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Table 3 Classification rules

From: A data review and re-assessment of ovarian cancer serum proteomic profiling

Classification Rule 1 based on the intensities at the 7 M/Z values:
Let
a1 = (1303,5.66302,5.48787.19.60743,-8.88828,-30.47983,-0.34510)',
a2 = (1413,6.44028,6.36701,20.84677,-11.04580,-32.04436,0.03553)',
c1 = -2984,
c2 = -3521.
Let X be the vector that represents the intensities from a subject at the 7 M/Z values:
2.7921478, 245.53704, 261.8864, 418.1136, 435.0751, 464.3617, 4003.645. Classify X into the cancer group if
(a1 - a2)' X + (c1 - c2) ≥ 0;
Otherwise classify X into the control group.
Classification Rule 2 based on the intensities at the 13 M/Z values:
Let
a1 = (24.58884,-15.09887,0.95772,-3.16411,-10.93854,31.7966,8.11259,6.59602,-53.15727, -7.49888,149.18784,399.67258,112.83481)',
a2 = (26.26343,-19.06632,1.07975,-1.89482,-9.83188,29.47779,7.69470,8.54597,-49.99409, -7.32192,142.08982,389.53254,116.55493)',
c1 = -1386,
c2 = -1312.
Let X be the vector that represents the intensities from a subject at the following 13 M/Z values: 2665.397, 3969.469, 3991.844, 4003.645, 4027.3, 4056.967, 4744.889, 6801.495, 7756.437, 8349.266, 14796.14, 15955.47, 17034.05.
Classify X into cancer if
(a1 - a2)' X + (c1 -c2) ≥ 0.
Otherwise classify X into control.
Classification rule #3 based on 7 M/Z values:
Let
a1 = (6.04377,3.42186,-1.99804,0.23374,2.46593,-1.87559,17.37384)',
a2 = (7.35920,1.86527,-1.32486,0.92386, 1.18336,4.76619,9.95349)',
c1 = -218.19592,
c2 = -254.33039.
Let X be the column vector that represents the intensities from a subject at the following 7 M/Z values:
418.1136, 435.0751, 464.3617,4003.645, 4906.962, 6599.823, 6801.495.
Classify X into cancer if
(a1 - a2)' X + (c1 - c2) ≥ 0.
Otherwise classify X into control.