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Prevalence threshold (ϕe) and the geometry of screening curves

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  • Jacques Balayla

Abstract

The relationship between a screening tests’ positive predictive value, ρ, and its target prevalence, ϕ, is proportional—though not linear in all but a special case. In consequence, there is a point of local extrema of curvature defined only as a function of the sensitivity a and specificity b beyond which the rate of change of a test’s ρ drops precipitously relative to ϕ. Herein, we show the mathematical model exploring this phenomenon and define the prevalence threshold (ϕe) point where this change occurs as:ϕ e = a ( - b + 1 ) + b - 1 ( ε - 1 )where ε = a + b. From the prevalence threshold we deduce a more generalized relationship between prevalence and positive predictive value as a function of ε, which represents a fundamental theorem of screening, herein defined as:lim ε → 2 ∫ 0 1 ρ ( ϕ ) d ϕ = 1Understanding the concepts described in this work can help contextualize the validity of screening tests in real time, and help guide the interpretation of different clinical scenarios in which screening is undertaken.

Suggested Citation

  • Jacques Balayla, 2020. "Prevalence threshold (ϕe) and the geometry of screening curves," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-12, October.
    • Handle: RePEc:plo:pone00:0240215
    DOI: 10.1371/journal.pone.0240215
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