Efficient estimation of partially linear additive Cox model under monotonicity constraint

Minggen Lu, Tao Lu, Chin-Shang Li

Research output: Contribution to journalArticle

Abstract

We provide a simple and practical, yet flexible spline estimation method for partially linear additive Cox model with monotonicity constraint. We propose to approximate the unknown monotone function by monotone B-splines, and employ a hybrid numerical approach based on the Newton-Raphson algorithm and the isotonic regression to compute the spline estimates. We show that the spline estimators of the nonparametric components achieve the optimal rate of convergence under the smooth condition, and that the estimators of the regression parameters are asymptotically normal and efficient. Moreover, a direct variance estimation method based on the least-squares estimation is proposed. The finite-sample performance of the spline estimates is evaluated by a Monte Carlo study. The methodology is illustrated with a synovial sarcoma dataset.

Original languageEnglish (US)
JournalJournal of Statistical Planning and Inference
DOIs
StateAccepted/In press - 2017

Fingerprint

Cox Model
Additive Models
Efficient Estimation
Splines
Spline
Monotonicity
Newton-Raphson Algorithm
Isotonic Regression
Estimator
Optimal Rate of Convergence
Variance Estimation
Least Squares Estimation
Monotone Function
Monte Carlo Study
B-spline
Estimate
Monotone
Regression
Unknown
Cox model

Keywords

  • Additive Cox model
  • Efficient estimation
  • Isotonic regression
  • Monotone B-spline
  • Partial likelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

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title = "Efficient estimation of partially linear additive Cox model under monotonicity constraint",
abstract = "We provide a simple and practical, yet flexible spline estimation method for partially linear additive Cox model with monotonicity constraint. We propose to approximate the unknown monotone function by monotone B-splines, and employ a hybrid numerical approach based on the Newton-Raphson algorithm and the isotonic regression to compute the spline estimates. We show that the spline estimators of the nonparametric components achieve the optimal rate of convergence under the smooth condition, and that the estimators of the regression parameters are asymptotically normal and efficient. Moreover, a direct variance estimation method based on the least-squares estimation is proposed. The finite-sample performance of the spline estimates is evaluated by a Monte Carlo study. The methodology is illustrated with a synovial sarcoma dataset.",
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AU - Lu, Tao

AU - Li, Chin-Shang

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N2 - We provide a simple and practical, yet flexible spline estimation method for partially linear additive Cox model with monotonicity constraint. We propose to approximate the unknown monotone function by monotone B-splines, and employ a hybrid numerical approach based on the Newton-Raphson algorithm and the isotonic regression to compute the spline estimates. We show that the spline estimators of the nonparametric components achieve the optimal rate of convergence under the smooth condition, and that the estimators of the regression parameters are asymptotically normal and efficient. Moreover, a direct variance estimation method based on the least-squares estimation is proposed. The finite-sample performance of the spline estimates is evaluated by a Monte Carlo study. The methodology is illustrated with a synovial sarcoma dataset.

AB - We provide a simple and practical, yet flexible spline estimation method for partially linear additive Cox model with monotonicity constraint. We propose to approximate the unknown monotone function by monotone B-splines, and employ a hybrid numerical approach based on the Newton-Raphson algorithm and the isotonic regression to compute the spline estimates. We show that the spline estimators of the nonparametric components achieve the optimal rate of convergence under the smooth condition, and that the estimators of the regression parameters are asymptotically normal and efficient. Moreover, a direct variance estimation method based on the least-squares estimation is proposed. The finite-sample performance of the spline estimates is evaluated by a Monte Carlo study. The methodology is illustrated with a synovial sarcoma dataset.

KW - Additive Cox model

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KW - Isotonic regression

KW - Monotone B-spline

KW - Partial likelihood

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