Hierarchical Changepoint Models for Biochemical Markers Illustrated by Tracking Postradiotherapy Prostate-Specific Antigen Series in Men With Prostate Cancer

PurposeBiomarkers 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.MethodsWe base our analysis on a population-based cohort of 470 men treated with radiotherapy for prostate cancer; after treatment, the log2PSA concentrations follow a piecewise-linear pattern. We illustrate the flexibility of Bayesian hierarchical changepoint models by estimating the individual and population postradiotherapy log2PSA 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.ResultsPrecise 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.ConclusionsThe 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.