Detecting trends in noisy data series: application to biomarker series

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.