Nonparametric inference of complier quantile treatment effects in randomized trials with imperfect compliance

Abstract

To analyze randomized trials with imperfect compliance, a standard approach is to estimate the local average treatment effect in the sub-population of compliers using randomization status as an instrumental variable. Though quantile analysis has been popular in general, the local (or complier) quantile treatment effect (cQTE) as a causal estimand has received insufficient attention. In this paper, we map out the details for the estimation, inference, and sensitivity analysis of the cQTE in a completely nonparametric setting. We propose to estimate the cQTE using nonparametric plug-in estimators of the cumulative distribution functions for the potential outcomes of the compliers. The cQTE estimator is shown to be asymptotically normal, with asymptotic variance estimated through kernel-smoothed density estimators. The procedure is easily extended to adjust for discrete covariates for gains in statistical efficiency. Moreover, by exploiting the stochastic monotonicity of the quantile functional, we develop sensitivity bounds for the cQTE when key assumptions such as exclusion restriction and instrument monotonicity are violated. Extensive simulations show that the proposed methods provide valid inference of the target local estimand and outperform standard intent-to-treat tests, especially under low compliance rates and/or heterogeneous treatment effects. A recent study on a government-funded health insurance program in India is analyzed as an illustration.

Keywords:

• Causal inference
• instrumental variable
• kernel density estimator
• local treatment effects
• sensitivity analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the U.S. National Science Foundation grant DMS2015526.

Notes on contributors

Lu Mao

Lu Mao joined the Department of Biostatistics and Medical Informatics at University of Wisconsin (UW)-Madison as an Assistant Professor after obtaining his doctoral degree in Biostatistics from UNC Chapel Hill in 2016. His research interests include survival analysis (particularly composite outcomes), causal inference, semiparametric theory, and clinical trials. He is currently the PI of an NIH R01 grant on statistical methodology for composite time-to-event outcomes in cardiovascular trials and an NSF grant on causal inference in randomized trials with noncompliance. Besides methodological studies, he also collaborates with medical researchers in cardiology, radiology, cancer, and health behavioral interventions, where time-to-event and longitudinal data are routinely collected and analyzed.