The Screening Paradox and Dynamic Systems

In this chapter, we explore the screening paradox that arises following the analysis of a dynamic SIR (susceptible-infected-recovered) system for conditions whose prevalence vary over time. More explicitly, if a disease process is screened for and subsequently treated, its prevalence would drop in the population, which as per Bayes’ theorem, would make the tests’ predictive value drop in return. Put another way, a very powerful screening test would, by performing and succeeding at the very task it was developed to do, paradoxically reduce its ability to correctly identify individuals with the disease it screens for in the future—over some finite time t. We use the prevalence threshold to establish the point at which the dynamic system is most stable, providing different scenarios as a function of the initial prevalence and its fluctuations over time. Finally, we introduce Markov chains and the Markov Chain transition matrix as applied in clinical diagnostic settings.