Hazard is a crucial estimand in both applied and methodological contexts. However, its causal interpretation is challenging due to inherent selection biases and the ambiguity in defining populations for comparison across different treatment groups. To address these issues, we introduce a novel definition of counterfactual hazard based on the framework of possible worlds. Rather than conditioning on prior survival status as a conditional probability, our definition involves intervening in the prior status, treating it as a marginal probability. Using single-world intervention graphs, we show that the proposed counterfactual hazard represents a controlled direct effect. Conceptually, intervening in survival status at each time point creates a new possible world. The proposed hazards at these time points represent risks in these hypothetical scenarios, forming a “multiverse.”

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Causal Inference in the Multiverse of Hazard

  • En-Yu Lai,
  • Yen-Tsung Huang

摘要

Hazard is a crucial estimand in both applied and methodological contexts. However, its causal interpretation is challenging due to inherent selection biases and the ambiguity in defining populations for comparison across different treatment groups. To address these issues, we introduce a novel definition of counterfactual hazard based on the framework of possible worlds. Rather than conditioning on prior survival status as a conditional probability, our definition involves intervening in the prior status, treating it as a marginal probability. Using single-world intervention graphs, we show that the proposed counterfactual hazard represents a controlled direct effect. Conceptually, intervening in survival status at each time point creates a new possible world. The proposed hazards at these time points represent risks in these hypothetical scenarios, forming a “multiverse.”