TLDR: This research introduces a new method to estimate causal effects (e.g., how a drug affects health) in situations where a key influencing factor (confounder) is unobserved. It uses an observable “proxy” variable (like price for hotel quality) and data from multiple environments to identify and estimate the causal effect in a new, unseen environment, even if only the proxy is observed there. The paper proposes two consistent estimators, provides confidence intervals, and validates the approach with simulations and a real-world study on hotel ranking and consumer choices.
Understanding cause-and-effect relationships is crucial in many fields, from medicine to marketing. However, a significant challenge arises when trying to determine if a ‘treatment’ (like a new drug or a website ranking) truly causes an ‘outcome’ (like patient survival or consumer choice), especially when there are hidden factors influencing both. These hidden factors are known as unobserved confounders, and they can lead to misleading conclusions if not properly accounted for.
A new research paper, “Transferring Causal Effects using Proxies,” tackles this complex problem by proposing a novel approach to estimate causal effects even when key confounders remain unobserved. The researchers, Manuel Iglesias-Alonso, Felix Schur, Julius von Kügelgen, and Jonas Peters, introduce a methodology that leverages ‘proxy’ variables – observable factors that are related to the hidden confounders – and data from multiple different environments or “domains.”
Imagine you want to know if a hotel’s position in a search result list (the ‘treatment’) causes users to click on it (the ‘outcome’). A hidden confounder might be the hotel’s overall appeal or quality, which influences both its ranking and whether a user clicks. This quality might not be directly observed, but its ‘proxy’ could be the hotel’s price. The paper explores how to use such proxies, along with data collected from various scenarios (different hotels or search contexts), to accurately estimate the true causal effect.
Key Innovations
The core contribution of this work lies in proving that the causal effect in a new, unseen domain can be identified and estimated, even when only the proxy variable is observed in that new domain. This is a significant step forward, as it means we don’t need to observe the treatment or outcome directly in the target environment to understand the causal link.
The researchers developed two main estimation techniques: one based on a “causal parametrisation” that explicitly models the underlying causal mechanisms, and another using a “reduced parametrisation” that focuses only on the necessary components for estimation. Both methods are shown to be consistent, meaning they provide increasingly accurate estimates as more data becomes available. The reduced parametrisation also offers the advantage of providing confidence intervals, giving a measure of certainty around the estimates.
A crucial aspect for the success of this method is the “informativeness” of the proxy variable. The paper highlights that the proxy must be sufficiently related to the unobserved confounder across different domains. If the proxy is not informative enough, the identifiability of the causal effect can be lost.
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Real-World Application and Performance
The theoretical findings are supported by extensive simulation studies, demonstrating that the proposed estimators perform well, especially when compared to simpler “no-adjustment” or “W-adjustment” baselines that fail to properly account for hidden confounding. The confidence intervals derived from the reduced estimator also show valid coverage, confirming their reliability.
A compelling real-world example is presented using the Expedia Hotel Searches dataset. Here, the goal was to understand the causal effect of a hotel’s ranking position on user clicks. The unobserved confounder could be the hotel’s inherent desirability, with price acting as a proxy. The study successfully applied the methodology to estimate this causal effect, showing that certain ranking positions significantly increase the probability of a click. The estimates from their method were closer to a ‘ground truth’ (obtained from randomized ranking data) than other baseline approaches.
This research offers valuable tools for causal inference in settings where unobserved confounders are prevalent and data is available from diverse sources. For more technical details, the full paper can be accessed here: Transferring Causal Effects using Proxies.
