Figure 2.

Top panel: Individual biomarker densities for 𝒞̃⁻ ~ 𝒩(3, 0.25) and 𝒞̃⁺ ~ 𝒩(6, 1). Under our measurement error density assumption, 𝒞|𝒞̃ ~ 𝒩(𝒞̃, 0.0025), the threshold τ^* = 4.11 maximizes Youden’s index for individual testing. Middle and bottom panels: Densities of the pooled biomarker measurements, $f_{{\mathcal{C}}_{{\mathcal{P}}_{sl}}}(u)={\int }_{-\infty }^{\infty }{f}_{\epsilon }(u\mid v)n_s{f}_{{\sum }_{i\in {\mathcal{P}}_{sl}}{\stackrel{\sim }{\mathcal{C}}}_i}^{m(n_s-m)}(n_{s}v)dv$, for different m (the number of positive individuals in ℘_sl) when the pool size is n_s = 5 and n_s = 10.