First, we performed a two-sample MR analysis to identify causal relationships between immune diseases and migraine in the forward direction. Genetic IVs were employed as proxies for exposures to test the association with migraine and its major subtypes from 3 separate data sources, and then estimated the effect of exposures on outcomes. Second, reverse MR analysis was performed to determine whether migraine and its subtypes were risk factors for the immune disorders included in the current study. Third, we conducted multivariable MR (MVMR) of exposure to estimate whether immune disorders were independently associated with migraine by adjusting for potential pleiotropic factors, including smoking, alcohol consumption, obesity, sleep disorders, depression, and anxiety. In addition, we conducted a genetic correlation to identify shared genetic variants for these two associations. The summary-level data were obtained from publicly available GWAS studies or public databases. Such utilized data were already in the public domain, so no additional ethical approvals were required. The current study followed the Strengthening the Reporting of Observational Studies in Epidemiology using Mendelian Randomization (STROBE-MR) guidelines (Additional file 3, template available here: https://www.strobe-mr.org). A schematic overview of the present study design is presented in Figure 1 .

Summary statistics for migraine were obtained from three separate data sources: GWAS meta-analyses from the International Headache Genetics Consortium (IHGC) (14), the UK Biobank, and the FinnGen consortium. Detailed information about data sources is shown in Additional File 2 : Supplementary Table 1 .

The IHGC is a population-level GWAS meta-analysis of 24 migraine cohorts from 5 study collections with a total sample of 102,084 cases and 771,257 controls. Because of privacy protection for participants, we had no access to the 23andMe cohort. Present GWAS summary statistics contain 599,356 European ancestry individuals (48,975 cases and 550,381 controls) after excluding the 23andMe cohort’s sample. Migraine cases were identified through clinical phenotyping or based on self-reported information. Genetic IVs for MO and MA were identified from earlier GWAS meta-analyses (23), respectively, including 14,7970 individuals (8,348 cases and 139,622 controls, European descent) and 151,215 individuals (6,332 cases and 144,883 controls, European descent).

The UK Biobank Consortium is a prospective, large-scale biomedical database that collected health and genetic information on over 500,000 general UK populations between 2006 and 2010 (24). SNPs associated with migraine were identified from summary statistics of the UK Biobank on a broad migraine definition (13,597 cases and 449,336 controls). All analyses were restricted to European ancestry.

The migraine GWAS of the FinnGen was based on the FinnGen data R9 with a total of 306,314 participants (18,477 cases and 287,837 controls) of British ancestry. Genetic IVs for MA and MO were also extracted from the FinnGen (MA: 7,917 cases and 287,837 controls; MO: 6,730 cases and 287,837 controls).

The estimate from a two-sample MR analysis is less biased, and any bias is in the direction of the null when risk factor and outcome data are taken from non-overlapping datasets. However, using gene clusters with partially overlapping participants resulted in different extents and directions of bias (25). To eliminate potential bias associated with sample overlap, we chose GWAS studies of six immunological diseases after excluding the UK Biobank and FinnGen cohorts. The genetic backgrounds of the study populations were of European ancestry to avoid bias associated with race-related confounders.

All included GWAS studies of immunological diseases are publicly available. We selected the largest study with replication when there were multiple available GWAS studies for a single trait. We extracted SNPs associated with each autoimmune disease in each independent GWAS study. Notably, the current research has no overlap between GWAS populations used for exposure and outcome analyses. Detailed data sources can be found in Additional File 2 : Supplementary Table 1 .

We performed quality control procedures on all summary datasets: (1) removing SNPs for non-binary alleles; (2) deleted SNPs in the major histocompatibility complex region (chr6: 25.5–33.5 Mb); (3) excluded SNPs with minor alleles frequency (MAF) < 0.01; (4) Ambiguous SNPs with incongruent alleles and palindromic SNPs with an ambiguous strand were excluded.

