Journal of Mathematics

Research Article

New Cure Rate Survival Models Generated by Poisson Distribution and Different Regression Structures with Applications to Cancer Data Set

Table 7

Simulated ML estimators, RMSE, SE, and CP of the parameters in the simulation studies with covariates based on different link functions (when the true link is the logit).


Model		Parameter	Logit (RMSE, SE, CP)	Cauchit (RMSE, SE, CP)	Aranda-Ordaz (RMSE, SE, CP)	Probit (RMSE, SE, CP)	Log-log (RMSE, SE, CP)	Skewed logit (RMSE, SE, CP)	Skewed probit (RMSE, SE, CP)

PGcr	150		3.3724 (2.7849, 1.8165, 0.8240)	3.3970 (2.7338, 1.9473, 0.8659)	2.7669 (1.2054, 1.3153, 0.7454)	3.3973 (2.8911, 1.8443, 0.8356)	3.5121 (2.9145, 1.8474, 0.8508)	3.6561 (3.5202, 1.2397, 0.7158)	3.1939 (2.0992, 1.6742, 0.8162)
			1.9345 (1.6645, 1.7834, 0.8503)	1.8449 (1.4212, 1.8256, 0.8617)	1.4985 (0.4386, 0.9784, 0.9522)	1.9405 (1.6500, 1.7721, 0.8366)	1.7221 (1.1764, 1.6802, 0.8379)	2.1529 (4.1970, 1.2223, 0.7349)	1.7699 (1.3181, 1.7476, 0.8754)
			1.9402 (0.6654, 0.3762, 0.7291)	1.9365 (0.6568, 0.3756, 0.7468)	1.6939 (0.5831, 0.3290, 0.7602)	1.9249 (0.6467, 0.3667, 0.7401)	1.9410 (0.6632, 0.3755, 0.7400)	2.0238 (0.7721, 0.4274, 0.7131)	1.8943 (0.6160, 0.3589, 0.7747)
			0.0614 (0.0165, 0.0135, 0.8103)	0.0615 (0.0162, 0.0131, 0.8265)	0.0778 (0.0443, 0.0191, 0.8125)	0.0617 (0.0160, 0.0130, 0.8186)	0.0613 (0.0163, 0.0131, 0.8065)	0.0566 (0.0216, 0.0132, 0.6666)	0.0616 (0.0161, 0.0132, 0.8162)
					1.6632 (2.8407, 0.4227, 0.0659)			1.1729 (1.6558, 0.7451, 0.3005)	1.0952 (1.8699, 0.6923, 0.2529)
			−1.3603 (0.2440, 0.2414, 0.9536)	−1.3921 (0.3985, 0.3663, 0.9244)	−1.2359 (0.4902, 0.3005, 0.8568)	−0.8333 (0.5726, 0.1374, 0.0318)	−0.4785 (0.9173, 0.1191, 0.000)	−1.4612 (1.0056, 0.9099, 0.5382)	−1.5547 (1.2938, 1.4473, 0.6146)
			0.0343 (0.1427, 0.1229, 0.9420)	0.0477 (0.2042, 0.1868, 0.9500)	0.0305 (0.1446, 0.1488, 0.9590)	0.0197 (0.0741, 0.0696, 0.9448)	0.0173 (0.0671, 0.0607, 0.9393)	0.0527 (0.1864, 0.2035, 0.9590)	0.0145 (0.0791, 0.0946, 0.9743)
			−0.0369 (0.1421, 0.1236, 0.9452)	−0.0431 (0.2053, 0.1868, 0.9446)	−0.0453 (0.1768, 0.1467, 0.9534)	−0.0219 (0.0818, 0.0693, 0.9416)	−0.0120 (0.0590, 0.0594, 0.9545)	−0.0892 (0.2677, 0.2434, 0.9672)	−0.0296 (0.1097, 0.0992, 0.9743)
			0.0005 (0.0468, 0.0442, 0.9536)	0.0009 (0.0695, 0.0689, 0.9723)	−0.0024 (0.0518, 0.0530, 0.9579)	0.0004 (0.0345, 0.0251, 0.8409)	0.0009 (0.0326, 0.0215, 0.7785)	−0.0088 (0.0723, 0.0744, 0.9125)	−0.0003 (0.0309, 0.0353, 0.9051)
