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Table 1 Illustrative examples of comparison of CubeX with PHASE [16] and MIDAS [7] (Hill EM).

From: Cubic exact solutions for the estimation of pairwise haplotype frequencies: implications for linkage disequilibrium analyses and a web tool 'CubeX'

    Haplotype frequencies (rounded to 5 decimal places) Haplotype numbers (rounded to nearest haplotype)
Example SNP pair Haplotype REAL frequency PHASE frequency MIDAS frequency CUBEX alpha CUBEX beta CUBEX gamma REAL number PHASE number MIDAS number CUBEX alpha CUBEX beta CUBEX gamma
1 Pair1_2 AC 0.0875 0.08689 0.0875 na 0.0875 na 14 14 14 na 14 na
  Pair1_2 AT 0.725 0.72561 0.725 na 0.725 na 116 116 116 na 116 na
  Pair1_2 TC 0 0.00061 0 na 0 na 0 0 0 na 0 na
  Pair1_2 TT 0.1875 0.18689 0.1875 na 0.1875 na 30 30 30 na 30 na
2 Pair1_5 AG 0.75 0.75318 0.75478 0.75478 na 0.75 120 121 * 121 * 121 * na 120
  Pair1_5 AA 0.0625 0.05932 0.05772 0.05772 na 0.0625 10 9 * 9 * 9 * na 10
  Pair1_5 TG 0.1875 0.18432 0.18272 0.18272 na 0.1875 30 29 * 29 * 29 * na 30
  Pair1_5 TA 0 0.00318 0.00478 0.00478 na 0 0 1 * 1 * 1 * na 0
3 Pair1_9 AT 0.05625 0.06477 0.05633 na 0.0563 0.075 9 10 * 9 na 9 12 *
  Pair1_9 AC 0.75625 0.74773 0.75617 na 0.7562 0.7375 121 120 * 121 na 121 118 *
  Pair1_9 TT 0.01875 0.01023 0.01867 na 0.0187 0 3 2 * 3 na 3 0 *
  Pair1_9 TC 0.16875 0.17727 0.16883 na 0.1688 0.1875 27 28 * 27 na 27 30 *
4 Pair2_3 CG 0.05625 0.04724 0.0465 0.0465 na na 9 8 * 7 * 7 * na na
  Pair2_3 CT 0.03125 0.04026 0.041 0.041 na na 5 6 * 7 * 7 * na na
  Pair2_3 TG 0.48125 0.49026 0.491 0.491 na na 77 78 * 79 * 79 * na na
  Pair2_3 TT 0.43125 0.42224 0.4215 0.4215 na na 69 68 * 67 * 67 * na na
5 pair5_9 GT 0.075 0.07313 0.06664 na 0.0666 0.075 12 12 11 * na 11 * 12
  pair5_9 GC 0.8625 0.86437 0.87086 na 0.8709 0.8625 138 138 139 * na 139 * 138
  pair5_9 AT 0 0.00187 0.00836 na 0.0084 0 0 0 1 * na 1 * 0
  pair5_9 AC 0.0625 0.06063 0.05414 na 0.0541 0.0625 10 10 9 * na 9 * 10
  1. A selection of comparisons using direct haplotyped APOE data [25]. Full data are present as a additional table. For haplotype numbers (rounded to the nearest number) incorrect answers are marked '*', correct answers are unmarked. Examples: (1) Phase, MIDAS and CubeX (1 solution) give correct answer. (2) Only CubeX gives the correct answer as one of its two solutions. (3) MIDAS and CubeX give the correct answer, PHASE and the other CubeX solution are wrong. (4) All three approaches are wrong. (5) PHASE and CubeX give the correct answer, MIDAS and the other CubeX solution are wrong.