Efficient estimation of a linear transformation model for current status data via penalized splines

Minggen Lu, Yan Liu, Chin-Shang Li

Research output: Contribution to journalArticle

Abstract

We propose a flexible and computationally efficient penalized estimation method for a semi-parametric linear transformation model with current status data. To facilitate model fitting, the unknown monotone function is approximated by monotone B-splines, and a computationally efficient hybrid algorithm involving the Fisher scoring algorithm and the isotonic regression is developed. A goodness-of-fit test and model diagnostics are also considered. The asymptotic properties of the penalized estimators are established, including the optimal rate of convergence for the function estimator and the semi-parametric efficiency for the regression parameter estimators. An extensive numerical experiment is conducted to evaluate the finite-sample properties of the penalized estimators, and the methodology is further illustrated with two real studies.

Original languageEnglish (US)
JournalStatistical Methods in Medical Research
DOIs
StateAccepted/In press - Jan 1 2018
Externally publishedYes

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Linear Transformation Model
Current Status Data
Penalized Splines
Efficient Estimation
Linear Models
Estimator
Routine Diagnostic Tests
Fisher Scoring
Semiparametric Efficiency
Isotonic Regression
Model Diagnostics
Optimal Rate of Convergence
Monotone Function
Model Fitting
Goodness of Fit Test
Hybrid Algorithm
B-spline
Asymptotic Properties
Monotone
Efficient Algorithms

Keywords

  • Current status data
  • efficient estimation
  • goodness-of-fit
  • penalized spline
  • transformation model

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability
  • Health Information Management

Cite this

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AB - We propose a flexible and computationally efficient penalized estimation method for a semi-parametric linear transformation model with current status data. To facilitate model fitting, the unknown monotone function is approximated by monotone B-splines, and a computationally efficient hybrid algorithm involving the Fisher scoring algorithm and the isotonic regression is developed. A goodness-of-fit test and model diagnostics are also considered. The asymptotic properties of the penalized estimators are established, including the optimal rate of convergence for the function estimator and the semi-parametric efficiency for the regression parameter estimators. An extensive numerical experiment is conducted to evaluate the finite-sample properties of the penalized estimators, and the methodology is further illustrated with two real studies.

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