Probabilistic Variational Causal Approach in Observational Studies

TL;DR

The paper addresses causal inference in observational studies by introducing Probabilistic Variational Causal Effect (PACE), a direct causal effect metric that blends interventional variation with the natural availability of changing exposure values, controlled by a degree parameter $d$. It develops variants such as PEACE, SPACE, and APACE, plus MEAN versions and positive/negative forms, and provides identifiability criteria within SEMs. The framework is illustrated through analytic examples (e.g., Binary Symmetric Channel, rare disease on blood pressure, rain and sprinkler) and contrasted with Pearl/Rubin approaches, highlighting its emphasis on treatment-value rarity/frequency and subpopulation weighting. The results offer a flexible, interpretable toolkit for causal analysis in observational data with potential applications to reinforcement learning and medical data, while acknowledging limitations related to covariate selection and indirect effects.

Abstract

In this paper, we introduce a new causal methodology that accounts for the rarity and frequency of events in observational studies based on their relevance to the underlying problem. Specifically, we propose a direct causal effect metric called the Probabilistic vAriational Causal Effect (PACE) and its variations adhering to certain postulates applicable to both non-binary and binary treatments. The PACE metric is derived by integrating the concept of total variation, representing the purely causal component, with interventions on the treatment value, combined with the probabilities of hypothetical transitioning between treatment levels. PACE features a parameter $d$, where lower values of $d$ correspond to scenarios emphasizing rare treatment values, while higher values of $d$ focus on situations where the causal impact of more frequent treatment levels is more relevant. Thus, instead of a single causal effect value, we provide a causal effect function of the degree $d$. Additionally, we introduce positive and negative PACE to measure the respective positive and negative causal changes in the outcome as exposure values shift. We also consider normalized versions of PACE, referred to MEAN PACE. Furthermore, we provide an identifiability criterion for PACE to handle counterfactual challenges in observational studies, and we define several generalizations of our methodology. Lastly, we compare our framework with other well-known causal frameworks through the analysis of various examples.

Figures (4)

• Figure 1: These plots indicate that, in the example given in Section \ref{['simpson']}, from a causal perspective, the admission rate for women is higher regardless of whether the degree $d$ is high or low.
• Figure 2: The graphical view of the relationships between the random variables in the example given in Section \ref{['sprinkler']}
• Figure 3: The procedure to find the variational DCE of a variable along a path toward the outcome.
• Figure 4: The red and the blue graphs show $\mathcal{P}\mathcal{I}\mathcal{V}_d(X_P\to Y)$ and $\mathcal{P}\mathcal{I}\mathcal{V}_d(X_Q\to Y)$, where $P=\{0,1,2\}$ and $Q=\{0,2\}$.

Theorems & Definitions (22)

• Theorem 3.2
• proof
• Proposition 3.4
• proof
• Remark 3.6
• Theorem 3.9
• proof
• Theorem 3.10
• proof
• Proposition 3.11