A new cure model that corrects for increased risk of non-cancer death: analysis of reliability and robustness, and application to real-life data

Botta, Laura; Goungounga, Juste; Capocaccia, Riccardo; Romain, Gaelle; Colonna, Marc; Gatta, Gemma; Boussari, Olayidé; Jooste, Valérie

doi:10.1186/s12874-023-01876-x

Table 1 Performance indicators of Model(1) using Maximum likelihood (ML) estimation by different values of α

From: A new cure model that corrects for increased risk of non-cancer death: analysis of reliability and robustness, and application to real-life data

Scenario	ML estimation using	True value α	AB						SD						CVR
Scenario	ML estimation using	True value α	α	π₆₀	λ	γ	β	δ	α	π₆₀	λ	γ	β	δ	α	π₆₀	λ	γ	β	δ
BREAST^a	grouped	2	−0.005	−0.004	0	0.002	−0.011	− 0.005	0.115	0.043	0.012	0.048	0.199	0.157	94%	93%	93%	95%	93%	94%
	individual	2	0.004	−0.003	0.001	0.002	−0.002	− 0.007	0.11	0.04	0.012	0.041	0.187	0.15	93%	93%	94%	94%	93%	93%
	grouped	1.5	−0.001	−0.003	0	0.002	−0.007	−0.004	0.099	0.038	0.011	0.046	0.184	0.146	94%	93%	95%	95%	94%	94%
	individual	1.5	0.005	−0.002	0.001	0.002	−0.001	− 0.006	0.095	0.036	0.011	0.04	0.172	0.139	94%	93%	95%	95%	93%	94%
	grouped	1.2	0	−0.003	0	0.002	− 0.007	− 0.003	0.09	0.036	0.01	0.045	0.174	0.139	93%	94%	96%	96%	94%	94%
	individual	1.2	0.005	−0.002	0.001	0.002	−0.001	− 0.005	0.086	0.033	0.01	0.039	0.163	0.132	93%	93%	95%	95%	94%	94%
	grouped	1	−0.001	−0.003	0	0.002	−0.009	− 0.001	0.084	0.034	0.01	0.044	0.169	0.134	93%	94%	95%	96%	94%	93%
	individual	1	0.002	−0.002	0	0.002	− 0.003	− 0.004	0.08	0.032	0.01	0.038	0.158	0.127	93%	93%	95%	95%	94%	94%
	grouped	0.8	−0.001	−0.002	0	0.002	−0.007	−0.002	0.077	0.033	0.009	0.043	0.161	0.129	94%	92%	95%	95%	93%	93%
	individual	0.8	0.002	−0.002	0	0.002	−0.002	− 0.004	0.074	0.031	0.009	0.037	0.152	0.123	94%	92%	95%	95%	93%	94%
LUNG^b	grouped	2	− 0.006	0.002	− 0.009	− 0.001	0.003	0.003	0.206	0.004	0.014	0.015	0.065	0.023	96%	92%	89%	95%	95%	95%
	individual	2	0.005	0	0	0	0.001	−0.001	0.199	0.004	0.012	0.008	0.063	0.022	96%	97%	95%	94%	96%	94%
	grouped	1.5	−0.004	0.002	− 0.009	− 0.001	0.003	0.003	0.165	0.004	0.013	0.014	0.063	0.023	96%	92%	89%	94%	95%	94%
	individual	1.5	0.004	0	0	0	0	0	0.16	0.004	0.012	0.008	0.061	0.022	96%	96%	95%	95%	96%	94%
	grouped	1.2	0	0.002	−0.009	0	0.004	0.003	0.149	0.004	0.013	0.014	0.062	0.023	95%	92%	90%	94%	94%	93%
	individual	1.2	0.006	0	0	0	0.001	0	0.143	0.004	0.012	0.008	0.061	0.022	95%	96%	95%	95%	95%	94%
	grouped	1	0.001	0.002	−0.009	0	0.004	0.003	0.132	0.004	0.013	0.014	0.061	0.023	96%	91%	90%	94%	94%	94%
	individual	1	0.006	0	0	0	0.001	−0.001	0.127	0.004	0.012	0.008	0.06	0.022	95%	95%	95%	95%	95%	94%
	grouped	0.8	−0.002	0.002	− 0.009	0	0.003	0.003	0.121	0.004	0.013	0.014	0.06	0.022	95%	91%	90%	94%	94%	93%
	individual	0.8	0.001	0	0	0	0	0	0.117	0.004	0.012	0.007	0.059	0.022	95%	96%	95%	94%	95%	94%

Model parameters:
α: hazard ratio representing non-cancer death risk of patients versus general population; π₆₀: proportion of cured at age 60 at diagnosis; β: rate of increase of proportion of cured per 15 years of age; λ, γ: scale and shape parameters of the survival function of uncured patients; δ: age effect of uncured survival per 15 years. Estimated over 1000 simulation runs; Sample size 10,000; follow-up 15 years
Absolute Bias (AB) = Mean(estimates - true value); Standard Deviation (SD) = standard deviation over the set of 1000 estimates; Coverage (CVR) = the proportion of the time that the estimated 95% confidence intervals contained the true value
^aTrue values: π₆₀ = 0.7, λ =0.1, γ =1.1, β = − 0.15 and δ =0
^bTrue values: π₆₀ = 0.1, λ =0.9, γ =0.8, β = − 0.75 and δ = − 0.3

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ISSN: 1471-2288

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