Bayesian Approaches to Joint Cure‐Rate and Longitudinal Models with Applications to Cancer Vaccine Trials

Complex issues arise when investigating the association between longitudinal immunologic measures and time to an event, such as time to relapse, in cancer vaccine trials. Unlike many clinical trials, we may encounter patients who are cured and no longer susceptible to the time-to-event endpoint. If there are cured patients in the population, there is a plateau in the survival function, S(t), after sufficient follow-up. If we want to determine the association between the longitudinal measure and the time-to-event in the presence of cure, existing methods for jointly modeling longitudinal and survival data would be inappropriate, since they do not account for the plateau in the survival function. The nature of the longitudinal data in cancer vaccine trials is also unique, as many patients may not exhibit an immune response to vaccination at varying time points throughout the trial. We present a new joint model for longitudinal and survival data that accounts both for the possibility that a subject is cured and for the unique nature of the longitudinal data. An example is presented from a cancer vaccine clinical trial.

[1]  Victor DeGruttola,et al.  Modeling The Relationship Between Progression Of CD4-Lymphocyte Count And Survival Time , 1992 .

[2]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[3]  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 .

[4]  Joel B. Greenhouse,et al.  A competing risks derivation of a mixture model for the analysis of survival data , 1984 .

[5]  M. Wulfsohn,et al.  A joint model for survival and longitudinal data measured with error. , 1997, Biometrics.

[6]  Jeremy M G Taylor,et al.  The joint modeling of a longitudinal disease progression marker and the failure time process in the presence of cure. , 2002, Biostatistics.

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

[8]  D. Thomas,et al.  Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach. , 1996, Statistics in medicine.

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

[10]  A. Kuk,et al.  A SEMIPARAMETRIC MIXTURE MODEL FOR THE ANALYSIS OF COMPETING RISKS DATA , 1992 .

[11]  V. De Gruttola,et al.  Modelling progression of CD4-lymphocyte count and its relationship to survival time. , 1994, Biometrics.

[12]  Yan Wang,et al.  Jointly Modeling Longitudinal and Event Time Data With Application to Acquired Immunodeficiency Syndrome , 2001 .

[13]  Joseph G. Ibrahim,et al.  A New Bayesian Model For Survival Data With a Surviving Fraction , 1999 .

[14]  J G Ibrahim,et al.  Maximum Likelihood Methods for Cure Rate Models with Missing Covariates , 2001, Biometrics.

[15]  S L Zeger,et al.  The Evaluation of Multiple Surrogate Endpoints , 2001, Biometrics.

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

[17]  M. Wulfsohn,et al.  Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS , 1995 .

[18]  Joseph G. Ibrahim,et al.  Monte Carlo Methods in Bayesian Computation , 2000 .

[19]  V. Sondak,et al.  High-dose interferon alfa-2b significantly prolongs relapse-free and overall survival compared with the GM2-KLH/QS-21 vaccine in patients with resected stage IIB-III melanoma: results of intergroup trial E1694/S9512/C509801. , 2001, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

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

[21]  A I Goldman,et al.  Survivorship analysis when cure is a possibility: a Monte Carlo study. , 1984, Statistics in medicine.