Correcting for misclassification and selection effects in estimating net survival in clinical trials

Goungounga, Juste Aristide; Touraine, Célia; Grafféo, Nathalie; Giorgi, Roch

doi:10.1186/s12874-019-0747-3

BMC Medical Research Methodology

Table 2 Performance in terms of net survival of various methods in various scenarios

From: Correcting for misclassification and selection effects in estimating net survival in clinical trials

Method & Misc.	Bias × 100	5-year net survival			Bias ×100	10-year net survival			Bias ×100	15-year net survival
Method & Misc.	Bias × 100	R.Bias	RMSE	ECR	Bias ×100	R.Bias	RMSE	ECR	Bias ×100	R.Bias	RMSE	ECR
Scenario 1 (α = 1)
Gold standard	0.012 (0.827 ^a)	0.0145	0.012	94.7	0.017 (0.667 ^a)	0.254	0.015	95.0	0.025 (0.575 ^a)	0.043	0.016	95.2
CSS methods
KM & 0%	0.126	0.152	0.012	94.5	0.434	0.650	0.016	93.5	0.778	1.353	0.018	92.8
KM & 20%	0.126	0.152	0.012	94.5	3.296	4.941	0.036	42.9	4.993	8.683	0.052	13.8
KM & 30%	0.126	0.152	0.012	94.5	4.803	7.200	0.050	10.2	7.245	12.60	0.074	0.4
Cox & 0%	0.036	0.043	0.011	95.7	0.036	0.053	0.015	97.6	0.046	0.080	0.016	97.7
Cox & 20%	0.036	0.043	0.011	95.7	2.869	4.301	0.032	60.6	4.144	7.206	0.041	38.5
Cox & 30%	0.036	0.043	0.011	95.7	4.364	6.54	0.045	23.8	6.366	11.071	0.065	4.7
wNA & 0%	0.027	0.032	0.012	94.4	0.089	0.133	0.015	94.6	0.143	0.248	0.016	94.3
wNA & 20%	0.027	0.032	0.012	94.4	2.991	4.484	0.033	50.7	4.432	7.707	0.047	21.3
wNA & 30%	0.027	0.032	0.012	94.4	4.520	6.776	0.047	14.8	6.726	11.697	0.069	1.8
PNS methods
PP	−0.359	−0.434	0.014	94.5	−0.574	−0.860	0.017	95.9	−0.999	−1.737	0.020	94.0
RBS	−0.102	−0.123	0.015	94.2	−0.445	−0.667	0.025	92.3	−0.459	−0.790	0.037	93.1
Scenario 2 (α = 0.5)
Gold standard	−0.005 (0.787 ^a)	− 0.006	0.011	95.4	0.022 (0.644 ^a)	0.034	0.013	96.8	0.048 (0.576 ^a)	0.083	0.014	96.7
CSS methods
KM & 0%	0.061	0.077	0.011	95.3	0.234	0 .363	0.014	96.7	0.437	0.758	0.015	94.7
KM & 20%	0.061	0.077	0.011	95.3	3.111	4.830	0.033	42.9	4.702	8.163	0.049	13.8
KM & 30%	0.061	0.077	0.011	95.3	4.636	7.198	0.048	9.5	6.984	12.449	0.071	0.4
Cox & 0%	0.033	0.041	0.010	97.2	0.041	0.063	0.013	97	0.071	0.123	0.014	98.0
Cox & 20%	0.033	0.041	0.010	97.2	2.876	4.465	0.031	65.6	4.173	7.244	0.044	44.6
Cox & 30%	0.033	0.041	0.010	97.2	4.377	6.796	0.045	30.4	6.404	11.118	0.065	7.0
wNA & 0%	−0.038	−0.048	0.011	95.3	−0.113	−0.175	0.014	96.8	−0.210	−0.364	0.014	97.2
wNA & 20%	−0.038	−0.048	0.011	95.3	2.804	4.354	0.033	50.5	4.130	7.170	0.047	23.8
wNA & 30%	−0.038	−0.048	0.011	95.3	4.351	6.756	0.045	14.8	6.458	11.21	0.066	1.8
PNS methods
