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Testing Identifiability and Transportability with Observational and Experimental Data

Konstantina Lelova, Gregory F. Cooper, Sofia Triantafillou

TL;DR

This work tackles external validity of causal effects across domains when the underlying graph is unknown. It introduces a Bayesian framework that defines an $s$-admissible backdoor set ($sABS$) and computes $P(\\mathcal{H}_{\\mathbf{Z}}|D_e,D_o^*)$ to decide whether a conditioning set yields both identifiability from observational data and transportability. A greedy FindsABS algorithm selects the most informative subset of covariates to maximize evidence from both data sources, with asymptotic guarantees. Simulations show correct identification of transportable backdoor sets and improved estimation in the target population, demonstrating practical impact for clinical decision support.

Abstract

Transporting causal information learned from experiments in one population to another is a critical challenge in clinical research and decision-making. Causal transportability uses causal graphs to model differences between the source and target populations and identifies conditions under which causal effects learned from experiments can be reused in a different population. Similarly, causal identifiability identifies conditions under which causal effects can be estimated from observational data. However, these approaches rely on knowing the causal graph, which is often unavailable in real-world settings. In this work, we propose a Bayesian method for assessing whether Z-specific (conditional) causal effects are both identifiable and transportable, without knowing the causal graph. Our method combines experimental data from the source population with observational data from the target population to compute the probability that a causal effect is both identifiable from observational data and transportable. When this holds, we leverage both observational data from the target domain and experimental data from the source domain to obtain an unbiased, efficient estimator of the causal effect in the target population. Using simulations, we demonstrate that our method correctly identifies transportable causal effects and improves causal effect estimation.

Testing Identifiability and Transportability with Observational and Experimental Data

TL;DR

This work tackles external validity of causal effects across domains when the underlying graph is unknown. It introduces a Bayesian framework that defines an -admissible backdoor set () and computes to decide whether a conditioning set yields both identifiability from observational data and transportability. A greedy FindsABS algorithm selects the most informative subset of covariates to maximize evidence from both data sources, with asymptotic guarantees. Simulations show correct identification of transportable backdoor sets and improved estimation in the target population, demonstrating practical impact for clinical decision support.

Abstract

Transporting causal information learned from experiments in one population to another is a critical challenge in clinical research and decision-making. Causal transportability uses causal graphs to model differences between the source and target populations and identifies conditions under which causal effects learned from experiments can be reused in a different population. Similarly, causal identifiability identifies conditions under which causal effects can be estimated from observational data. However, these approaches rely on knowing the causal graph, which is often unavailable in real-world settings. In this work, we propose a Bayesian method for assessing whether Z-specific (conditional) causal effects are both identifiable and transportable, without knowing the causal graph. Our method combines experimental data from the source population with observational data from the target population to compute the probability that a causal effect is both identifiable from observational data and transportable. When this holds, we leverage both observational data from the target domain and experimental data from the source domain to obtain an unbiased, efficient estimator of the causal effect in the target population. Using simulations, we demonstrate that our method correctly identifies transportable causal effects and improves causal effect estimation.
Paper Structure (8 sections, 5 theorems, 11 equations, 3 figures, 2 algorithms)

This paper contains 8 sections, 5 theorems, 11 equations, 3 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Motivating Examples
  4. Method
  5. Estimating the probability that a set is an sABS
  6. Looking for a maximally informative sABS
  7. Related Work
  8. Experiments

Key Result

Theorem 1

Let $D$ be the selection diagram characterizing $\Pi$ and $\Pi^*$, and $\mathbf {S}$ the set of selection variables in $D$. The $Z$-specific causal effect $P(Y \mid do(X), \mathbf {Z})$ is transportable from $\Pi$ to $\Pi^*$ if $\mathbf {Z}$ d-separates $Y$ from $\mathbf {S}$ in the $X$-manipulated

Figures (3)

  • Figure 1: Example of a selection diagram: $S_Z$ and $S_W$ variables indicate the difference in the distribution of $Z$ and $W$ respectively between $\Pi$ and $\Pi^*$ in $\mathcal{D}$. $S_X$ indicates the absence of the arrow from $W$ to $X$ in the target population. Variable $\mathbf {S}$ denotes the set of selection variables, i.e., $\mathbf {S}=\{S_X, S_Z, S_W\}$. $\mathbf {S}=\mathbf {s}$ indicates the distribution of the source domain, while $\mathbf {S}=\mathbf {s}^*$ indicates the distribution of the target domain. $(Z, W)$ is an s-admissible set and is also backdoor set in $\mathcal{G}^*$. $P(Y| do(X), Z, W, S=s)$ is transportable from $\Pi$ to $\Pi^*$, since $Z, W$ is s-admissible.
  • Figure 2: Causal structures among treatment $X$, outcome $Y$, and observed pre-treatment covariates $Z$ and $W$. (a) $\{Z, W\}$ is an s-admissible backdoor set. (b) $\{Z, W\}$ is s-admissible, but it is not a backdoor set. No s-admissible backdoor set exists. (c) $\{Z, W\}$ is a backdoor set, but not s-admissible. However, $\{Z\}$ is an s-admissible backdoor set. (d) $\{Z, W\}$ is neither an backdoor set, nor s-admissible, but $\{W\}$ and $\{ \emptyset\}$ are.
  • Figure 3: Areas under the ROC curve for predicting $h_{ \textbf{Z}}$ with $5000$ in $D_o^*$ and an increasing number of samples in $D_e$.

Theorems & Definitions (7)

  • Definition 1
  • Theorem 1: S-admissibility
  • Theorem 2: special case of Rule 2 of do-calculus
  • Theorem 3
  • proof
  • Theorem 4
  • Theorem 5