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.