  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 weighted proportional odds model (WPOM): a
regression-based, approximate 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 approximate double
robustness of WPOM with our adjusted weights via simulation studies. We further
extend WPOM to multi-stage DTR estimation with household interference, namely
dWPOM (dynamic WPOM). 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. Furthermore, considering
interference, we provide optimal treatment strategies for households to achieve
smoking cessation of the pair in the household.
