Causal Inference in the Multiverse of Hazard

Abstract: Hazard serves as a pivotal estimand in both practical applications and methodological frameworks. However, its causal interpretation poses notable challenges, including inherent selection biases and ill-defined populations to be compared between different treatment groups. In response, we propose a novel definition of counterfactual hazard within the framework of possible worlds. Instead of conditioning on prior survival status as a conditional probability, our new definition involves intervening in the prior status, treating it as a marginal probability. Using single-world intervention graphs, we demonstrate that the proposed counterfactual hazard is a type of controlled direct effect. Conceptually, intervening in survival status at each time point generates a new possible world, where the proposed hazards across time points represent risks in these hypothetical scenarios, forming a "multiverse of hazard." The cumulative and average counterfactual hazards correspond to the sum and average of risks across this multiverse, respectively, with the actual world's risk lying between the two. This conceptual shift reframes hazards in the actual world as a collection of risks across possible worlds, marking a significant advancement in the causal interpretation of hazards.