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It is common to define a change in health status or in a disease state on the basis of a sustained rise (or decline) in a biomarker over time. However, such observations are often subject to important variability unrelated to the underlying biologic process. The authors propose a method to evaluate rules that define an event on the basis of consecutive increases (or decreases) in the observations, given the presence of random variation. They examine how well these rules correctly identify a truly rising biomarker trajectory and, conversely, how often they can recognize a truly stable series or a slowly rising series. The method relies on simulation of realistic, sophisticated data sets that accurately reflect the systematic and random variations observed in marker series. These flexible, empirically based simulations enable estimation of the sensitivity and specificity of rules of consecutive rises as a function of the underlying trend, amount of random variation, and schedule of measurements (frequency and duration of follow-up). The authors illustrate the approach with postradiotherapy series of prostate-specific antigen, where three consecutive rises in prostate-specific antigen indicate treatment failure; the data are described by using a Bayesian hierarchical changepoint model. The method is particularly flexible and could be applied to evaluate other rules that purport to accurately detect upturns (downturns) in other noisy data series, including other medical data or other application areas.

Purpose: Biomarkers provide valuable information when detecting disease onset or monitoring disease progression; examples include bone mineral density (for osteoporosis), cholesterol (for coronary artery diseases), or prostate-specific antigens (PSA, for prostate cancer). Characteristics of markers series can then be used as prognostic factors of disease progression, such as the postradiotherapy PSA doubling time in men treated for prostate cancer. The statistical analysis of such data has to incorporate the within and between-series variabilities, the complex patterns of the series over time, the unbalanced format of the data, and the possibly nonconstant precision of the measurements., Methods: We base our analysis on a population-based cohort of 470 men treated with radiotherapy for prostate cancer; after treatment, the log(2)PSA concentrations follow a piecewise-linear pattern. We illustrate the flexibility of Bayesian hierarchical changepoint models by estimating the individual and population postradiotherapy log(2)PSA profiles; parameters such as the PSA nadir and the PSA doubling time were estimated, and their associations with baseline patient characteristics were investigated. The residual PSA variability was modeled as a function of the PSA concentration. For comparison purposes, two alternative models were briefly considered., Results: Precise estimates of all parameters of the PSA trajectory are provided at both the individual and population levels. Estimates suggest greater PSA variability at lower PSA concentrations, as well as an association between shorter PSAdts and greater baseline PSA levels, higher Gleason scores, and older age., Conclusions: The use of Bayesian hierarchical changepoint models accommodates multiple complex features of longitudinal data, permits realistic modeling of the variability as a function of the marker concentration, and provides precise estimates of all clinically important parameters. This type of model should be applicable to the study of marker series in other diseases.

Context: The appropriate therapy for men with localized prostate cancer is uncertain. Until results of clinical trials are available, men and their physicians need guidance., Objective: To estimate survival based on a competing risk analysis stratified by age at diagnosis and histologic findings for men diagnosed as having clinically localized prostate cancer and who were managed conservatively., Design: Retrospective cohort study., Setting: Connecticut Tumor Registry., Patients: A total of 767 men with localized prostate cancer diagnosed between 1971 and 1984, aged 55 to 74 years at diagnosis, either not treated or treated with immediate or delayed hormonal therapy, and followed up for 10 to 20 years after diagnosis., Main Outcome Measures: Estimates of the probability of dying from prostate cancer or other competing hazards., Results: Men with tumors that have Gleason scores of 2 to 4, 5, 6, 7, and 8 to 10 face a 4% to 7%, 6% to 11%, 18% to 30%, 42% to 70%, and 60% to 87% chance, respectively, of dying from prostate cancer within 15 years of diagnosis depending on their age at diagnosis., Conclusions: Men whose prostate biopsy specimens show Gleason score 2 to 4 disease face a minimal risk of death from prostate cancer within 15 years of diagnosis. Conversely, men whose biopsy specimens show Gleason score 7 to 10 disease face a high risk of death from prostate cancer when treated conservatively, even when cancer is diagnosed as late as age 74 years. Men with Gleason score 5 or 6 tumors face a modest risk of death from prostate cancer that increases slowly over at least 15 years of follow-up.