Estimating dynamic treatment regimes for ordinal outcomes with household interference: Application in household smoking cessation

The focus of precision medicine is on decision support, often in the form of dynamic treatment regimes (DTRs), which are sequences of decision rules. At each decision point, the decision rules determine the next treatment according to the patient's baseline characteristics, the information on treatments and responses accrued by that point, and the patient's current health status, including symptom severity and other measures. However, DTR estimation with ordinal outcomes is rarely studied, and rarer still in the context of interference - where one patient's treatment may affect another's outcome. In this paper, we introduce the proposed weighted proportional odds model (WPOM): a regression-based, doubly-robust approach to single-stage DTR estimation for ordinal outcomes. This method also accounts for the possibility of interference between individuals sharing a household through the use of covariate balancing weights derived from joint propensity scores. Examining different types of balancing weights, we verify the double robustness of WPOM with our adjusted weights via simulation studies. We further extend WPOM to multi-stage DTR estimation with household interference. Lastly, we demonstrate our proposed methodology in the analysis of longitudinal survey data from the Population Assessment of Tobacco and Health study, which motivates this work.