marker in the mediation models. All multiple regression results were FDR corrected for the number of regressions run for the marker pair.

Replication

Multiple regression, as well as a, b, and c-path analyses were replicated with independent immune-marker GWAS to assess whether the study’s findings are robust across different datasets. However, only nine out of the 14 included markers were available in an independent dataset and five of the ones that were available were underpowered. This resulted in replications testing the relationship of the genetic liability for Interleukin 1 receptor antagonist (IL-1RA) [86], tumor necrosis factor alpha (TNF-α) [86], C-C motif chemokine 3 (CCL3) [86], and C-reactive protein (CRP) [87] with psychiatric disorders and immune diseases. Additionally, multiple regressions of significant a and b-paths for CRP were run including IL-6 from the original set of markers along with the independent CRP GWAS. The original IL-6 GWAS was used for replication models with CRP due to the next largest available IL-6 GWAS [86] being underpowered for these analyses. Mediations were then modeled for psychiatric disorder, immune disease, and immune marker combinations that had significant a, b, and c-paths, which was only the association between autoimmune diseases and ADHD as mediated by TNF-α in the replication. We report the results of the replications for the remaining four well-powered markers in the Supplemental Results in the Online Supplement.

Mendelian randomization

To support the inclusion of IL-6, disentangle the causal hierarchy of IL-6 and CRP, and isolate their specific direct effects on psychiatric disorders, we performed a series of bidirectional MR and MVMR analyses using the TwoSampleMR package in R [88]. These analyses are described in more detail in the Supplemental Methods in the Online Supplement.

Multiple mediators

Multiple psychiatric – immune relationships were significantly mediated by more than one immune marker. This result, alongside the strong genetic intercorrelations of the markers, indicates that some markers likely operate via shared biological pathways. To better understand the total mediation effect of all contributing markers combined, as well as the conditional mediating effects of each marker when accounting for correlated genetic signal, we fit a multiple mediator model to each of these immune-psychiatric relationships in Genomic SEM. For the multiple mediation models, the collective indirect effects were calculated as Indirect_Collective = (a_k b_k) + (a_j b_j) + (a_i b_i) with k, j, and i denoting three different markers. The total effects were calculated as Total_Collective = Indirect_Collective + c’. Model specifications in genomic SEM for the multiple mediation models are given in the Online Supplement, the path diagram for these multiple mediations is given in S3 Fig.