  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.