			0.0004 (0.0398, 0.0443, 0.9757)	0.0014 (0.0665, 0.0691, 0.9787)	−0.0025 (0.0522, 0.0534, 0.9659)	0.0012 (0.0247, 0.0250, 0.9618)	0.0007 (0.0217, 0.0216, 0.9568)	−0.0024 (0.0697, 0.0758, 0.9754)	0.0002 (0.0313, 0.0359, 0.9841)
	300		3.1925 (1.8480, 1.5297, 0.8119)	3.2169 (1.9260, 1.5018, 0.7822)	2.7899 (1.0652, 1.1293, 0.6881)	3.0807 (1.7512, 1.2974, 0.7924)	3.1172 (1.7028, 1.3587, 0.8187)	3.3346 (2.1929, 1.1740, 0.7331)	3.1664 (1.8992, 1.3882, 0.8154)
			1.8148 (1.3970, 1.4527, 0.8363)	1.8160 (1.3140, 1.4974, 0.8212)	1.5053 (0.4267, 0.9092, 0.9178)	1.8204 (1.1833, 1.4305, 0.8366)	1.6760 (0.9003, 1.3515, 0.8408)	1.5258 (1.4339, 0.9808, 0.7085)	1.6693 (1.0381, 1.2894, 0.8657)
			1.8672 (0.5654, 0.2411, 0.4112)	1.8402 (0.5291, 0.2332, 0.7293)	1.6982 (0.5287, 0.2225, 0.4189)	1.8890 (0.5911, 0.2442, 0.3688)	1.9081 (0.6057, 0.2494, 0.3487)	2.0122 (0.7448, 0.2824, 0.3742)	1.8685 (0.5647, 0.2389, 0.3791)
			0.0616 (0.0146, 0.0089, 0.6695)	0.0621 (0.0140, 0.0087, 0.6966)	0.0732 (0.0229, 0.0109, 0.5947)	0.0608 (0.0153, 0.0088, 0.6259)	0.0604 (0.0156, 0.0088, 0.6153)	0.0567 (0.0208, 0.0089, 0.5276)	0.0614 (0.0151, 0.0089, 0.6560)
					1.9318 (2.6749, 0.2267, 0.0480)			1.1741 (1.4555, 0.6154, 0.2791)	1.2242 (1.8273, 0.5801, 0.2281)
			−1.3667 (0.1568, 0.1669, 0.9670)	−1.3762 (0.2341, 0.2462, 0.9599)	−1.2228 (0.4201, 0.2036, 0.7857)	−0.8389 (0.5539, 0.0953, 0.0000)	−0.4662 (0.9234, 0.0831, 0.0000)	−1.2637 (0.7351, 0.6495, 0.5061)	−1.2622 (1.1798, 0.9342, 0.5268)
			0.0207 (0.0796, 0.0803, 0.9659)	0.0307 (0.1177, 0.1225, 0.9729)	0.0157 (0.0904, 0.0994, 0.9793)	0.0111 (0.0495, 0.0468, 0.9441)	0.0088 (0.0440, 0.0409, 0.9462)	0.0230 (0.0950, 0.1069, 0.9785)	0.0160 (0.0565, 0.0580, 0.9670)
			−0.0155 (0.0784, 0.0821, 0.9713)	−0.0181 (0.1108, 0.1213, 0.9761)	−0.0214 (0.0913, 0.0983, 0.9697)	−0.0067 (0.0451, 0.0462, 0.9515)	−0.0074 (0.0408, 0.0404, 0.9430)	−0.0301 (0.1151, 0.1114, 0.9785)	−0.0086 (0.0530, 0.0567, 0.9832)
			0.0002 (0.0362, 0.0300, 0.9128)	−0.0011 (0.0460, 0.0449, 0.9631)	−0.0004 (0.0396, 0.0361, 0.9423)	0.0001 (0.0291, 0.0169, 0.6838)	0.00007 (0.0283, 0.0147, 0.5721)	−0.0050 (0.0388, 0.0380, 0.8865)	−0.0008 (0.0302, 0.0206, 0.7449)
			−0.0001 (0.0263, 0.0300, 0.9829)	−0.0007 (0.0382, 0.0448, 0.9902)	−0.0031 (0.0316, 0.0359, 0.9807)	0.0003 (0.0168, 0.0169, 0.9462)	−0.0001 (0.0150, 0.0147, 0.9420)	−0.0012 (0.0365, 0.0394, 0.9815)	0.00003 (0.0202, 0.0208, 0.9664)

