Hierarchical Changepoint Models for Biochemical Markers Illustratedby Tracking Postradiotherapy Prostate-Specific Antigen Series inMen With Prostate C

PURPOSE: Biomarkers provide valuable information when detecting disease onset or monitoring diseaseprogression; examples include bone mineral density (for osteoporosis), cholesterol (for coronary artery dis-eases), or prostate-specific antigens (PSA, for prostate cancer). Characteristics of markers series can then beused as prognostic factors of disease progression, such as the postradiotherapy PSA doubling time in mentreated for prostate cancer. The statistical analysis of such data has to incorporate the within and be-tween-series variabilities, the complex patterns of the series over time, the unbalanced format of thedata, and the possibly nonconstant precision of the measurements.

METHODS: We base our analysis on a population-based cohort of 470 men treated with radiotherapy forprostate cancer; after treatment, the log2PSA concentrations follow a piecewise-linear pattern. We illus-trate the flexibility of Bayesian hierarchical changepoint models by estimating the individual and popula-tion postradiotherapy log2PSA profiles; parameters such as the PSA nadir and the PSA doubling time wereestimated, and their associations with baseline patient characteristics were investigated. The residual PSA variability was modeled as a function of the prostate-specific antigen 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 individualand population levels. Estimates suggest greater PSA variability at lower PSA concentrations, as well as anassociation between shorter PSAdts and greater baseline PSA levels, higher Gleason scores, and older age.

CONCLUSIONS: The use of Bayesian hierarchical changepoint models accommodates multiple com-plex features of longitudinal data, permits realistic modeling of the variability as a function of the markerconcentration, 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.