Statistical Analysis

For univariable MR analysis, the random-effects inverse variance-weighted (IVW) meta-analysis was conducted as the primary analysis to estimate the associations between HF and stroke subtypes (28). The MR pleiotropy residual sum and outlier (MR-PRESSO) method was applied to examine pleiotropic outlier SNPs (29). Significant outlier SNPs (p < 0.05) were removed in the subsequent MR analysis. The IVW method is equivalent to a weighted regression of SNP-outcome effects on SNP exposure, with the y-axis intercept fixed to zero (30). Considering that the potential horizontal pleiotropy may cause bias in association statistics, we performed a sensitivity analysis with alternative MR models regarded as more robust to pleiotropic SNPs, but at the cost of reduced statistical power. In the first sensitivity analysis, we used the weighted median method, which can generate valid estimates under the condition of at least 50% of the information contributing to the analysis comes from valid SNPs (31). In the second sensitivity analysis, we also performed the MR-Egger regression, which can provide a valid estimate of the causal effect and depends on the assumption that the pleiotropic effects of genetic instruments are independent of instrument strength (32). The intercept from MR-Egger regression tested with a p < 0.05 is an indication of average directional pleiotropy (33). Generally, the MR-Egger method is considered conservative in the presence of pleiotropic variants and suffers from less precise estimates (31). A genome-wide suggestive significance (p < 5^e−6) with more IVs was provided as a sensitivity analysis to estimate the direct causal association between HF and stroke. Statistically significant findings (p < 0.05) of univariable MR analysis were further investigated in subsequent multivariable MR analysis by adjusting for AF, CHD, and SBP. For multivariable MR, the multiplicative random-effects IVW method was performed as the primary analysis method, a Bonferroni correction threshold (p < 0.05/X/Y, X means the number of exposure phenotypes, Y means the number of outcome phenotypes) was used to ascertain statistical significance. The strength of the genetic instrument was tested using F-statistics (34). F-statistics >10 indicated a small possibility of weak instrument bias (34). All statistical analyses were conducted using R (version 4.1.1) using the TwoSampleMR and MR-PRESSO packages (30).