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

Table 3

ML estimators, standard errors (SEs), and information criteria for the melanoma data set based on the PGcr and PGEcr models and different link functions.

Model	Parameter	Logit (SE)	Cauchit (SE)	Aranda-Ordaz(SE)	Probit (SE)	Log-log(SE)	Skewed logit (SE)	Skewed probit (SE)
PGcr		3.4855 (0.1985)	4.9055(1.2437)	3.6414(0.4794)	3.5422(0.4492)	2.0920(0.7721)	2.4997(0.8053)	3.4981 (0.3751)
		3.7155 (1.3458)	2.0039(0.6724)	3.6391(1.8977)	3.7449(2.8534)	5.6320(2.5568)	4.7515(1.5617)	3.4417 (1.2519)
		0.0751 (0.0973)	0.0607(0.0153)	0.0644 (0.0781)	0.0700 (0.1487)	0.2009 (0.1890)	0.1674 (0.1786)	0.0916 (0.1255)
		0.1595 (0.1030)	0.5679(0.1944	0.1638 (0.2975)	0.1486 (0.1890)	0.1948(0.0992)	0.15108(0.0618)	0.1570 (0.1912)
				0.4658 (10.7250)			0.1271(0.0042)	0.9026 (0.5960)
		−1.9866 (3.0497)	5.8042 (6.5991)	−2.4234 (2.3495)	−1.2115 (2.2726)	0.2012 (1.2733)	−2.7757 (14.3335)	−1.0102 (1.3632)
		−0.1680 (0.1571)	−69.2146(22.6631)	−0.1641 (0.3893)	−0.0730 (0.1488)	−0.1338 (0.1476)	−1.0178 (1.0858)	−0.0916 (0.1481)
		−0.1205 (0.1153)	−82.9428(20.5605)	−0.1369 (0.2363)	−0.0572 (0.0975)	−0.0645 (0.0855)	−0.9200 (0.9695)	−0.0683 (0.0976)
		−0.4218 (0.1826)	−105.9257(11.8936)	−0.4077 (0.4548)	−0.1912 (0.2186)	−0.2982 (0.2662)	−4.0981 (3.4816)	−0.2433 (0.2245)
		−0.4183 (0.2267)	−112.9999(9.8166)	−0.3980 (0.6421)	−0.1952 (0.2822)	−0.3565 (0.3628)	−4.2877 (4.1393)	−0.2336 (0.2523)
	−2 Log L	401.289	400.5922	401.1493	401.5682	403.0112	402.4641	401.7631
	AIC	419.28	418.59	421.14	419.56	421.01	422.46	421.76
	BIC	449.19	448.49	454.37	449.47	450.91	455.69	454.99
PGEcr		5.0780 (4.2127)	5.7012 (5.8373)	3.5246 (18.1024)	1.4535 (1.94792)	1.47523 (1.9437)	5.27687 (7.5574)	1.7862(0.1220)
		1.0887 (1.0229)	1.1166 (1.3485)	1.7217 (10.6067)	5.1897 (10.7165)	5.0262 (10.1182)	1.04206 (1.6870)	3.8142(0.1857)
		0.2600(0.1272)	0.1480(0.0245)	0.2598 (0.4519)	0.4557(0.2680)	0.4587(0.2654)	0.2584(0.1404)	0.4257(0.0975)
				1.6900 (1.7052)			1.58017 (5.2750)	0.0134(0.0046)
		0.8888 (1.2297)	14.6255(7.2624)	1.0580 (5.0455)	1.0467(0.4746)	1.5455(0.7282)	0.5552 (1.9399)	−3.7595(1.3619)
		−0.7105 (0.4449)	−18.3212(6.58800	−0.7538 (0.4727)	−0.3600 (0.2216)	−0.3200 (0.2453)	−0.4476 (1.5374)	−1.9353 (1.3394)
		−0.6997(0.4569)	−19.7765(6.4635)	−0.6928 (0.5928)	−0.3388 (0.2196)	−0.24951 (0.2399)	−0.4409 (1.5182)	−2.5125(1.2984)
		−1.2355(0.5141)	−28.3639(11.0545)	−1.3210(0.4363)	−0.6477(0.2435)	−0.6704(0.2885)	−0.7712 (2.6071)	−4.1661(1.4066)
		−1.5617(0.5324)	−25.2151(12.5562)	−1.8048(0.3390)	−0.8603(0.2533)	−1.0131(0.3186)	−0.9970 (3.3504)	−5.2111(1.2716)
	−2 Log L	408.5335	404.2471	409.5273	408.8996	411.0726	408.5264	407.4518
	AIC	424.53	420.24	427.52	424.89	427.076	426.52	425.45
	BIC	451.11	446.83	457.43	451.48	453.65	456.43	455.35
Signif. codes:	0.001 “”	0.01 “”	0.05 “”	0.1 “.”