Towards more plausible point-identifying assumptions in two-sample Mendelian randomization

Introduction to the show: ident: Statistics. The day in statistics: methods, theory and the inference under them.

Tom: We're looking at the paper: "Towards more plausible point-identifying assumptions in two-sample Mendelian randomization".

Jane: Here's the gist of the paper. Two-sample Mendelian randomization (MR) methods can be interpreted as estimators of the average causal effect under weaker identification assumptions than previously thought.

Tom: This clarification contributes to the plausibility and interpretation of these methods in at least some practical applications.

Jane: Two-sample MR is a widely applied methodology in epidemiology where summary data are used to estimate causal effects, but most methods were developed under strong assumptions that summary-level homogeneity holds, meaning the association of each genetic variant with the exposure and the causal effect of the exposure on the outcome are constant in an additive scale.

Tom: These strong homogeneity conditions may raise concerns about their plausibility in practice.

Title and authors: Tom: So we're looking at this paper now, "Towards more plausible point-identifying assumptions in two-sample Mendelian randomization," and the authors are Fernando Pires Hartwig, Neil Martin Davies, and George Davey Smith. Jane, what’s the main idea here without getting too deep into the math?

Jane: Well, Tom, basically this paper is looking at two-sample MR—the method where we use genetic variants as instruments to figure out a causal effect—and it says that the assumptions we usually make are way too strong. They call this "summary-level homogeneity."

Lu: That's right. Most two-sample MR methods were built assuming that the association of each genetic variant with the exposure, and the causal effect of that exposure on the outcome, are constant across different parts of our population in an additive way.

Meng: Constant across all strata? That sounds a bit too neat for real-world epidemiology, doesn't it? We see so much variation depending on where you are or what conditions apply to a person.

Lalam: Exactly. The authors show that this strong condition is actually implied by much weaker assumptions, which makes the whole method way more plausible in practice when we try to use it on real data, as they say >

Tom: So they’re essentially saying we can relax those identification requirements and still get reasonable estimates if we use these new conditions. Where does this lead us?

Jane: It opens up the interpretation of what those MR estimators are actually estimating, showing that under these weaker conditions, typical two-sample MR methods are estimators of the average causal effect.

The paper's summary: Tom: Okay, so if we accept these weaker assumptions, what does that mean for how we interpret the results? Jane?

Jane: It means that if those specific identification conditions hold—which they call NOSH, or Non Simultaneous Heterogeneity—then the Wald estimand from a two-sample MR method equals the average causal effect.

Lu: That’s a big deal because it gives us a concrete target for what we are measuring. The authors write that this leads to expressions like theta j equals E

beta Y(U): plus b j, where b j is just some bias parameter of theta j >

Meng: So they're saying the genetic variant estimate isn't just some weird artifact specific to that one instrument; it’s actually pointing towards the average causal effect across the whole population, as long as that bias term stays centered.

Lalam: And for this interpretation to work well, they set a condition: the median of those bias parameters b j has to be zero, and also the mode has to be zero >

Tom: That’s a specific requirement for their identification conditions to hold for them to interpret it as the average causal effect. It puts a lot of pressure on how well we need to satisfy those assumptions.

Jane: And they point out that assuming NOSH holds for every single genetic variant seems more promising than assuming monocity, which they say isn't enough on its own to make the estimand IV-specific or sufficient for summary-level homogeneity >

Lu: They also mention that this assumption is more realistic when we are dealing with continuous exposures and outcomes, which aligns better with how these conditions actually behave in data >

Meng: But the paper also flags a limitation, saying NOSH itself isn't enough to guarantee that the two-sample MR estimators are well-defined in every relevant way, especially concerning gene environment equivalence >

The paper's improvements: Tom: So what are these specific improvements they propose? They're not just saying "we need better assumptions," they’re proposing a new way to think about the necessary conditions. Lu, can you walk us through those key ideas?

Lu: They show that summary-level homogeneity is implied by two things: first, the causal effect has to be additive and linear, but it doesn't have to be constant across all population strata >

Jane: And the second part is a correlation condition: there needs to be no correlation between how much the causal effect varies across strata and how much each genetic variant is associated with the exposure >

Meng: That’s essentially saying that the way X affects Y shouldn't systematically change depending on which genetic variant you pick as your instrument >

Lalam: And to achieve this summary-level homogeneity, they introduce a specific assumption called NOSH, which involves assuming that the average effect of X on Y is linear and additive within strata of U >

Tom: So it’s moving from a very rigid constant effect requirement to something more flexible, but still structured by linearity and additivity across groups. What about the actual IV assumptions? Are they assumed to hold everywhere?

Lu: Yes, the core instrumental variable assumptions—relevance, independence, and exclusion restriction—are assumed to hold for every genetic variant >

Jane: That’s important because it grounds this new finding. They aren't changing what we know about individual instruments; they are relaxing the constraint on how those instruments interact across the whole population >

Meng: From a deployment standpoint, if we have to check these strata conditions, that adds complexity. How do we practically check if this NOSH assumption holds when running actual analyses?

Tom: The authors suggest that empirical assessment could come from genome-wide scans and case-by-case assessments of effect modification >

Conclusion: Jane: So to wrap up, the main point of "Towards more plausible point-identifying assumptions in two-sample Mendelian randomization" is that we can interpret two-sample MR methods as estimators of the average causal effect if we assume these weaker identification conditions, specifically NOSH >

Tom: That means the paper provides a framework where typical MR methods become interpretable causal effect estimates, provided those specific bias parameters are zero on average >

Lu: It’s a step forward because it shows that summary-level homogeneity isn't as restrictive as we thought; it's implied by additive linearity and some correlation constraints >

Meng: But we have to be careful because the authors admit that NOSH alone isn't sufficient for those two-sample MR estimators to be fully well-defined, especially when dealing with gene environment equivalence >

Lalam: So they’re giving us a clearer path forward, even if it’s not a perfect solution yet, by showing what assumptions are actually necessary for interpretation >

Jane: That's the gist of it. This paper moves us closer to having better-defined causal effect estimates from two-sample MR methods, provided we respect these weaker assumptions about how effects vary across populations and genetic variants >