Predicting time to prostate cancer recurrence based on joint models for non‐linear longitudinal biomarkers and event time outcomes

Abstract

Biological markers that are both sensitive and specific for tumour regrowth or metastasis are increasingly becoming available and routinely monitored during the regular follow-up of patients treated for cancer. Obtained by a simple blood test, these markers provide an inexpensive non-invasive means for the early detection of recurrence (or progression). Currently, the longitudinal behaviour of the marker is viewed as an indicator of early disease progression, and is applied by a physician in making clinical decisions. One marker that has been studied for use in both population screening for early disease and for detection of recurrence in prostate cancer patients is PSA. The elevation of PSA levels is known to precede clinically detectable recurrence by 2 to 5 years, and current clinical practice often relies partially on multiple recent rises in PSA to trigger a change in treatment. However, the longitudinal trajectory for individual markers is often non-linear; in many cases there is a decline immediately following radiation therapy or surgery, a plateau during remission, followed by an exponential rise following the recurrence of the cancer. The aim of this article is to determine the multiple aspects of the longitudinal PSA biomarker trajectory that can be most sensitive for predicting time to clinical recurrence. Joint Bayesian models for the longitudinal measures and event times are utilized based on non-linear hierarchical models, implied by unknown change-points, for the longitudinal trajectories, and a Cox proportional hazard model for progression times, with functionals of the longitudinal parameters as covariates in the Cox model. Using Markov chain Monte Carlo sampling schemes, the joint model is fit to longitudinal PSA measures from 676 patients treated at Massachusetts General Hospital between the years 1988 and 1995 with follow-up to 1999. Based on these data, predictive schemes for detecting cancer recurrence in new patients based on their longitudinal trajectory are derived.

Estimating nonlinear regression with and without change-points by the LAD method

“…We give the convergence rate and the limiting distribution of the LAD estimator under the condition that the number of change-points is known. A concrete example of application of this type of model can be found in Pauler and Finkelstein (2002) on the recurrence in prostate cancer.…”

Bayesian statistics in medicine: a 25 year review

“…An observational study modelled survival and pulmonary function in cystic fibrosis allowing for non-ignorable non-response using Empirical Bayes [513]. Joint modelling of non-linear longitudinal biomarkers and event time outcomes were used to predict cancer recurrence in prostate cancer from PSA levels [514]. Modelling of bovine abortion and foetal survival used mixture modelling allowing for herd effects and incompletely observed data [515].…”

Dynamic optimal strategy for monitoring disease recurrence

“…For example, Prostate Specific Antigen (PSA) values are used to monitor for recurrence of prostate cancer and changes in Standard Uptake Value (SUV) measurements obtained by Positron Emission Tomography (PET) are known to precede clinically detectable and symptomatic recurrence in several cancers. The availability of longitudinal observations of biomarker values has led to increasing recognition that the longitudinal trajectory of the biomarker may provide important additional information beyond the biomarker's current value ([11], [12], [13], [14]). As noted in recent studies, the trajectory describes biomarker behavior and risk factors over time and is influenced by characteristics of patients and disease, such as age, gender, tumor size, and tumor stage.…”