On estimating the time to statistical cure

Table 2 Bias and CIL of the cure point estimate in simulated data

			ARS model		FMC model		NRS model		Weibull mixture
	ε	t_ε	Bias	\(\overline {\text {CIL}}(\hat {t}_{\epsilon })\)	Bias	\(\overline {\text {CIL}}(\hat {t}_{\epsilon })\)	Bias	\(\overline {\text {CIL}}(\hat {t}_{\epsilon })\)	Bias	\(\overline {\text {CIL}}(\hat {t}_{\epsilon })\)
Conditional probability of cure
Scenario 1
	0.05	3.39	0.67	0.65	0.18	0.87			0.11	0.53
	0.10	2.90	0.42	0.65	0.13	0.61			0.09	0.45
	0.15	2.58	0.27	0.59	0.10	0.49			0.08	0.40
Scenario 2
	0.05	6.04	1.13	0.61	1.39	4.94			0.42	2.08
	0.10	4.59	0.59	0.70	0.85	3.09			0.31	1.55
	0.15	3.73	0.37	0.71	0.59	2.18			0.25	1.26
Scenario 3
	0.05	2.17	0.15	0.71	0.44	0.65			0.10	0.48
	0.10	1.63	0.09	0.42	0.13	0.39			0.07	0.36
	0.15	1.27	0.07	0.32	0.08	0.31			0.06	0.29
Conditional probability of cancer-related death
Scenario 1
	0.05	3.39	0.66	0.66	0.18	0.86	0.52	1.76	0.11	0.53
	0.10	2.89	0.41	0.65	0.13	0.61	0.30	1.25	0.09	0.44
	0.15	2.57	0.27	0.59	0.10	0.48	0.23	0.97	0.08	0.39
Scenario 2
	0.05	5.95	1.06	0.62	1.23	4.59	18.95	11.43	0.40	1.99
	0.10	4.52	0.54	0.70	0.77	2.86	11.94	12.48	0.30	1.49
	0.15	3.67	0.34	0.71	0.54	2.00	7.62	11.66	0.24	1.20
Scenario 3
	0.05	2.17	0.14	0.70	0.19	0.64	0.33	1.09	0.10	0.48
	0.10	1.62	0.09	0.41	0.10	0.38	0.20	0.67	0.07	0.35
	0.15	1.26	0.07	0.31	0.07	0.30	0.15	0.49	0.06	0.29
Loss of lifetime
Scenario 1
	1.00	3.34	0.60	0.64	0.16	0.80	0.34	1.47	0.10	0.50
	2.00	2.86	0.36	0.61	0.12	0.57	0.21	1.01	0.09	0.42
	3.00	2.55	0.23	0.55	0.09	0.45	0.16	0.77	0.08	0.37
Scenario 2
	1.00	5.52	0.79	0.61	0.85	3.43	8.81	7.48	0.33	1.63
	2.00	4.20	0.38	0.67	0.52	2.13	4.67	6.72	0.25	1.22
	3.00	3.42	0.24	0.66	0.36	1.48	2.60	5.17	0.20	0.99
Scenario 3
	1.00	2.15	0.13	0.64	0.16	0.59	0.22	0.92	0.09	0.46
	2.00	1.62	0.08	0.38	0.08	0.36	0.13	0.55	0.07	0.34
	3.00	1.27	0.06	0.29	0.06	0.29	0.10	0.40	0.06	0.28

The cure point estimates were based on the probabiltiy of cure, the probability of cancer-related death, and the loss of lifetime function. The NRS model was not evaluated for the latter measure since this is not a cure model. ARS: relative survival model by Andersson et al. [28], FMC: flexible mixture cure model by Jakobsen et al. [17], NRS: relative survival model by Nelson et al. [27], CIL: confidence interval length

ISSN: 1471-2288