PP	0.897	1.139	0.015	88.0	1.731	2.687	0.022	82.9	2.618	4.545	0.031	67.4
RBS	−0.023	−0.029	0.012	94.9	−0.303	− 0.470	0.019	91.8	−0.251	− 0.435	0.028	90.1
Scenario 3 (α = 2)
Gold standard	0.008 (0.827 ^a)	0.009	0.012	95.6	0.016 (0.667 ^a)	0.023	0.015	95.9	0.057 (0.575 ^a)	0.099	0.016	95.7
CSS methods
KM & 0%	0.233	0.281	0.012	94.3	0.818	1.226	0.017	93.2	1.513	2.631	0.023	87.2
KM & 20%	0.233	0.281	0.012	94.3	3.624	5.433	0.039	38.7	5.611	9.758	0.058	11.7
KM & 30%	0.233	0.281	0.012	94.3	5.116	7.670	0.053	8.8	7.830	13.617	0.079	0.2
Cox & 0%	0.036	0.043	0.011	97.3	0.062	0.092	0.015	98.5	0.113	0.196	0.017	98.5
Cox & 20%	0.036	0.043	0.011	97.3	2.877	4.313	0.032	65.1	4.175	7.260	0.044	45.1
Cox & 30%	0.036	0.043	0.011	97.3	4.347	6.517	0.045	29.4	6.386	11.106	0.065	7.3
wNA & 0%	0.136	0.164	0.012	94.5	0.484	0.725	0.016	95.0	0.919	1.598	0.020	94.5
wNA & 20%	0.136	0.164	0.012	94.5	3.329	4.991	0.036	44.3	5.087	8.846	0.053	18.1
wNA & 30%	0.136	0.164	0.012	94.5	4.842	7.259	0.050	13.0	7.347	12.777	0.075	0.8
PNS methods
PP	−2.784	−3.366	0.031	50.7	−4.693	−7.035	0.049	27.1	−6.831	−11.88	0.070	8.2
RBS	−0.284	−0.343	0.021	93.4	−0.667	−1.000	0.036	92.7	−0.668	−1.161	0.053	94.0
Scenario 4 (α = 4)
Gold standard	0.012 (0.727 ^a)	0.015	0.012	95.1	0.082 (0.644 ^a)	0.127	0.016	95.8	0.083 (0.575 ^a)	0.144	0.017	95.8
CSS methods
KM & 0%	0.493	0.626	0.013	93.2	1.633	2.535	0.023	80.6	2.812	4.890	0.034	66.0
KM & 20%	0.493	0.626	0.013	93.2	4.335	6.731	0.046	25.2	6.775	11.782	0.070	6.1
KM & 30%	0.493	0.626	0.013	93.2	5.754	8.934	0.059	6.7	8.867	15.42	0.090	0.3
Cox & 0%	0.037	0.047	0.011	97.3	0.077	0.105	0.016	97.5	0.047	0.081	0.019	97.7
Cox & 20%	0.037	0.047	0.011	97.3	2.894	4.493	0.033	67.5	4.127	1.177	0.045	53.0
Cox & 30%	0.037	0.047	0.011	97.3	4.369	6.784	0.046	31.2	6.329	11.006	0.065	12.6
wNA & 0%	0.397	0.504	0.013	93.7	1.315	2.041	0.021	85.0	2.276	3.958	0.030	74.3
wNA & 20%	0.397	0.504	0.013	93.7	4.054	6.295	0.043	30.7	6.304	10.963	0.065	9.1
wNA & 30%	0.397	0.504	0.013	93.7	5.492	8.527	0.057	8.6	8.428	14.657	0.086	0.6
PNS methods
PP	−7.274	−9.268	0.074	0.1	−11.690	18.152	0.118	0.00	−15.629	−27.173	0.157	0.00
RBS	−0.469	−0.595	0.0311	93.1	−0.869	−1.349	0.0532	93.6	−0.934	−1.624	0.0762	93.8

a The true net survival values are provided at 5, 10, and 15 years of follow-up for each scenarios
Misc misclassification rate , RMSE root mean square error, ECR empirical coverage rate, CSS cause-specific survival, KM Kaplan-Meier, wNA weighted Nelson-Aalen, PNS population-based net survival, PP Pohar-Perme, RBS rescaled B-spline, R.Bias relative bias

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