Randomized controlled trial (RCT) refers to a design commonly employed by clinical and sociological studies where study participants are randomly assigned to an investigational treatment arm, or to a control arm to serve as comparison. With randomization as the unique device to eliminate systematic bias in treatment choice, RCT has been rightfully enshrined as the gold standard for any scientific inquiry, especially those involving human subjects. A challenging yet pervasive issue arises, however, when some participants in an RCT do not comply with the random assignment and instead self-select into the treatment of their choice. This self-selection compromises the objectivity of treatment assignment and thereby weakens the rigor of the experiment. A seminal paper by Angrist, Imbens, and Rubin (1996) provided invaluable insight into the difficult task of drawing valid causal inference in RCTs plagued by non-compliance. However, their work is focused on the average of a quantitative outcome as the metric of treatment effect and thus does not apply to other commonly encountered outcome types such as ordinal data (for example, tumor grade). Moreover, it is unclear whether their approach has utilized the available information on each participant to the fullest extent. With the advent of modern statistical/mathematical tools such as empirical processes, semiparametric theory, and functional analysis, the PI seeks to extend the Angrist-Imbens-Rubin (AIR) approach by targeting a much wider scope of effect size measures, or causal estimands, and studying their efficient estimation under a unified framework. The PI will also develop user-friendly software packages implementing the corresponding inference procedures and involve graduate students in the project. Successful completion of this project will equip investigators with more versatile and powerful tools to address non-compliance in RCTs, the mainstay of medical and sociological investigations.
Specifically, the general causal estimand is defined by an arbitrary smooth contrast in the marginal (potential) outcome distribution between the two arms. This formulation unifies seemingly disparate effect size measures for all kinds of outcome types, such as the average treatment effect (ATE), Mann-Whitney effect (i.e., probability of an outcome under treatment being greater than one under control), quantile treatment effect, distributional treatment effect, the win ratio, and so forth. Due to non-identifiability associated with non-compliance, interest is focused on a “local†version of treatment effects, that is, contrasts made on the sub-population of compliers. These are natural extensions of the local ATE thoroughly studied by AIR. Under standard assumptions, simple nonparametric plug-in estimators are constructed for the local treatment effects based on nonparametric estimators for the complier outcome distributions. The operating characteristics of testing procedures based on these estimators will also be investigated. Finally, the entire framework will be re-cast in semiparametric-theoretical terms to optimize the statistical efficiency of both the estimation and testing procedures. This research will lay the groundwork for future extensions to accommodate baseline covariates, censored outcomes, and non-binary (and possibly time-dependent) treatment.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
