My research interests fall under the large scope of causal inference and personalized medicine. Personalized medicine is an approach to healthcare in which treatment decisions are tailored to the patients’ characteristics rather than to the diagnostic. The statistical study of personalized medicine is known as dynamic treatment regime, or DTR. A DTR is a set of treatment decision rules, each rule corresponding to a certain time point, which inputs patient’s characteristics at that time and outputs a treatment action to be taken. It is especially relevant in the chronic care environment where the patient’s health condition is changing over time and treatment must correspondingly be altered. Of particular interest is to identify an optimal DTR, that is, the sequence of decision rules that yields the best possible outcome for that specific individual, or for similar individuals.
My work principally focuses on extending a theoretically robust, easy to implement DTR method called dynamic weighted ordinary least square, or dWOLS. Briefly, dWOLS models the counterfactual outcome of interest, that is, the outcome had the patient received the sequence of treatments a. In the simplest scenario with two competing treatments at a single time point, the optimal treatment is identified by comparing the counterfactual outcome under treatment a = 1 and a = 0, and choosing the treatment that yields the best outcome. Most important, the optimal treatment may depend on fixed or time-varying patient’s characteristics such that the resulting optimal treatment decision rule is tailored to the patient.
DWOLS currently handles continuous outcomes. However, in the chronic care environment, treatment goals are often to keep patients “symptom-free” and avoid complications for as long as possible. An optimal DTR aims to identify a treatment, or a sequence of treatments, that maximizes the survival time from treatment initiation to the occurrence of any undesirable event. An estimated optimal DTR could be of the form “at the time of diagnostic, prescribe treatment option 1 if the patient is under 55 years old, otherwise prescribe treatment option 2. At a 3 month follow-up visit, if the patient was on treatment option 1, and if his systolic blood pressure is in a normal range, continue with treatment option 1, otherwise switch to treatment option 3.” And so on.
DWOLS and its survival time counterpart face an important inferential challenge: the DTR estimators have non-regular limiting distributions. This essentially implies that the standard asymptotic theory used for deriving confidence intervals around a point estimate may not hold, but also that standard alternatives for constructing confidence intervals, such as the standard bootstrap, may not hold either. My research involves evaluating the performance of alternative methods to construct valid confidence intervals for the DTR parameters, such as the m-out-of-n bootstrap.