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.
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- Award ID(s):
- 1914496
- NSF-PAR ID:
- 10469974
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Canadian Journal of Statistics
- ISSN:
- 0319-5724
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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.
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1002/cjs.11740
