Table 2. Overview of MR methods available in MR-Base.
| Method | Details | References |
|---|---|---|
| Wald ratio | The Wald ratio method is also known as the ratio of coefficients method. It divides the
regression coefficient of the instrument on the outcome by the regression coefficient of the instrument on the exposure and can be used when only one instrument SNP is available. |
18 |
| Maximum likelihood | This method maximizes the likelihood of a model, which is based on the exposure-
outcome relationship and the distribution of the estimates of the genetic association, to obtain a causal estimate. |
19 |
| MR Egger regression | MR Egger calculates Wald ratios for each of the instruments and combines the results
using an adapted Egger regression. The causal effect is the Egger regression slope coefficient and the intercept is an estimate of the average pleiotropic effect across instruments. Bootstrapping can help to improve the reliability of standard error estimates for non-zero causal effects. |
14 |
| MR Egger (bootstrap) | ||
| Simple median | These methods calculate Wald ratios for each of the instruments and select the median
value (according to the specified method) as the causal estimate. They provide valid estimates when more than half of the SNPs satisfy the instrumental variable assumptions. |
20, 21 |
| Weighted median | ||
| Penalised weighted median | ||
| Inverse variance weighted | This method calculates the Wald ratio for each of the instruments and combines the
results using an inverse-variance weighted meta-analysis approach. The slope from this approach can be interpreted at the causal effect of the exposure on the outcome. The variance of the effect can be estimated using either a fixed or multiplicative random effects model. The latter is usually implemented unless there is under-dispersion in the effect estimates, in which case a fixed effects model is used. |
19, 22 |
| Inverse variance weighted
(multiplicative random effects) | ||
| Inverse variance weighted
(fixed effects) | ||
| Simple mode | The mode-based methods use the causal effect estimates for individual SNPs to form
clusters. The causal effect estimate is then taken as the causal effect estimate from the largest cluster of SNPs. The weighted mode methods use the same process but assign weights to each SNP. Mode-based methods require ZEMPA, which states that the mode of the bias terms for the individual instruments is zero. |
23 |
| Weighted mode | ||
| Weighted mode (NOME) | ||
| Simple mode (NOME) |