Causal inference quantifies cause effect relationships by means of counterfactual responses had some variable been artificially set to a constant. A more refined notion of manipulation, where a variable is artificially set to a fixed function of its natural value is also of interest in particular domains. Examples include increases in financial aid, changes in drug dosing, and modifying length of stay in a hospital.We define counterfactual responses to manipulations of this type, which we call shift interventions. We show that in the presence of multiple variables being manipulated, two types of shift interventions are possible. Shift interventions on the treated (SITs) are defined with respect to natural values, and are connected to effects of treatment on the treated. Shift interventions as policies (SIPs) are defined recursively with respect to values of responses to prior shift interventions, and are connected to dynamic treatment regimes. We give sound and complete identification algorithms for both types of shift interventions, and derive efficient semi-parametric estimators for the mean response to a shift intervention in a special case motivated by a healthcare problem. Finally, we demonstrate the utility of our method by using an electronic health record dataset to estimate the effect of extending the length of stay in the intensive care unit (ICU) in a hospital by an extra day on patient ICU readmission probability.
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