Regression-based doubly robust estimation of optimal dynamic treatment regimes for binary outcomes

Thomas M. Menino Convention & Exhibition Center 

A dynamic treatment regime (DTR) is a sequence of treatment rules, each formulated as a function of a patient's treatment and covariate history, which recommends the next treatment. An optimal DTR can be estimated by backward induction using a sequence of outcome regression models. Since it is difficult to correctly specify outcome models across stages, double robustness for estimating the optimal DTR is a practically useful property. For binary outcomes, doubly robust estimators for multi-stage optimal DTRs have not been well developed because there is a fundamental trade-off in the choice of the link function for the blip model. Most existing methods employ a logit link function; however, because of its non-collapsibility, pseudo-outcomes cannot be constructed solely from the observed outcomes and the estimated blip parameters, hindering doubly robust estimation in multi-stage settings. Although this problem can be circumvented by using collapsible link functions, the resulting outcome mean under the estimated DTR may violate the natural bounds of a binary outcome. We propose a framework that employs doubly robust g-estimation for collapsible measures and a log-odds product for the nuisance treatment-free outcome model to prevent boundary violations of the estimated outcome mean. Simulation studies demonstrate that the proposed method outperforms the existing sequential regression approach (Q-learning) on some performance measures under complex outcome-generating mechanisms. We further illustrate the practical feasibility and utility of our approach by applying it to a multi-stage problem of e-cigarette use and smoking cessation using longitudinal epidemiological data.

Causal inference

Double robustness

Dynamic treatment regimes

G-estimation

Longitudinal data

Regression model 

Section on Statistics in Epidemiology