Maximum Likelihood Estimation in a Semiparametric Logistic/Proportional‐Hazards Mixture Model

We consider large sample inference in a semiparametric logistic/proportional-hazards mixture model. This model has been proposed to model survival data where there exists a positive portion of subjects in the population who are not susceptible to the event under consideration. Previous studies of the logistic/proportional-hazards mixture model have focused on developing point estimation procedures for the unknown parameters. This paper studies large sample inferences based on the semiparametric maximum likelihood estimator. Specifically, we establish existence, consistency and asymptotic normality results for the semiparametric maximum likelihood estimator. We also derive consistent variance estimates for both the parametric and non-parametric components. The results provide a theoretical foundation for making large sample inference under the logistic/proportional-hazards mixture model. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..

[1]  M. E. Ghitany,et al.  Exponential mixture models with long-term survivors and covariates , 1994 .

[2]  K. Dear,et al.  A Nonparametric Mixture Model for Cure Rate Estimation , 2000, Biometrics.

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

[4]  F. Scholz.  Maximum Likelihood Estimation , 2006 .

[5]  J W Denham,et al.  A generalized F mixture model for cure rate estimation. , 1998, Statistics in medicine.

[6]  K. Yamaguchi.  Accelerated Failure-Time Regression Models with a Regression Model of Surviving Fraction: An Application to the Analysis of “Permanent Employment” in Japan , 1992 .

[7]  J. P. Sy,et al.  Estimation in a Cox Proportional Hazards Cure Model , 2000, Biometrics.

[8]  Y Lo,et al.  The effect of fractionated doses of radiation on mouse spinal cord. , 1993, International journal of radiation oncology, biology, physics.

[9]  Richard D. Gill,et al.  A counting process approach to maximum likelihood estimation in frailty models , 1992 .

[10]  Susan A. Murphy,et al.  Maximum Likelihood Estimation in the Proportional Odds Model , 1997 .

[11]  V. Farewell,et al.  The use of mixture models for the analysis of survival data with long-term survivors. , 1982, Biometrics.

[12]  H. Sather,et al.  A comparison of tests of the difference in the proportion of patients who are cured. , 1992, Biometrics.

[13]  Gregg E. Dinse,et al.  A mixture model for the regression analysis of competing risks data , 1985 .

[14]  Jonathan J. Shuster,et al.  Parametric versus non-parametric methods for estimating cure rates based on censored survival data , 1992 .

[15]  Byron J. T. Morgan,et al.  A mixture model for interval-censored time-to-response quantal assay data , 1990 .

[16]  J M Taylor,et al.  Semi-parametric estimation in failure time mixture models. , 1995, Biometrics.

[17]  Anthony Y. C. Kuk,et al.  A mixture model combining logistic regression with proportional hazards regression , 1992 .

[18]  Vernon T. Farewell,et al.  Mixture models in survival analysis: Are they worth the risk? , 1986 .

[19]  Ross Maller,et al.  Estimating the proportion of immunes in a censored sample , 1992 .

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

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