A Data Fusion Method for Quantile Treatment Effects

TL;DR

This paper introduces a novel data fusion method for estimating quantile treatment effects by combining small validated datasets with large auxiliary datasets, improving efficiency and robustness in causal inference.

Contribution

The paper proposes the Fused Quantile Treatment Effects Estimator (FQTE), a doubly robust approach that leverages both datasets even with unmeasured confounders, enhancing estimation accuracy.

Findings

FQTE is asymptotically normal under mild conditions.

FQTE outperforms estimators using only validation data in efficiency.

Simulation studies confirm the empirical validity of the proposed method.

Abstract

With the increasing availability of datasets, developing data fusion methods to leverage the strengths of different datasets to draw causal effects is of great practical importance to many scientific fields. In this paper, we consider estimating the quantile treatment effects using small validation data with fully-observed confounders and large auxiliary data with unmeasured confounders. We propose a Fused Quantile Treatment effects Estimator (FQTE) by integrating the information from two datasets based on doubly robust estimating functions. We allow for the misspecification of the models on the dataset with unmeasured confounders. Under mild conditions, we show that the proposed FQTE is asymptotically normal and more efficient than the initial QTE estimator using the validation data solely. By establishing the asymptotic linear forms of related estimators, convenient methods for covariance estimation are provided. Simulation studies demonstrate the empirical validity and improved efficiency of our fused estimators. We illustrate the proposed method with an application.