Suitable IVs need to fulfill the three central assumptions of MR analysis. First, Genetic variants must be strongly associated with exposure. We selected independent SNPs related to exposure at genome-wide significance (P-value < 5×10^-8) as potential IVs. We increased the P-value < 5×10^-6 for AR due to no available SNPs. A linkage disequilibrium (LD) threshold of r² < 0.001 in a window size of 10 Mb was used to exclude the interference of LD. By calculating the F-statistic, the existence of weak instrumental variable bias for the selected SNPs can be measured. The formula for calculating the F-statistic is R² (N-2)/(1-R²). In this equation, N is the sample size of GWAS, and R² refers to the proportion of cumulative explained variance by the IVs. F > 10 indicates that no weak IV bias exists, thus further validating the association assumption. Secondly, genetic variant(s) must be associated with the outcome exclusively through the exposure. When IVs can affect outcomes through other pathways, genetic pleiotropy exists. The identification of confounders lacks specific evaluation criteria. In this study, six confounders, including smoking status, alcohol consumption, sleep disorders, obesity, stroke, myocardial infarction, depression, and anxiety, were considered as potential confounders. SNPs associated with outcome and these confounders were removed from IVs to exclude potential horizontal pleiotropy by searching and reviewing the Phenoscanner database. Moreover, a series of sensitivity analyses were conducted to validate the MR analysis assumptions and discussed in detail later. Finally, genetic variants must be independent of any measured and unmeasured confounders. The MR study was conducted using GWAS data for analysis, so the assumption is problematic to test directly. However, given that genetic variants precede the formation of acquired confounders, the genetic effects of genetic variants may be less affected by acquired confounders.

All analyses were performed using R version 4.3.2 statistical software. We employed the Bonferroni correction to control for false discovery rates. Estimates with p-value < 0.05/6 (p < 0.008) were considered as strong evidence for causal effects, whereas correlations with p-value < 0.05 but > 0.008 indicated a suggestive causal effect.

We first estimated the shared genetic architectures between immune diseases and migraine using the linkage disequilibrium score regression method (LDSC) before MR analysis. Software and procedures for conducting LDSC are publicly available (https://github.com/bulik/ldsc). The results of genetic correlation were corrected by applying the Bonferroni-corrected threshold of p-value < 0.05/6 (p < 0.008).

SNPs selected as IVs were harmonized with effective alleles in the outcome, and then causal analysis was performed. Three methods were employed to estimate causal effects: the inverse-variance weighted (IVW) method, weighted median regression, and the MR-Egger method. The IVW method is the current primary method for MR analysis owing to its higher test efficacy. The random-effects IVW was used if Cochran’s Q test showed heterogeneity between SNPs. Otherwise, we used a fixed-effects IVW. The remaining two MR methods were used as secondary methods to ascertain the robustness of the primary results. The weighted median regression also provides reliable estimates of causal effects when the valid IVs exceed more than 50% of the weights. In addition, we converted the beta values obtained to odds ratios and calculated confidence intervals to account for the results better. This ratio is an estimate of the causal effect of exposure on the outcome when the MR assumptions are fulfilled. Reverse MR analysis was performed using the same methods to estimate whether migraine is a risk factor for immune diseases. Considering the potential genetic correlations between immune diseases, as well as similar associations in epidemic studies, we performed MVMR to obtain independent estimates of effect sizes of exposure on outcomes by adjusting for genetically predicted immune diseases. Smoking, alcohol consumption, obesity, sleep disorders, depression, and anxiety were considered as potential pleiotropic factors in MVMR analyses.

We performed a series of sensitivity analyses to assess the reliability and stability of the MR analyses. MR-Egger intercept test and MR‐pleiotropy residual sum and outlier (MR‐PRESSO) global tests were employed to detect horizontal pleiotropy. MR-Egger intercepts are based on the same regression model using inverse variance weighted (IVW) analysis, which can assess whether IVs produce pleiotropic effects on outcomes that differ on average from zero and provide consistent estimates of causal effects under weaker assumptions (26). The MR-Egger intercepts term moves away from zero, indicating the presence of directional pleiotropy in the selected genetic variants. Furthermore, we employed the MR-PRESSO framework to detect and correct horizontal pleiotropy by excluding outliers. MR-PRESSO test is best appropriate when less than 50% of the instruments show horizontal pleiotropy. If the global MR-PRESSO test P-value < 0.05 indicated significant horizontal pleiotropy, we removed the outliers defined by P-value < 0.05 and repeated the MR analysis using the remaining IVs. If pleiotropy were still present, outliers with P-value < 1 would be removed. We could only draw an uncertain conclusion for estimates that remain horizontal pleiotropy after two rounds of MR analysis. MR-egger and IVW in Cochran’s Q statistic were applied to detect the heterogeneity of different genetic variants, which could provide evidence of heterogeneity due to pleiotropy or other causes. The “leave-one-out” method was employed to assess the potential impact of outlying and pleiotropic SNPs on the overall estimate. It was estimated by removing individual SNPs and recalculating the causal effect estimates using the remaining SNPs to identify whether a single SNP drives the selected effect.

