Since this study only used publicly available summary statistic from relevant genome-wide-association studies (GWAS) and did not use the individual data, ethical approval was not required.

To interpret the resulting estimates as causal effects, three common assumptions of IV estimation must hold: (1) the IV is associated with the exposure robustly, (2) the IV is independent of confounders, and (3) the IV influences the outcome exclusively via the exposure (27).

We performed MR using genetic variants (significance of SNPs: P < 5 × 10⁻⁸) associated with AF as IVs to investigate their effect on lung function (FEV1, FVC, and FEV1/FVC), and vice versa. Among others, violations of the second and third assumption occur in case of population stratification, when different ethnic subgroups are present with different allele frequencies. We overcame this issue by focusing on individuals with European ancestry (29). Violations of the third assumption occur in case of linkage disequilibrium (LD) between the included SNPs or in case of pleiotropy. Horizontal pleiotropy, i.e., the same SNP independently influences multiple phenotypes, leads to violations of the third assumption and to biased estimates (27). In view of that, only independent variants (LD, r² = 0.0001) based on European ancestry reference data from the 1,000 Genomes Project were retained.

In brief, the process for selecting IVs was as follows: we first extract significant SNPs (P < 5 × 10⁻⁸) from exposure GWAS; then prune SNPs for linkage disequilibrium (r² = 0.0001); next, extract the retained SNPs from the outcome datasets; last, harmonize the exposure and outcome SNPs (e.g., removing the SNPs for being palindromic with intermediate allele frequencies).

The mvMR approach takes into account the inter-relationship between FEV1, FVC, and FEV1/FVC and the IVs used in the mvMR analyses are often associated with all exposures. This method is based on the above-mentioned standard IVs method which allow for multiple exposures. We selected independent SNPs (r² < 0.0001) that were associated with FEV1, FVC, or FEV1/FVC at P < 5 × 10⁻⁸; then we merged all SNPs related to any lung-function traits by removing duplicate SNPs with higher p-values; next, we extracted the relevant information of the merged SNPs from the original exposure datasets; finally, we used the last extracted SNPs as IVs for mvMR analysis.

We estimated the R² [R² = 2×EAF× (1-EAF) × Beta²] of each SNP and summed them up to calculate the overall R² and F statistics [R² × (N-2)/(1-R²); N represents the number of individuals in the exposure GWAS] using the sample size of exposure GWAS (30). Higher R² and F statistic indicate lower risk of weak IVs bias (31).

LDSC regression regresses χ² statistics for two phenotypes to estimate SNP based coheritability on LDSCs. Genetic correlations between lung function and AF can be evaluated by the regression slope (24).

For uvMR, we used inverse variance weighted (IVW) method as the main analysis. The IVW analysis does not consider the intercept (constrained to zero) in the regression and uses the reciprocal of the outcome variance as the weight for fitting (32). Results may be biased if IVs exhibit horizontal pleiotropy, influencing outcomes by other pathways other than the exposure (33). Therefore, we supplemented sensitivity analyses, including the MR-Egger regression and weighted median (WM). The MR-Egger regression analysis allows free evaluation of the intercept (not set to zero) as an indicator of average pleiotropic bias (33) and gives a consistent estimate when all genetic variants are invalid IVs. If more than half of the weight derived from effective IVs, the WM method may come to an unbiased estimate of causality (34). For mvMR, we used the extension of the IVW approach (variants uncorrected, random effect model) which performed multivariable weighted linear regression (33), and the extension of the MR-Egger regression approach to correct for both measured and unmeasured pleiotropy in mvMR (35).

To evaluate the robustness of significant results, we conducted leave-one-out sensitivity analysis, the Cochran Q heterogeneity test and I² statistics (36), and the MR Egger intercept test (37) on horizontal pleiotropy to detect heterogeneity. In addition, horizontal pleiotropy can be evaded by applying mvMR approaches (i.e., by considering the overlapping IVs directly in the estimation) (23). Pleiotropy Residual Sum and Outlier (MR-PRESSO) was applied to detect and correct for outlier SNPs reflecting pleiotropic biases (38).

The MR results are expressed as odds ratios (ORs) with 95% confidence intervals (CIs) interpreted as AF risk per SD increase in log odds of the lung function traits (or alternatively, the risk of impaired lung function per SD increase in log odds of AF). We use a two-sided α of 0.017 based on testing three lung function traits against AF outcome to define significant or not. MR analyses were performed using the packages “MendelianRandomization,” “TwoSampleMR,” and “MR-PRESSO” packages (https://cran.r-project.org/package) in the Rstudio (R version 4.0.3, R Project for Statistical Computing). Power calculation was performed using mRnd developed by Brion et al. (39) (https://cnsgenomics.com/shiny/mRnd/).

We performed LDSC analysis to estimate the genetic correlation between lung function and AF as well as different lung-function traits using LDSC software: https://github.com/bulik/ldsc. There was no evidence for genetic correlations of AF with all lung function traits (rg = NA, P = NA), namely no coheritability between two traits. There was evidence for higher genetic correlations of FEV1 with FVC and FEV1/FVC (FEV1 vs. FVC: rg = 0.8717, P = 0.0; FEV1 vs. FEV1/FVC: rg = 0.3859, P = 2.93e-14; FVC vs. FVC: rg = −0.1287, P = 0.0144) (Table 1).

