Steiger Filtering

Summary

Steiger filtering is a method used in Mendelian Randomization (MR) to confirm the causal direction of an association. It tests whether the genetic variants chosen as instrumental variables explain significantly more variance in the exposure than in the outcome. Variants that explain more variance in the outcome than the exposure are filtered out, as they violate the assumption of causal directionality and may indicate reverse causation.

Mathematical Principle

The method is based on the Steiger test for comparing two dependent correlation coefficients. Given a genetic variant $G$, exposure $X$, and outcome $Y$, the test compares: - $r_{GX}$: the correlation between the variant and the exposure. - $r_{GY}$: the correlation between the variant and the outcome.

Under the assumed causal direction $X \to Y$, the genetic variant must act as an instrument for $X$, meaning:

$$r_{GX}^2 > r_{GY}^2$$

If $r_{GY}^2 > r_{GX}^2$, the variant explains more variance in the outcome, suggesting the true direction is $Y \to X$ (reverse causation) or that the variant exerts a direct pleiotropic effect on $Y$. Steiger filtering removes any variants where $r_{GY}^2 > r_{GX}^2$ with a statistically significant difference.

Applications

Steiger filtering is implemented as a standard diagnostic in MR pipelines, such as the TwoSampleMR R package, and is crucial for validating instruments in complex physiological networks (e.g., Chemosensory Mendelian Randomization).

Citations

• Hemani, G., Tilling, K., & Davey Smith, G. (2017). Orienting the causal relationship between imprecisely measured traits using genomic data. PLoS Genetics, 13(11), e1007081. DOI: 10.1371/journal.pgen.1007081