PGEcr	150		3.2659 (1.6432, 3.5329, 1)	3.4141 (2.7344, 4.3618, 0.8672)	2.9331 (4.0990, 2.0307, 0.8840)	3.1961 (1.7907, 3.5788, 0.9733)	3.3986 (1.9159, 4.0480, 0.9822)	3.8058 (3.4507, 5.8878, 0.7886)	3.6684 (2.1890, 4.9004, 0.7686)
			1.5023 (0.7209, 1.3830, 1)	1.7342 (1.0413, 1.4635, 0.9905)	1.9753 (1.0482, 1.4739, 0.9768)	1.6156 (08264, 1.4100, 1)	1.5054 (0.7710, 1.3694, 1)	1.9405 (1.5992, 1.5975, 0.9943)	1.6493 (1.3162, 1.5893, 0.9944)
			1.4727 (0.1855, 0.1974, 0.9551)	1.4941 (0.2118, 0.1954, 0.9178)	1.5074 (0.2110, 0.1849, 0.9206)	1.4815 (0.1955, 0.1955, 0.9397)	1.4716 (0.1904, 0.1968, 0.9421)	1.4928 (0.2186, 0.1972, 0.9037)	1.4745 (0.2063, 0.2098, 0.9221)
					1.7046 (5.9420, 2.6540, 0.1159)			1.6969 (1.7213, 1.1873, 0.0528)	2.4506 (3.2814, 14.1751, 0.6852)
			−1.2973 (0.5794, 0.6262, 0.9654)	−1.3565 (0.8294, 0.9256, 0.9420)	−1.1682 (1.6051, 1.0679, 0.9389)	−0.8261 (0.6720, 0.3582, 0.6431)	−0.4431 (0.9983, 0.3160, 0.1227)	−1.2869 (0.9474, 2.6470, 0.4207)	−1.5824 (2.1652, 10.4636, 0.9644)
			−0.0691 (0.6001, 0.5671, 0.9470)	0.0285 (0.6875, 0.8183, 0.9567)	−0.0108 (0.9097, 0.8479, 0.9499)	0.0238 (0.2904, 0.3199, 0.9803)	0.0217 (0.2971, 0.2865, 0.9338)	0.0020 (0.6824, 1.2947, 0.8867)	0.0071 (0.5103, 0.9896, 1)
			0.0056 (0.5365, 0.5632, 0.9781)	0.0095 (0.6995, 0.8286, 0.9578)	0.0173 (0.9984, 0.8149, 0.9536)	0.0238 (0.3343, 0.3218, 0.9490)	0.0098 (0.2988, 0.2837, 0.9374)	0.0058 (0.6589, 0.9515, 0.8773)	−0.0161 (0.5061, 0.9792, 0.9988)
			−0.0044 (0.2028, 0.2022, 0.9539)	0.0060 (0.3133, 0.2916, 0.9683)	−0.0010 (0.3164, 0.2835, 0.9536)	0.0008 (0.1204, 0.1160, 0.9397)	−0.0015 (0.1069, 0.1022, 0.9456)	0.0159 (0.2456, 0.5401, 0.9226)	0.0036 (0.1786, 0.3540, 0.9988)
			−0.0036 (0.1968, 0.2022, 0.9574)	−0.0001 (0.3005, 0.2895, 0.9704)	−0.0008 (0.3527, 0.2911, 0.9597)	0.0017 (0.1155, 0.1162, 0.9466)	0.0020 (0.1017, 0.1025, 0.9442)	−0.0102 (0.2360, 0.3885, 0.9566)	0.0128 (0.1812, 0.3511, 0.9977)
