α1 α2 β1 β2 β3 σ0 σ1
Sample size 20            
true value 5 0 50 30000 1 1 500
naive model 2.3538 (0.0337) 0.0108 (0.0348) 21673.99 (73.67) 8063.19 (72.22) 1.8432 (0.0062) 1.5515 (0.1377) 505.9 (4.52)
integrated model 4.4653 (0.08) -0.0161 (0.0139) -274276.76 (52197.04) 304133.74 (52200.42) 1.2805 (0.011) 0.9099 (0.0111) 457.39 (1.95)
true value 5 -0.1 50 30000 1 1 500
naive model 2.3656 (0.0399) -0.0895 (0.0592) 21700.84 (71.7) 8041.22 (70.25) 1.8401 (0.0059) 1.6134 (0.1588) 504.84 (3.24)
integrated model 4.5686 (0.0859) -0.0693 (0.0418) -330800.61 (56594.51) 360639.78 (56591.54) 1.2918 (0.0288) 0.9732 (0.0742) 458.96 (2)
true value 5 -0.3 50 30000 1 1 500
naive model 2.3695 (0.0275) -0.3577 (0.0482) 21516.03 (74.6) 8221.13 (73.15) 1.8385 (0.0057) 1.5135 (0.1068) 505.61 (3.97)
integrated model 4.403 (0.0769) -0.308 (0.0123) -249677.33 (50408.57) 279512.95 (50405.41) 1.2762 (0.0105) 0.8937 (0.0099) 456.25 (1.72)
true value 5 -0.5 50 30000 1 1 500
naive model 2.4446 (0.0374) -0.7107 (0.0782) 21269.05 (74.86) 8464.35 (73.51) 1.8481 (0.0059) 1.6564 (0.1521) 507.56 (2.77)
integrated model 4.5227 (0.0783) -0.5035 (0.0123) -250395.86 (48590.31) 280258.79 (48592.42) 1.2486 (0.0097) 0.8891 (0.0102) 457.35 (1.82)
true value 5 -1 50 30000 1 1 500
naive model 2.7712 (0.0505) -1.4615 (0.1208) 19902.57 (90.02) 9814.9 (88.76) 1.8388 (0.0058) 2.1685 (0.1959) 527.34 (4.87)
integrated model 4.1187 (0.0636) -1.0024 (0.0148) -52274.05 (21283.7) 82100.65 (21281.33) 1.2984 (0.0263) 0.8417 (0.0365) 469.74 (2.81)
true value 5 -1.3 50 30000 1 1 500
naive model 2.9411 (0.0548) -1.7328 (0.0838) 18770.02 (98.58) 10936.33 (97.49) 1.828 (0.0054) 2.2838 (0.2277) 539.5 (4.31)
integrated model 4.1799 (0.0528) -1.3159 (0.0145) -81574.65 (30566.75) 111394.19 (30567.8) 1.2845 (0.0095) 0.8634 (0.0125) 478.65 (2.39)
true value 5 -1.5 50 30000 1 1 500
naive model 3.2206 (0.0717) -2.3778 (0.1593) 18002.82 (105.51) 11696.6 (104.59) 1.8231 (0.0057) 2.9557 (0.2621) 560.41 (7.25)
integrated model 3.6493 (0.6203) -0.964 (0.6069) -51974.4 (22391.12) 81776.04 (22386.56) 1.2932 (0.0201) 0.8548 (0.0355) 488.64 (3.71)
Sample size 50            
true value 5 0 50 30000 1 1 500
naive model 2.7437 (0.0369) -0.0469 (0.0526) 20499.39 (63.98) 9225.41 (62.87) 1.7402 (0.0037) 2.7635 (0.2377) 485.25 (2.14)
integrated model 3.5198 (0.0405) 0.0089 (0.0067) 8598.57 (1581.12) 21172.62 (1582.55) 1.4285 (0.0103) 0.8595 (0.0138) 489.77 (1.59)
true value 5 -0.1 50 30000 1 1 500
naive model 2.7316 (0.0347) -0.1643 (0.0384) 20463.66 (65.62) 9261.85 (64.57) 1.738 (0.0038) 2.6338 (0.2266) 484.29 (1.72)
integrated model 3.4811 (0.0385) -0.0898 (0.0067) 9927.86 (1621.29) 19842.78 (1622.67) 1.434 (0.0104) 0.8728 (0.0129) 491.19 (1.61)
true value 5 -0.3 50 30000 1 1 500
naive model 2.8069 (0.0401) -0.4472 (0.047) 20293.49 (66.02) 9426.7 (65.05) 1.7416 (0.0037) 2.9565 (0.2576) 486.58 (1.97)
