Biostatistics 3:547-563 (2002)
© 2002 Oxford University Press
The joint modeling of a longitudinal disease progression marker and the failure time process in the presence of cure
Celera Diagnostics, 1401 Harbor Bay Parkway, Alameda, CA 94502, USA ngayee.law{at}celeradiagnostics.com
Department of Biostatistics, University of Michigan, Ann Arbor, 1420 Washington Heights, Ann Arbor, MI 48109, USA
Department of Radiation Oncology, University of Michigan, Ann Arbor, 1500 East Medical Center Dr., Ann Arbor, MI 48109, USA
*To whom correspondence should be addressed
In this paper we present an extension of cure models: to incorporate a longitudinal disease progression marker. The model is motivated by studies of patients with prostate cancer undergoing radiation therapy. The patients are followed until recurrence of the prostate cancer or censoring, with the PSA marker measured intermittently. Some patients are cured by the treatment and are immune from recurrence. A joint-cure model is developed for this type of data, in which the longitudinal marker and the failure time process are modeled jointly, with a fraction of patients assumed to be immune from the endpoint. A hierarchical nonlinear mixed-effects model is assumed for the marker and a time-dependent Cox proportional hazards model is used to model the time to endpoint. The probability of cure is modeled by a logistic link. The parameters are estimated using a Monte Carlo EM algorithm. Importance sampling with an adaptively chosen t-distribution and variable Monte Carlo sample size is used. We apply the method to data from prostate cancer and perform a simulation study. We show that by incorporating the longitudinal disease progression marker into the cure model, we obtain parameter estimates with better statistical properties. The classification of the censored patients into the cure group and the susceptible group based on the estimated conditional recurrence probability from the joint-cure model has a higher sensitivity and specificity, and a lower misclassification probability compared with the standard cure model. The addition of the longitudinal data has the effect of reducing the impact of the identifiability problems in a standard cure model and can help overcome biases due to informative censoring.
Keywords: Cure models; Longitudinal models; Monte Carlo EM; Prostate cancer; Prostate specific antigen; Survival analysis
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