	300		3.2088 (1.2764, 2.1830, 0.9208)	2.9930 (1.5287, 2.0767, 0.8914)	2.8861 (1.1968, 1.5878, 0.9982)	2.9837 (0.9621, 1.8057, 1)	3.0859 (1.4198, 2.1166, 0.9942)	3.4165 (2.3672, 2.7744, 0.8356)	2.7729 (1.1816, 1.7428, 0.8992)
			1.4267 (0.6753, 0.9153, 1)	1.6162 (0.7430, 0.9654, 1)	1.4994 (0.4595, 0.8863, 0.9947)	1.4512 (0.4922, 0.9162, 1)	1.4997 (0.6031, 0.9306, 1)	1.6283 (1.0392, 0.9776, 0.9939)	1.6671 (0.7680, 1.0127, 0.9969)
			1.4644 (0.1564, 0.1357, 0.8887)	1.4863 (0.1733, 0.1339, 0.8461)	1.4763 (0.1582, 0.1301, 0.8939)	1.4712 (0.1574, 0.1347, 0.8935)	1.4745 (0.1617, 0.1348, 0.8839)	1.4824 (0.1823, 0.1352, 0.8196)	1.4827 (0.1643, 0.1367, 0.8902)
					1.4602 (5.9314, 2.2880, 0.0883)			1.4937 (1.2833, 0.1328, 0.0280)	2.3502 (2.5107, 7.6897, 0.6300)
			−1.3086 (0.4512, 0.4325, 0.9415)	−1.2397 (0.5500, 0.5887, 0.9293)	−1.1519 (1.3638, 0.8293, 0.9310)	−0.7917 (0.6473, 0.2478, 0.3248)	−0.4247 (0.9875, 0.2192, 0.0058)	−1.1391 (0.6735, 0.2044, 0.4128)	−1.2821 (1.7760, 5.3658, 0.9669)
			−0.0196 (0.4030, 0.3892, 0.9461)	0.0298 (0.4456, 0.5326, 0.9662)	0.0283 (0.6864, 0.5316, 0.9522)	0.0316 (0.1945, 0.2232, 0.9822)	0.0250 (0.1980, 0.1991, 0.9489)	0.0206 (0.4035, 0.3220, 0.9098)	0.0011 (0.3114, 0.4700, 0.9984)
			0.0156 (0.3998, 0.3885, 0.9564)	−0.0368 (0.4224, 0.5262, 0.9863)	−0.0262 (0.6830, 0.5655, 0.9505)	0.0048 (0.2307, 0.2227, 0.9467)	−0.0025 (0.1980, 0.1968, 0.9466)	0.0274 (0.3638, 0.3210, 0.8957)	−0.0038 (0.3182, 0.4622, 0.9969)
			−0.0057 (0.1450, 0.1413, 0.9449)	−0.0042 (0.2045, 0.1949, 0.9483)	0.0042 (0.2385, 0.2041, 0.9452)	−0.0038 (0.0849, 0.0813, 0.9379)	−0.0042 (0.0765, 0.0719, 0.9350)	−0.0057 (0.1461, 0.1229, 0.9238)	−0.0058 (0.1200, 0.1741, 0.9984)
			−0.0040 (0.1430, 0.1412, 0.9415)	−0.0009 (0.1998, 0.1941, 0.9504)	0.0016 (0.2281, 0.1962, 0.9487)	−0.0013 (0.0822, 0.0813, 0.9445)	−0.0009 (0.0734, 0.0719, 0.9396)	−0.0035 (0.1373, 0.1232, 0.9478)	−0.0011 (0.1119, 0.1632, 0.9969)