A SAS macro for parametric and semiparametric mixture cure models

Cure models have been developed to analyze failure time data with a cured fraction. For such data, standard survival models are usually not appropriate because they do not account for the possibility of cure. Mixture cure models assume that the studied population is a mixture of susceptible individuals, who may experience the event of interest, and non-susceptible individuals that will never experience it. The aim of this paper is to propose a SAS macro to estimate parametric and semiparametric mixture cure models with covariates. The cure fraction can be modelled by various binary regression models. Parametric and semiparametric models can be used to model the survival of uncured individuals. The maximization of the likelihood function is performed using SAS PROC NLMIXED for parametric models and through an EM algorithm for the Cox's proportional hazards mixture cure model. Indications and limitations of the proposed macro are discussed and an example in the field of cancer clinical trials is shown.

[1]  D. Y. Fong,et al.  Estimating the proportion of cured patients in a censored sample , 2005, Statistics in medicine.

[2]  K Borch-Johnsen,et al.  Heterogeneity models of disease susceptibility, with application to diabetic nephropathy. , 1994, Biometrics.

[3]  J Carpenter,et al.  Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians. , 2000, Statistics in medicine.

[4]  J G Ibrahim,et al.  Bayesian Semiparametric Models for Survival Data with a Cure Fraction , 2001, Biometrics.

[5]  D. A. Sprott,et al.  The use of a mixture model in the analysis of count data. , 1988, Biometrics.

[6]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

[7]  R. Maller,et al.  Survival Analysis with Long-Term Survivors , 1996 .

[8]  J. Lewins Contribution to the Discussion , 1989 .

[9]  Eric J. Feuer,et al.  Parametric cure models of relative and cause-specific survival for grouped survival times , 2000, Comput. Methods Programs Biomed..

[10]  J. Suchorzewska Głos w dyskusji , 2005 .

[11]  K K Yau,et al.  Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma. , 2001, Statistics in medicine.

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

[13]  J. Kirkwood,et al.  Interferon alfa-2b adjuvant therapy of high-risk resected cutaneous melanoma: the Eastern Cooperative Oncology Group Trial EST 1684. , 1996, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[14]  S R Cole Simple bootstrap statistical inference using the SAS system. , 1999, Computer methods and programs in biomedicine.

[15]  Ram C Tiwari,et al.  Cure fraction estimation from the mixture cure models for grouped survival data , 2004, Statistics in medicine.

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

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

[18]  Jianguo Sun,et al.  Maximum Likelihood Estimation in a Semiparametric Logistic/Proportional‐Hazards Mixture Model , 2005 .

[19]  B. Efron,et al.  Bootstrap confidence intervals , 1996 .

[20]  Debashis Kushary,et al.  Bootstrap Methods and Their Application , 2000, Technometrics.

[21]  Odd O. Aalen,et al.  Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution , 1992 .

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

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

[24]  Chin-Shang Li,et al.  Identifiability of cure models , 2001 .

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

[26]  O. Aalen,et al.  Heterogeneity in survival analysis. , 1988, Statistics in medicine.

[27]  Yingwei Peng,et al.  Estimating baseline distribution in proportional hazards cure models , 2003, Comput. Stat. Data Anal..