Fitting semiparametric cure models

Survival data with a sizable cure fraction are commonly encountered in some cancer clinical researches and the semiparametric proportional hazards cure model has been recently investigated to analyze such data. However the estimation method of the model requires a special C program. The restrictive assumptions of the model also limit its application in broader settings. We present a new computational method for the cure model in this article. The method combines the computational methods for logistic regression and the Cox proportional hazards models and is easy to implement in many statistical packages. We also show how this method allows a number of useful extensions of the model to relax the restrictive assumptions. An illustrative example with survival times of lymphoma patients is provided.

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

[2]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[3]  J W Denham,et al.  The follicular non-Hodgkin's lymphomas--I. The possibility of cure. , 1996, European journal of cancer.

[4]  D. Cox.  Regression Models and Life-Tables , 1972 .

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

[6]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

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

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

[9]  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 .

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

[11]  P. Grambsch,et al.  Modeling Survival Data: Extending the Cox Model , 2000 .

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

[13]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

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