Probabilistic Variational Causal Approach in Observational Studies
This work addresses causal inference problems for researchers in fields relying on observational data, offering a novel metric but appearing incremental as it builds on existing causal frameworks.
The paper tackles the challenge of measuring causal effects in observational studies by introducing the Probabilistic vAriational Causal Effect (PACE) metric, which accounts for event rarity and frequency, and provides a causal effect function with parameter d, along with identifiability criteria and comparisons to existing frameworks.
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.