Hazards, causality and (non-) Markov event histories

Hazard ratios, assumed constant in Cox regression model, are arguably the most common measure of effect in time-to-event trials. Because hazards condition on previous survival, there is a worry that such hazard contrasts do not permit a causal interpretation even in randomized trials. At the same time, it is undisputed that a transformation of hazard contrasts onto the probability scale "is causal". I will argue that the backtransformation is causal, too. I will then consider a very handy version of g-computation via Aalen-Johansen where the aim is to intervene on a specific hazard, equating it with zero (and yielding both contrasts of hazards and probabilities.) Causal inference requires strong assumptions, and we require a time-inhomogeneous Markov property. This is somewhat in contrast to other recent efforts in multi-state and recurrent events modelling and I'll wrap up by briefly discussing nonparametric non-Markov inference and bootstrapping.

References:

Erdmann, A., Loos, A., and Beyersmann, J. (2023). A connection between survival multistate models and causal inference for external treatment interruptions. Statistical Methods in Medical Research, 32:267–286

Nießl, A., Allignol, A., Beyersmann, J., and Mueller, C. (2023). Statistical inference for state occupation and transition probabilities in non-Markov multi-state models subject to both random left-truncation and right-censoring. Econometrics and Statistics, 25:110–124