skip to main content

Attention:

The NSF Public Access Repository (PAR) system and access will be unavailable from 11:00 PM ET on Thursday, February 13 until 2:00 AM ET on Friday, February 14 due to maintenance. We apologize for the inconvenience.


Title: Debiased inference on heterogeneous quantile treatment effects with regression rank scores
Abstract

Understanding treatment effect heterogeneity is vital to many scientific fields because the same treatment may affect different individuals differently. Quantile regression provides a natural framework for modelling such heterogeneity. We propose a new method for inference on heterogeneous quantile treatment effects (HQTE) in the presence of high-dimensional covariates. Our estimator combines an ℓ1-penalised regression adjustment with a quantile-specific bias correction scheme based on rank scores. We study the theoretical properties of this estimator, including weak convergence and semi-parametric efficiency of the estimated HQTE process. We illustrate the finite-sample performance of our approach through simulations and an empirical example, dealing with the differential effect of statin usage for lowering low-density lipoprotein cholesterol levels for the Alzheimer’s disease patients who participated in the UK Biobank study.

 
more » « less
Award ID(s):
2310578
PAR ID:
10439599
Author(s) / Creator(s):
;
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Journal of the Royal Statistical Society Series B: Statistical Methodology
Volume:
85
Issue:
5
ISSN:
1369-7412
Format(s):
Medium: X Size: p. 1561-1588
Size(s):
p. 1561-1588
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Quantile regression for right‐ or left‐censored outcomes has attracted attention due to its ability to accommodate heterogeneity in regression analysis of survival times. Rank‐based inferential methods have desirable properties for quantile regression analysis, but censored data poses challenges to the general concept of ranking. In this article, we propose a notion of censored quantile regression rank scores, which enables us to construct rank‐based tests for quantile regression coefficients at a single quantile or over a quantile region. A model‐based bootstrap algorithm is proposed to implement the tests. We also illustrate the advantage of focusing on a quantile region instead of a single quantile level when testing the effect of certain covariates in a quantile regression framework.

     
    more » « less
  2. Abstract

    We propose an efficient estimator for the coefficients in censored quantile regression using the envelope model. The envelope model uses dimension reduction techniques to identify material and immaterial components in the data, and forms the estimator based only on the material component, thus reducing the variability of estimation. We will demonstrate the guaranteed asymptotic efficiency gain of our proposed envelope estimator over the traditional estimator for censored quantile regression. Our analysis begins with the local weighing approach that traditionally relies on semiparametric ‐estimation involving the conditional Kaplan–Meier estimator. We will instead invoke the independent identically distributed (i.i.d.) representation of the Kaplan–Meier estimator, which eliminates this infinite‐dimensional nuisance and transforms our objective function in ‐estimation into a ‐process indexed by only an Euclidean parameter. The modified ‐estimation problem becomes entirely parametric and hence more amenable to analysis. We will also reconsider the i.i.d. representation of the conditional Kaplan–Meier estimator.

     
    more » « less
  3. Abstract

    Quantiles and expected shortfalls are commonly used risk measures in financial risk management. The two measurements are correlated while having distinguished features. In this project, our primary goal is to develop a stable and practical inference method for the conditional expected shortfall. We consider the joint modelling of conditional quantile and expected shortfall to facilitate the statistical inference procedure. While the regression coefficients can be estimated jointly by minimizing a class of strictly consistent joint loss functions, the computation is challenging, especially when the dimension of parameters is large since the loss functions are neither differentiable nor convex. We propose a two‐step estimation procedure to reduce the computational effort by first estimating the quantile regression parameters with standard quantile regression. We show that the two‐step estimator has the same asymptotic properties as the joint estimator, but the former is numerically more efficient. We develop a score‐type inference method for hypothesis testing and confidence interval construction. Compared to the Wald‐type method, the score method is robust against heterogeneity and is superior in finite samples, especially for cases with many confounding factors. The advantages of our proposed method over existing approaches are demonstrated by simulations and empirical studies based on income and college education data.

     
    more » « less
  4. Abstract

    Over the past decade, there has been growing enthusiasm for using electronic medical records (EMRs) for biomedical research. Quantile regression estimates distributional associations, providing unique insights into the intricacies and heterogeneity of the EMR data. However, the widespread nonignorable missing observations in EMR often obscure the true associations and challenge its potential for robust biomedical discoveries. We propose a novel method to estimate the covariate effects in the presence of nonignorable missing responses under quantile regression. This method imposes no parametric specifications on response distributions, which subtly uses implicit distributions induced by the corresponding quantile regression models. We show that the proposed estimator is consistent and asymptotically normal. We also provide an efficient algorithm to obtain the proposed estimate and a randomly weighted bootstrap approach for statistical inferences. Numerical studies, including an empirical analysis of real-world EMR data, are used to assess the proposed method's finite-sample performance compared to existing literature.

     
    more » « less
  5. Summary

    In many observational longitudinal studies, the outcome of interest presents a skewed distribution, is subject to censoring due to detection limit or other reasons, and is observed at irregular times that may follow a outcome-dependent pattern. In this work, we consider quantile regression modeling of such longitudinal data, because quantile regression is generally robust in handling skewed and censored outcomes and is flexible to accommodate dynamic covariate-outcome relationships. Specifically, we study a longitudinal quantile regression model that specifies covariate effects on the marginal quantiles of the longitudinal outcome. Such a model is easy to interpret and can accommodate dynamic outcome profile changes over time. We propose estimation and inference procedures that can appropriately account for censoring and irregular outcome-dependent follow-up. Our proposals can be readily implemented based on existing software for quantile regression. We establish the asymptotic properties of the proposed estimator, including uniform consistency and weak convergence. Extensive simulations suggest good finite-sample performance of the new method. We also present an analysis of data from a long-term study of a population exposed to polybrominated biphenyls (PBB), which uncovers an inhomogeneous PBB elimination pattern that would not be detected by traditional longitudinal data analysis.

     
    more » « less