EFFICIENT ESTIMATION FOR THE PROPORTIONAL HAZARDS MODEL WITH LEFT-TRUNCATED AND "CASE 1" INTERVAL-CENSORED DATA

The maximum likelihood estimator (MLE) for the proportional hazards model with left-truncated and "Case 1" interval-censored data is studied. Under appropriate regularity conditions,the MLE of the regression parameter is shown to be asymptotically normal with a root-n convergence rate and achieves the informa- tion bound,even though the difference between left-truncation time and censoring time of the MLE of the baseline cumulative hazard function converges only at rate n 1/3 . Two methods to estimate the variance-covariance matrix of the MLE of the regression parameter are considered. One is based on a generalized missing in- formation principle and the other is based on the profile information procedure. Simulation studies show that both methods work well in terms of bias and variance for samples of moderate sizes. An example is provided to illustrate the methods.

[1]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[2]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[3]  W. Wong,et al.  On Maximum Likelihood Estimation in Infinite-Dimensional Parameter Spaces , 1991 .

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

[5]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

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

[7]  Jian Huang,et al.  Efficient estimation for the proportional hazards model with interval censoring , 1996 .

[8]  Jon E. Hyde,et al.  Testing survival under right censoring and left truncation , 1977 .

[9]  Nicholas P. Jewell,et al.  A note on the product-limit estimator under right censoring and left truncation , 1987 .

[10]  D. Finkelstein,et al.  A proportional hazards model for interval-censored failure time data. , 1986, Biometrics.

[11]  李幼升,et al.  Ph , 1989 .

[12]  S A Murphy,et al.  Observed Information in Semiparametric Models , 2022 .

[13]  J. Klein,et al.  Survival Analysis: Techniques for Censored and Truncated Data , 1997 .

[14]  P. Massart,et al.  Rates of convergence for minimum contrast estimators , 1993 .

[15]  D G Hoel,et al.  Statistical analysis of survival experiments. , 1972, Journal of the National Cancer Institute.

[16]  S W Lagakos,et al.  Analyzing doubly censored data with covariates, with application to AIDS. , 1993, Biometrics.

[17]  D. Q. Lamb.  STATISTICAL MODELS BASED ON THE FERMI MODEL. , 1970 .

[18]  A Alioum,et al.  A proportional hazards model for arbitrarily censored and truncated data. , 1996, Biometrics.

[19]  Susan A. Murphy,et al.  Observed information in semi-parametric models , 1999 .

[20]  Aad Van Der Vbart,et al.  ON DIFFERENTIABLE FUNCTIONALS , 1988 .

[21]  S. Geer.  Hellinger-Consistency of Certain Nonparametric Maximum Likelihood Estimators , 1993 .

[22]  M. Birman,et al.  PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES $ W_{p}^{\alpha}$ , 1967 .

[23]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[24]  A. V. D. Vaart,et al.  On Differentiable Functionals , 1991 .

[25]  B. Turnbull.  The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[26]  Jian Huang,et al.  Interval Censored Survival Data: A Review of Recent Progress , 1997 .