integrated model 3.4894 (0.0357) -0.2882 (0.0067) 12135.89 (534.51) 17635.35 (537.21) 1.4246 (0.0101) 0.8701 (0.0131) 491.18 (1.66)
true value 5 -0.5 50 30000 1 1 500
naive model 2.828 (0.0387) -0.6441 (0.0451) 19946.91 (69.44) 9770.55 (68.46) 1.7402 (0.0038) 2.8163 (0.2509) 491.23 (2.77)
integrated model 3.5327 (0.0365) -0.4769 (0.0067) 11365.82 (735.99) 18404.38 (738.2) 1.4188 (0.01) 0.8762 (0.0124) 493.4 (1.7)
true value 5 -1 50 30000 1 1 500
naive model 3.2183 (0.047) -1.7113 (0.0905) 18367.63 (79.4) 11331.51 (78.56) 1.7405 (0.0037) 3.9333 (0.301) 506.65 (2.69)
integrated model 3.4259 (0.029) -0.9716 (0.0072) 13477.54 (288.17) 16260.6 (291.47) 1.4497 (0.0086) 0.7908 (0.0171) 512.56 (1.84)
true value 5 -1.3 50 30000 1 1 500
naive model 3.5889 (0.0593) -2.5651 (0.1361) 17174.96 (86.16) 12514.49 (85.49) 1.7375 (0.0037) 5.4373 (0.3774) 521.52 (3.13)
integrated model 3.2866 (0.1729) -1.4043 (0.1428) 13337.94 (260.58) 16383.67 (263.67) 1.4403 (0.0146) 0.8708 (0.1229) 528.37 (2.55)
true value 5 -1.5 50 30000 1 1 500
naive model 3.8296 (0.0621) -2.9831 (0.1416) 16141.61 (89.86) 13546.24 (89.49) 1.7198 (0.0039) 6.1208 (0.3784) 523.94 (2.07)
integrated model 3.305 (0.1669) -1.3648 (0.105) 13436.45 (198.21) 16273.32 (201.3) 1.4225 (0.0332) 0.9029 (0.1719) 536.53 (2.56)
Sample size 100            
true value 5 0 50 30000 1 1 500
naive model 2.9087 (0.0269) -0.039 (0.0434) 19661.6 (56.83) 10058.46 (56.2) 1.6748 (0.003) 3.337 (0.2366) 468.53 (1.22)
integrated model 3.0493 (0.0261) -0.0055 (0.006) 16387.53 (641.05) 13333.07 (642.19) 1.5292 (0.0075) 0.8232 (0.0178) 501.83 (1.1)
true value 5 -0.1 50 30000 1 1 500
naive model 2.9097 (0.0291) -0.1508 (0.043) 19584.67 (57.9) 10137.22 (57.29) 1.6675 (0.0028) 3.2625 (0.2545) 469.76 (1.53)
integrated model 3.0247 (0.0234) -0.0985 (0.0065) 17062.36 (191.54) 12657.31 (194.2) 1.5329 (0.0073) 0.8748 (0.0133) 502.86 (1.06)
true value 5 -0.3 50 30000 1 1 500
naive model 2.9106 (0.0275) -0.3621 (0.0361) 19313.04 (62.78) 10404.89 (62.09) 1.6712 (0.003) 3.0649 (0.2302) 469.78 (0.91)
integrated model 3.0442 (0.0224) -0.3021 (0.0073) 16981.12 (176.62) 12738.09 (179.23) 1.5236 (0.007) 0.8185 (0.0172) 504.55 (1.09)
true value 5 -0.5 50 30000 1 1 500
naive model 3.0186 (0.0323) -0.7679 (0.044) 18919.14 (64.29) 10793.17 (63.66) 1.674 (0.003) 3.701 (0.2824) 474.8 (1.61)
integrated model 3.0784 (0.0226) -0.4853 (0.0049) 16620.4 (198.41) 13095.57 (200.87) 1.5193 (0.0068) 0.8203 (0.0165) 508.61 (1.12)
true value 5 -1 50 30000 1 1 500
naive model 3.5281 (0.0442) -2.0565 (0.0999) 17213.8 (74.03) 12482.15 (73.63) 1.6745 (0.003) 5.9013 (0.3507) 486.43 (0.92)
integrated model 3.1546 (0.0163) -0.9644 (0.0055) 16182.07 (131.53) 13518.68 (133.43) 1.5056 (0.0053) 0.7447 (0.0202) 521.9 (1.12)
true value 5 -1.3 50 30000 1 1 500
naive model 3.8155 (0.0476) -2.6141 (0.0999) 15813.29 (80.09) 13875.57 (79.85) 1.6668 (0.0034) 7.1509 (0.3873) 504.16 (2.87)