Each specific exposure was performed separately in each migraine outcome database of GWAS of the IHGC study, UK Biobank, and FinnGen study. Then, we conduct a meta-analysis to yield estimates of the pooled causal effect for each immune disease on migraine. We calculated I² to statistics the heterogeneity between the estimates from multiple data sources and the p-values from Cochran’s Q-tests. When heterogeneity was less than 50%, a fixed-effects model was applied to summarize the instrumental variable estimates for each exposure. If not, we use random-effects models (27).

The summary information about instruments identified for immune disorders and migraine and its subtypes are available in Additional File 2: Supplementary Table 1 . Detailed information about the genetic variants and their associations in the respective outcome databases are given in Additional File 1 : S1 – S4 . The F-statistics of all genetic instruments were all above the threshold of weak instruments of 10, indicating no weak instrumental variable bias.

Using the LDSC, we detected no genetic correlation between migraine and immune disorders, including RA, SLE, T1D, AR, asthma, and psoriasis. The detailed results of genetic correlations are shown in Additional File 2: Supplementary Table 3 .

Overall, the primary MR analyses using IVW genetically determined immune diseases, including RA, SLE, T1D, AR, and asthma, were not associated with the risk of overall migraine when pooled in any of the three databases ( Figure 2 , Additional File 2: Supplementary Table 4 ). The findings of MR-Egger and WM were consistent. In general consistency with the findings for overall migraine, no associations were observed between the two main migraine subtypes, MA and MO, and genetically predicted immune disorders (Figures 3, 4; Additional File 2: Supplementary Tables 5, 6).

IVW analysis showed that only the result from the IHGC database indicated a suggestive association between psoriasis and overall migraine (P-value < 0.05). Yet, when pooling the results from three databases using a random-effects model, psoriasis and overall migraine risk became unrelated. Notably, after correcting multiple comparisons, psoriasis was not correlated with migraine. The estimates from weighted median regression and the MR-Egger method showed no evidence of a causal relationship between migraine and psoriasis.

Subsequently, we performed further MVMR analysis by removing potential pleiotropic factors to obtain an independent causal relationship between immune diseases and migraine ( Additional File 2: Supplementary Table 13 ). The results of MVMR analyses indicated no genetic causality between immune disorders and migraine.

In reverse MR, migraine was used as exposure, and six immune diseases were used as outcomes to explore the causal relationship. As shown in Figure 5 and Additional File 2: Supplementary Table 10 , no significant causal relationship was found between migraine and the risk of any immune diseases included in the present study. This finding was similar to weighted median regression and the MR-Egger method.

MR-Egger intercept test suggested no significant deviation from zero for all analyses, implying no horizontal pleiotropy ( Additional File 2: Supplementary Tables 7 - 9 ). In the MRPRESS analysis, significant horizontal pleiotropy (P-value < 0.05) was detected in five outcomes ( Additional File 2: Supplementary Table 12 ), but no outlier SNP (all P-value > 0.05) was identified in any of the databases. We removed genetic variants (P-value < 1) detected in the MR-PRESSO analysis and repeated the MR analysis using the remaining IVs. The horizontal pleiotropy was controlled. The results of Cochran’s Q-test showed significant heterogeneity in some causal estimates. We did not perform the “leave-one-out” method because the current MR analysis did not identify an optimistic causal estimate.

The present study has three main strengths, which enhance the validity and reliability of the results. Three data sources were meta-analyzed for gene-outcome correlations in this study, encompassing almost all available European population-based summary statistics on migraine except for the 23andMe cohort. Results from the three databases were generally consistent, enhancing the accuracy and reliability of the MR estimates. Secondly, using MVMR allowed us to explore independent causal estimates of the association between immune disorders and migraine. In addition, we used multiple sensitivity analyses to demonstrate the robustness of the results, which showed no pleiotropic effects.

The following limitations need to be considered. First, all the GWAS populations were of European ancestry. Though it reduced the bias induced by population stratification, to some extent, the findings may not be generalizable to other ethnic groups. Second, migraine cases were defined by ICD codes or self-reports, which may result in lower reliability for phenotype categorization. Third, considering the size of the immune disease GWAS, it is possible that some SNPs associated with these diseases have not yet been sequenced. Thus, the null results in the current study may be overturned when more significant alleles are identified. Finally, the recent null results may only represent the overall effect of genetically determined immune disorders on migraine, not the association of underlying specific biological or biomarker changes in immune disorders. Future studies should probably focus on identifying particular biomarkers of immune disease to provide more precise evidence for determining the relationship (55).