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. 2018 Oct 26;21(3):417–431. doi: 10.1093/biostatistics/kxy058

Table 1.

Efficiency of two- and three-stage algorithms with Inline graphic and Inline graphic for testing all pools (regardless of size) and individuals. H2 and H3 (hierarchical) algorithms are from Tebbs and others (2013) and Hou and others (2017), respectively. Pool sizes are chosen to minimize the expected number of tests per individual. The maximum allowable array size for ATM is Inline graphic. For Cases 1–4, the marginal disease probabilities Inline graphic and Inline graphic are equal. For Cases 5–8, the marginal disease probabilities are unequal

    Stages Algorithm Efficiency     Stages Algorithm Efficiency
      Inline graphic 0.594       Inline graphic 0.591
Case 1 Inline graphic
Inline graphic
Inline graphic
Inline graphic
2 Inline graphic 0.530 Case 5 Inline graphic
Inline graphic
Inline graphic
Inline graphic
2 Inline graphic 0.537
3 Inline graphic 0.572 3 Inline graphic 0.564
Inline graphic 0.543 Inline graphic 0.544
    2 Inline graphic 0.433       Inline graphic 0.431
Case 2 Inline graphic
Inline graphic
Inline graphic
Inline graphic
  Inline graphic 0.344 Case 6 Inline graphic
Inline graphic
Inline graphic
Inline graphic
2 Inline graphic 0.352
3 Inline graphic 0.371 3 Inline graphic 0.368
Inline graphic 0.354 Inline graphic 0.356
      Inline graphic 0.345       Inline graphic 0.342
Case 3 Inline graphic
Inline graphic
Inline graphic
Inline graphic
2 Inline graphic 0.258 Case 7 Inline graphic
Inline graphic
Inline graphic
Inline graphic
2 Inline graphic 0.260
3 Inline graphic 0.273 3 Inline graphic 0.268
Inline graphic 0.282 Inline graphic 0.279
      Inline graphic 0.209       Inline graphic 0.208
Case 4 Inline graphic
Inline graphic
Inline graphic
Inline graphic
2 Inline graphic 0.123 Case 8 Inline graphic
Inline graphic
Inline graphic
Inline graphic
2 Inline graphic 0.128
3 Inline graphic 0.135 3 Inline graphic 0.134
Inline graphic 0.150 Inline graphic 0.150