Open Access
2021 A penalized likelihood approach for efficiently estimating a partially linear additive transformation model with current status data
Yan Liu, Minggen Lu, Christopher S. McMahan
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Electron. J. Statist. 15(1): 2247-2287 (2021). DOI: 10.1214/21-EJS1820

Abstract

Current status data are commonly encountered in medical and epidemiological studies in which the failure time for study units is the outcome variable of interest. Data of this form are characterized by the fact that the failure time is not directly observed but rather is known relative to an observation time, i.e., the failure times are either left- or right-censored. Due to its structure, the analysis of such data can be challenging. To circumvent these challenges and to provide for a flexible modeling construct which can be used to analyze current status data, herein a partially linear additive transformation model is proposed. In the formulation of this model, constrained B-splines are employed to model the monotone transformation function and nonparametric covariate effects. To provide for more efficient estimators, a penalization technique is used to regularize the estimation of all unknown functions. An easy to implement hybrid algorithm is developed for model fitting, and a simple and consistent estimator of the large-sample variance-covariance matrix for regression parameter estimators is proposed. It is shown theoretically that the proposed estimators of the finite-dimensional regression coefficients are root-n consistent, asymptotically normal, and achieve the semiparametric information bound, while the estimators of the nonparametric components attain the optimal rate of convergence. The finite-sample performance of the proposed methodology is evaluated through extensive numerical studies and is further demonstrated through the analysis of human papillomavirus (HPV) data.

Funding Statement

This research was supported by the National Institutes of Health grants R01-AI121351, National Science Foundation grant OIA-1826715, and Department of Defense’s Office of Naval Research grant N00014-19-1-2295. Christopher S. McMahan was funded by Grant R01 AI121351 from the National Institutes of Health, Grant OIA-1826715 from the National Science Foundation, and Grant N00014-19-1-2295 from the Office of Naval Research.

Citation

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Yan Liu. Minggen Lu. Christopher S. McMahan. "A penalized likelihood approach for efficiently estimating a partially linear additive transformation model with current status data." Electron. J. Statist. 15 (1) 2247 - 2287, 2021. https://doi.org/10.1214/21-EJS1820

Information

Received: 1 June 2020; Published: 2021
First available in Project Euclid: 20 April 2021

Digital Object Identifier: 10.1214/21-EJS1820

Keywords: B-spline , Current status data , isotonic regression , partially linear additive transformation model , penalized estimation

Vol.15 • No. 1 • 2021
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