Dynamic treatment regimes with interference

Precision medicine describes health care where patient-level data are used to inform treatment decisions. Within this framework, dynamic treatment regimes (DTRs) are sequences of decision rules that take individual patient information as input data and then output treatment recommendations. DTR estimation from observational data typically relies on the assumption of no interference: i.e., the outcome of one individual is unaffected by the treatment assignment of others. However, in many social network contexts, such as friendship or family networks, and for many health concerns, such as infectious diseases, this assumption is questionable. We investigate the DTR estimation method of dynamic weighted ordinary least squares (dWOLS), which boasts of easy implementation and the so-called double-robustness property, but relies on the assumption of no interference. We define a network propensity function and build on it to establish an implementation of dWOLS that remains doubly robust under interference associated with network links. The method's properties are demonstrated via simulation and applied to data from the Population Assessment of Tobacco and Health (PATH) study to investigate cigarette dependence within two-person household networks.