Fig 1.
Inferences about the causal effect of an exposure on an outcome in MR and its comparison with RCT.
The fundamental conditions for a genetic variant to be an IV are summarized as the following: i. the variant is associated with the exposure, ii. the variant is not associated with the outcome via a confounding pathway, and iii. the variant does not affect the outcome directly, only possibly indirectly via the exposure [12]. Assuming that the RCT is properly blinded and randomized and that the IVs for MR analysis are valid, subgroups should differ systematically in the exposure but not in any other factor except for those causally downstream of the exposure. Therefore, a difference in the average outcome between these subgroups would indicate a causal effect of the exposure on the outcome. Inferring a causal effect of the exposure on the outcome from an association between the IV and the outcome is analogous to inferring an intention-to-treat effect from an association between randomization and the outcome in an RCT [12, 13].
Fig 2.
Directed acyclic graph of BIMR and MVMR.
(A) BIMR: Gx can be used to estimate the causal effect of exposure X on outcome Y. Gy can be used to estimate the causal effect of outcome Y on exposure X. Genetic variants that are IVs for exposure X(Gx) and that are IVs for outcome Y(Gy) should be completely different. U indicates all confounders, which are assumed to be unknown. (B) MVMR: the total and direct effects of T1DM and 25-OHD level on SLE, based on the following IV assumptions for a genetic variant in MVMR: i. the variant is associated with one or more of the exposures, ii. the variant is not associated with the outcome via a confounding pathway, and iii. the variant does not affect the outcome directly, only possibly indirectly via one or more of the exposures. The direct effect of T1DM on SLE is the effect that T1DM has on SLE not via any other exposure variables, which is equal to βxz; similarly, the direct effect of the 25-OHD level on SLE is equal to βyz. The total effect of T1DM and 25-OHD level on SLE is the effect of T1DM on SLE directly plus the effect of T1DM on SLE via the 25-OHD level, which is equal to βxz + βxyβyz. U indicates all confounders, which are assumed to be unknown.
Table 1.
Causal relationship between SLE, T1DM and 25-OHD level estimated by BIMR.
Table 2.
Causal relationship of T1DM and 25-OHD on SLE estimated by MVMR.
Fig 3.
Odds ratios and 95% confidence intervals for the causal effect of T1DM and 25-OHD level on SLE in UVMR and MVMR-Lasso analyses.
The colours of the fitted lines indicate two MR analyses. UVMR, univariable Mendelian randomization; MVMR, multivariable Mendelian randomization; SLE, systemic lupus erythematosus; T1DM, type 1 diabetes; 25-OHD, 25 hydroxyvitamin D; N. SNPs, number of SNPs used in MR; IV, instrumental variables; IVW inverse variance weighted.