Joint Parametric Modeling and Estimation of Time to Cancer Recurrence and Disease Stage at Recurrence.

Abstract

A clinical trial with bladder cancer patients who went through surgery and were followed up for tumor recurrence was used as motivation for this research. The surgery was conducted on patients with an early bladder cancer stage. During the follow-up, patients were evaluated for cancer recurrence at 3 months, 6 months, 9 months, and at about 5 year visits unless they had cancer recurrence in between visits or died prior to a scheduled visit. One of the main objectives of the study was to evaluate the time to cancer recurrence. At the time of cancer recurrence, the disease stage was also evaluated. The stage of the cancer at recurrence significantly impacts future treatment and quality of life. Therefore, modeling and analyzing the time to cancer recurrence and the stage at recurrence jointly makes more sense than an analysis based on the time to recurrence alone.

In our research, we describe a model for the joint distribution of time to recurrence and cancer stage at recurrence that accounts for the recurrence caused by the cancer cells surviving treatment or surgery, and for the recurrence caused by spontaneous carcinogenesis. First, we proceeded with a continuous follow-up assumption using stochastic models of cancer recurrence. Then we extend the approach to allow for a discrete follow-up process. We provide methods for full maximum likelihood estimation based on the EM algorithm. The methods are illustrated through modeling and estimation of data from a clinical trial in patients with bladder cancer described above. Simulations are used to assess the sensitivity of the methods. An added benefit of such modeling is that it permits using the cancer stage at recurrence to provide adjusted estimates for the time to recurrence distribution and allows for more powerful inference.