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We consider the problem of learning about and comparing the consequences ofdynamic treatment strategies on the basis of observational data. We formulatethis within a probabilistic decision-theoretic framework. Our approach iscompared with related work by Robins and others: in particular, we show howRobins's 'G-computation' algorithm arises naturally from thisdecision-theoretic perspective. Careful attention is paid to the mathematicaland substantive conditions required to justify the use of this formula. Theseconditions revolve around a property we term stability, which relates theprobabilistic behaviours of observational and interventional regimes. We showhow an assumption of 'sequential randomization' (or 'no unmeasuredconfounders'), or an alternative assumption of 'sequential irrelevance', can beused to infer stability. Probabilistic influence diagrams are used to simplifymanipulations, and their power and limitations are discussed. We compare ourapproach with alternative formulations based on causal DAGs or potentialresponse models. We aim to show that formulating the problem of assessingdynamic treatment strategies as a problem of decision analysis brings clarity,simplicity and generality.

Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview