With rapid improvements in medical treatment and health care, many datasets dealing with time to relapse or death now reveal a substantial portion of patients who are cured (i.e., who never experience the event). Extended survival models called cure rate models account for the probability of a subject being cured and can be broadly classified into the classical mixture models of Berkson and Gage (BG type) or the stochastic tumor models pioneered by Yakovlev and extended to a hierarchical framework by Chen, Ibrahim, and Sinha (YCIS type). Recent developments in Bayesian hierarchical cure models have evoked significant interest regarding relationships and preferences between these two classes of models. Our present work proposes a unifying class of cure rate models that facilitates flexible hierarchical model-building while including both existing cure model classes as special cases. This unifying class enables robust modeling by accounting for uncertainty in underlying mechanisms leading to cure. Issues such as regressing on the cure fraction and propriety of the associated posterior distributions under different modeling assumptions are also discussed. Finally, we offer a simulation study and also illustrate with two datasets (on melanoma and breast cancer) that reveal our framework's ability to distinguish among underlying mechanisms that lead to relapse and cure.
Bibliographical noteFunding Information:
Freda Cooner is Mathematical Statistician in Division of Biostatistics, Office of Surveillance and Biometrics, Center for Devices and Radiological Health, Food and Drug Administration. Sudipto Banerjee is Assistant Professor of Biostatistics (E-mail: firstname.lastname@example.org), and Bradley P. Carlin is Professor of Biostatistics and Mayo Professor in Public Health, Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455. Debajyoti Sinha is Professor, Department of Biostatistics and Bioinfor-matics, Medical University of South Carolina, Charleston, SC 29425. The work of the first three authors was supported in part by National Institutes of Health grants 1-R01-CA95955 and 1-R01-CA112444. The work of Dr. Sinha was supported by National Cancer Institute grant 9-R01-CA69222. The authors thank the joint editor, associate editor, and three referees for several suggestions, and also Minghui Chen, University of Connecticut, for useful discussions.
- Bayesian hierarchical model
- Cure fraction
- Cure rate model
- Latent activation scheme
- Markov chain Monte Carlo algorithm
- Moment-generating functions
- Survival analysis