Xi Lu (Lucy)

I am a PhD candidate at the Department of Statistics at the University of Michigan. My PhD Advisor is Dr. Susan Murphy, and I am also collaborating with my mentor Dr. Daniel Almirall.

As a member of Dr. Murphy's Statistical Reinforcement Learning Lab, I am mostly interested in sequential decision making in health-related problems. More specifically, I am interested in developing statistical methodologies to evaluate and/or compare adaptive interventions (OR dynamic treatment regimes), using data arising from an innovative class of clinical trials: Sequential Multiple Assignment Randomized Trials.

Read More?


Work in Progress


Brief introduction of two main aspects of my works in PhD

Policy evaluation/comparison with assistance of the Structural Nested Mean Models

Oftentimes researchers are interested in evaluating the quality of a treatment policy (aka adaptive intervention, or dynamic treatment regime). A simple example of a policy (in the treatment of kids with ADHD): assign behavioral modification (BMOD) therapy to all patients initially; after two months, evaluate early response, then augment BMOD with medication for non-responders and continue BMOD for responders. The quality of such a policy (aka policy value) is defined as the mean of a clinically meaningful outcome (e.g. score of classroom performance rated by teacher at month 8), if the entire population had followed this particular policy to receive the treatment.

With data arising from the Sequential Multiple Assignment Randomized Trials (SMARTs), this type of problem can be solved. Part of my dissertation is concerned with this policy evaluation, with the assistance of parametric estimates of the treatment effects at each treatment stage. The idea is that scientists may have some knowledge about how the treatment interacts with the preceding covariates - for example, they may suggest {age, gender, baseline severity} as moderators for first stage treatment, and {severity at month 2, adherence in stage one} as moderators for second stage treatment. This information guides us to parametrically estimate the interaction treatment effect at each stage, which we will utilize to construct an estimator for the policy value.

This assisted estimator is semi-parametric, thus enjoying lower variance than the Inverse-Probability-Weighting type of non-parametric estimator. Different from existing model-based methods (e.g., Q-learning or Marginal Structural Models), the modeling in our methodology is only determined by scientific knowledge about the treatment, and thus does not have to be modified when one switches the focus to a different treatment policy. That is, the estimated treatment effects can be utilized to evalute ANY policy, from the simple one presented above, to very deeply tailored policy involving many covariates!!

Modeling of repeated measures outcomes under embedded policies in a SMART

In addition to an end-of-study primary outcome, researchers may be interested in the trend of a repeated-measures outcome (aka longitudinal outcome), and how the trend differs among a set of pre-specified simple policies. For example, in the ADHD study, we are interested in the longitudinal trajectory of teacher-evaluated kid's classroom performance.

For a traditional 2-arm randomized clinical trial (RCT), the repeated-measures outcome may be modeled as 2 straight lines with different slopes. However, special features of SMARTs make this type of traditional models invalid: if we are comparing two policies that both assign BMOD as the initial treatment, and only differ in the remedy treatment for non-responders (say, assigning intensified BMOD VERSUS assigning BMOD+medication), then the two mean trajectories associated to the two policies should share path until the first time point where patients can transition to second stage as non-responders. As many SMART studies are more complex in terms of the scheme of patients transitioning to second stage, and when each of the (re-)randomizations occurs, we need to be respect unique features of each type of SMART in developing longitudinal models for SMART data.



Contact Information

Xi Lu
2451 Institute for Social Research
426 Thompson Street
University of Michigan
Ann Arbor, Michigan 48104-2321

luxi at umich dot edu