In the univariable bidirectional MR analyses, we obtained 18/11/10/93 LD-independent SNPs which achieved genome wide significance (P < 5 × 10⁻⁸) for FEV1/FVC, FEV1, FVC, and AF, respectively, then we extracted those SNPs from corresponding outcome dataset. Finally, 16/9/8/82 SNPs remained after harmonizing the datasets of exposure and outcome (2/2/2/11 palindrome SNPs with intermediate allele frequencies were removed from FEV1/FVC, FEV1, FVC, and AF).

In mvMR analysis, all 39 (11+10+18) above-mentioned LD-independent (r² < 0.0001) SNPs associated with FEV1, FVC, and FEV1/FVC at P < 5 × 10⁻⁸ were included. Five of these SNPs (rs10888384, rs8033889, rs3754512, rs34712979, rs13361953) represent the same signal, so we aggregate a list of SNP (34 = 39 – 5) by selecting the SNPs with the lowest P-value. This resulted in 34 SNPs, of which seven were related to FEV1 but not FVC and FEV1/FVC at P < 5 × 10⁻⁸, 14 were associated with FEV1/FVC but not FEV1 and FVC at P < 5 × 10⁻⁸, eight were associated with FVC but not FEV1 and FEV1/FVC at P < 5 × 10⁻⁸, and five were associated with any two traits at P < 5 × 10⁻⁸. Then, we extracted relevant information of 34 SNPs from the original exposure datasets, respectively. Finally, 28 (28 = 34–6, six palindrome SNPs with intermediate allele frequencies were removed) SNPs for any lung function trait were obtained after harmonizing with SNP-outcome (the flow chart of SNPs selection was shown in Figure 1).

The number of SNPs for FEV1 [nine, variance explained (R²): 0.6%], FVC [eight, variance explained (R²): 0.5%], FEV1/FVC [16, variance explained (R²): 1.3%] were small and the statistical power was insufficient. However, the F statistics (>10, ranging from 32.7 to 21,355.5) for each SNP and the power of IVs in the mvMR (28, variance explained (R²): 2%; power: 100%) were sufficient, indicating that those SNPs satisfy the strong relevance assumption and the weak IV bias would not likely affect the causal inference. The number of IVs included for exposures were listed in Table 2, and details for the characteristics of SNPs used in uvMR and mvMR were shown in Supplementary Tables 1A–C, respectively.

According to the same method as above, we obtained 167/161/186/25 SNPs for FEV1, FVC, FEV1/FVC, and AF, respectively, in the uvMR replication analyses, and 470 SNPs for lung function in the mvMR analyses. They were described in detail in the Supplementary Material.

All models in reverse MR analyses consistently suggested that genetically instrumented AF has no significant correlation with FEV1 (OR = 0.986, 95% CI = 0.966–1.007, P = 0.187), FVC (OR = 0.985, 95% CI = 0.965–1.006, P = 0.158) and FEV1/FVC (OR = 0.994, 95% CI = 0.973–1.015, P = 0.545). Pleiotropy bias (intercept_FEV1/FVC = 0.002, P_FEV1/FVC = 0.199; intercept_FEV1 = 0.001, P_FEV1 = 0.747; intercept_FVC = −0.001, P_FVC = 0.419) was not detected and heterogeneity (FEV1: Q_pval = 0.213, I² = 11%; FVC: Q_pval = 0.162, I² = 13%; FEV1/FVC: Q_pval = 0.127, I² = 15%) was not found. These main estimates from IVW were broadly consistent with estimates from the WM and MR-Egger sensitivity analyses. All reverse leave-one-out sensitivity analyses (Figures 4A–C) and the MR-PRESSO tests indicated that the correlation between AF with FEV1, FVC, or FEV1/FVC was not significantly affected by any individual SNP, indicating the robustness of the reverse MR analyses results (Table 4 and Supplementary Tables 4, 5). The funnel plot indicated no evidence of asymmetry, so there was no directional pleiotropy (Figures 5A–C).

The estimate effects from the mvMR analysis showed that the direct effect of FEV1 or FVC (OR_FEV1 = 0.501, 95% CI = 0.056–4.457, P = 0.496; OR_FVC = 1.969, 95% CI = 0.288–13.474, P = 0.490) controlling for another two lung function arguments was similar with the univariable setting. Additionally, no effect of FEV1/FVC (OR = 1.523, 95% CI = 0.445–5.217, P = 0.503) on AF could be observed, which was inconsistent with the univariable MR Egger result. Consistent with standard IVW regression results, mvMR-Egger regression (orientated to FEV1/FVC) and MR-PRESSO (detect no significant outliers) results also showed no significant association between lung function and AF, suggesting that the mvMR method successfully overcomes the bias caused by horizontal pleiotropy in the univariable MR analysis (Table 5 and Supplementary Table 6).

In the replication MR analyses, there were more IVs and greater statistical power for lung function but less IVs for AF, and the MR results were basically consistent with original results (Table 6). We presented the detailed results as Supplementary Material.