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Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):705-718; doi:10.1093/biomet/asm057
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Copyright © 2007 Biometrika Trust

Articles

Estimation of the mean function with panel count data using monotone polynomial splines

Minggen Lu and Ying Zhang

Department of Biostatistics, The University of Iowa, 200 Hawkins Drive, C22 GH, Iowa City, Iowa 52242, U.S.A.

Jian Huang

Department of Statistics and Actuarial Science, The University of Iowa, 221 Schaeffer Hall, Iowa City, Iowa 52242, U.S.A.

minggen-lu{at}uiowa.edu

ying-j-zhang{at}uiowa.edu

jian-huang{at}uiowa.edu

Received for publication 1 April 2006. Revision received 1 January 2007.
  Abstract

We study nonparametric likelihood-based estimators of the mean function of counting processes with panel count data using monotone polynomial splines. The generalized Rosen algorithm, proposed by Zhang & Jamshidian (2004), is used to compute the estimators. We show that the proposed spline likelihood-based estimators are consistent and that their rate of convergence can be faster than n1/3. Simulation studies with moderate samples show that the estimators have smaller variances and mean squared errors than their alternatives proposed by Wellner & Zhang (2000). A real example from a bladder tumour clinical trial is used to illustrate this method.

Key Words: Counting process • Empirical process • Isotonic regression • Maximum likelihood estimator • Maximum pseudolikelihood estimator • Monotone polynomial spline • Monte Carlo


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