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

TL;DR

This paper presents a decision-theoretic framework for evaluating dynamic treatment strategies using observational data, clarifying conditions like stability and assumptions such as sequential randomization, and compares it with existing causal methods.

Contribution

It introduces a decision-theoretic approach to analyze dynamic treatment strategies, connecting Robins's G-computation with a formal probabilistic framework and discussing stability conditions.

Findings

Robins's G-computation naturally arises from the decision-theoretic perspective.

Stability conditions are crucial for valid causal inference in this framework.

Probabilistic influence diagrams help clarify the manipulations and assumptions involved.

Abstract

We consider the problem of learning about and comparing the consequences of dynamic treatment strategies on the basis of observational data. We formulate this within a probabilistic decision-theoretic framework. Our approach is compared with related work by Robins and others: in particular, we show how Robins's 'G-computation' algorithm arises naturally from this decision-theoretic perspective. Careful attention is paid to the mathematical and substantive conditions required to justify the use of this formula. These conditions revolve around a property we term stability, which relates the probabilistic behaviours of observational and interventional regimes. We show how an assumption of 'sequential randomization' (or 'no unmeasured confounders'), or an alternative assumption of 'sequential irrelevance', can be used to infer stability. Probabilistic influence diagrams are used to simplify manipulations, and their power and limitations are discussed. We compare our approach with alternative formulations based on causal DAGs or potential response models. We aim to show that formulating the problem of assessing dynamic treatment strategies as a problem of decision analysis brings clarity, simplicity and generality.