Nonparametric k-sample tests with panel count data

We study the nonparametric k-sample test problem with panel count data. The asymptotic normality of a smooth functional of the nonparametric maximum pseudo-likelihood estimator (Wellner & Zhang, 2000) is established under some mild conditions. We construct a class of easy-to-implement nonparametric tests for comparing mean functions of k populations based on this asymptotic normality. We conduct various simulations to validate and compare the tests. The simulations show that the tests perform quite well and generally have good power to detect differences among the mean functions. The method is illustrated with a real-life example. Copyright 2006, Oxford University Press.

[1]  J. Wellner,et al.  Information Bounds and Nonparametric Maximum Likelihood Estimation , 1992 .

[2]  Jian Huang,et al.  Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1 , 1995 .

[3]  P F Thall,et al.  Mixed Poisson likelihood regression models for longitudinal interval count data. , 1988, Biometrics.

[4]  Jon A. Wellner,et al.  TWO LIKELIHOOD-BASED SEMIPARAMETRIC ESTIMATION METHODS FOR PANEL COUNT DATA WITH COVARIATES , 2005, math/0509132.

[5]  Jian Huang,et al.  Efficient Estimation for the Cox Model with Interval Censoring Efficient Estimation for the Cox Model with Interval Censoring , 1994 .

[6]  Jianwen Cai,et al.  Some Graphical Displays and Marginal Regression Analyses for Recurrent Failure Times and Time Dependent Covariates , 1993 .

[7]  J. Kalbfleisch,et al.  The Analysis of Panel Data under a Markov Assumption , 1985 .

[8]  Jianguo Sun,et al.  A nonparametric test for panel count data , 2003 .

[9]  W. Liu,et al.  A nonparametric two‐sample test of the failure function with interval censoring case 2 , 2001 .

[10]  R J Cook,et al.  Robust tests for treatment comparisons based on recurrent event responses. , 1996, Biometrics.

[11]  D. Byar,et al.  Comparisons of placebo, pyridoxine, and topical thiotepa in preventing recurrence of stage I bladder cancer. , 1977, Urology.

[12]  Eric R. Ziegel,et al.  Data: A Collection of Problems From Many Fields for the Student and Research Worker , 1987 .

[13]  Jon A. Wellner,et al.  Two estimators of the mean of a counting process with panel count data , 2000 .

[14]  Xingwei Tong,et al.  Regression Analysis of Panel Count Data with Dependent Observation Times , 2007, Biometrics.

[15]  A. V. Peterson,et al.  On the regression analysis of multivariate failure time data , 1981 .

[16]  J. Wellner,et al.  A Semiparametric Regression Model for Panel Count Data: When Do Pseudo-likelihood Estimators Become Badly Inefficient? , 2004 .

[17]  Zhiliang Ying,et al.  Semiparametric regression for the mean and rate functions of recurrent events , 2000 .

[18]  Jerald F. Lawless,et al.  Some Simple Robust Methods for the Analysis of Recurrent Events , 1995 .

[19]  Lee-Jen Wei,et al.  Regression analysis of panel count data with covariate‐dependent observation and censoring times , 2000 .

[20]  D P Byar,et al.  The Veterans Administration Study of Chemoprophylaxis for Recurrent Stage I Bladder Tumours: Comparisons of Placebo, Pyridoxine and Topical Thiotepa , 1980 .

[21]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .

[22]  D. Gaver,et al.  Robust empirical bayes analyses of event rates , 1987 .

[23]  Ying Zhang,et al.  A semiparametric pseudolikelihood estimation method for panel count data , 2002 .

[24]  Anton Schick,et al.  Consistency of the GMLE with Mixed Case Interval‐Censored Data , 2000 .

[25]  John M. Lachin,et al.  Analysis of Recurrent Events: Nonparametric Methods for Random-Interval Count Data , 1988 .

[26]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[27]  L. J. Wei,et al.  Regression analysis of multivariate incomplete failure time data by modeling marginal distributions , 1989 .