integrated model 3.28 (0.0142) -1.2628 (0.0074) 15230.07 (110.54) 14467.41 (111.99) 1.4792 (0.0047) 0.7278 (0.0212) 531.28 (1.16)
true value 5 -1.5 50 30000 1 1 500
naive model 4.23 (0.0626) -3.6045 (0.1408) 14844.17 (83.8) 14844.17 (83.59) 1.6571 (0.0034) 9.335 (0.4778) 513.6 (2.09)
integrated model 3.4028 (0.016) -1.4779 (0.0122) 14282.26 (116.92) 15415.65 (118.47) 1.4536 (0.0046) 0.6573 (0.0252) 539.12 (1.27)
Sample size 300            
true value 5 0 50 30000 1 1 500
naive model 3.0135 (0.0208) 0.0285 (0.0232) 18437.53 (67.92) 11288.37 (67.65) 1.5908 (0.003) 3.2476 (0.263) 451.57 (1.21)
integrated model 2.9 (0.0112) 5e-04 (0.0039) 18348.42 (75.58) 11365.95 (76.43) 1.5243 (0.0043) 0.8799 (0.0187) 498.43 (0.68)
true value 5 -0.1 50 30000 1 1 500
naive model 3.0361 (0.0228) -0.1808 (0.0329) 18456.78 (69.96) 11268.42 (69.74) 1.592 (0.0032) 3.577 (0.2943) 454.1 (2.08)
integrated model 2.9366 (0.0163) -0.0989 (0.0074) 18113.81 (121.05) 11603.85 (122.77) 1.516 (0.0054) 0.879 (0.0201) 496.92 (0.77)
true value 5 -0.3 50 30000 1 1 500
naive model 3.0804 (0.027) -0.3768 (0.0336) 18175.54 (74.23) 11545.95 (73.97) 1.5939 (0.0032) 4.1281 (0.3787) 453.35 (1.29)
integrated model 2.9395 (0.0132) -0.2858 (0.004) 18058.62 (94.19) 11655.43 (95.21) 1.5166 (0.0046) 0.8667 (0.0213) 498.87 (0.69)
true value 5 -0.5 50 30000 1 1 500
naive model 3.1502 (0.0254) -0.7234 (0.0412) 17717.61 (82.68) 11998.41 (82.46) 1.5974 (0.0034) 3.9477 (0.3312) 454.13 (0.75)
integrated model 2.9937 (0.0129) -0.4811 (0.0042) 17680.24 (87.96) 12031.57 (88.86) 1.5063 (0.0047) 0.8291 (0.0251) 500.36 (0.78)
true value 5 -1 50 30000 1 1 500
naive model 3.5669 (0.043) -1.7535 (0.09) 15740.25 (113.86) 13964.36 (113.86) 1.5926 (0.0043) 6.4576 (0.5025) 471.3 (3.33)
integrated model 3.2607 (0.0177) -0.9702 (0.0074) 15650.42 (130.59) 14066.12 (132.08) 1.4461 (0.0057) 0.8718 (0.0259) 505.15 (0.98)
true value 5 -1.3 50 30000 1 1 500
naive model 4.0045 (0.1514) -2.2565 (0.5547) 13772.02 (120.38) 15929.25 (120.41) 1.5632 (0.0045) 12.2208 (2.356) 480.58 (3.11)
integrated model 3.1969 (0.3036) -0.7316 (0.5495) 13720.47 (126.43) 16004.76 (128) 1.3919 (0.0097) 2.9218 (2.2545) 514.38 (4.56)
true value 5 -1.5 50 30000 1 1 500
naive model 4.4603 (0.0723) -3.707 (0.1756) 12633.68 (117.4) 17067.83 (117.75) 1.5489 (0.0043) 12.0708 (0.7155) 485.18 (1.18)
integrated model 3.6474 (0.0193) -1.4779 (0.0129) 12443.71 (145.16) 17289.63 (147.48) 1.3512 (0.0055) 0.6374 (0.0466) 510.48 (1.31)
Table 2: Table for the detailed point estimates of all unknown parameters and their standard error;Sample size was from 20 to 300and the protein intensity located in the upper part of sigmoidal curve. Truncation was applied to the boundary of intensity level; the integrated model consistently yielded parameter estimates of α2 with similar or much less standard errors than the naïve model