Synthesis of clinical prediction models under different sets of covariates with one individual patient data

Yoneoka, Daisuke; Henmi, Masayuki; Sawada, Norie; Inoue, Manami

doi:10.1186/s12874-015-0087-x

BMC Medical Research Methodology

Table 1 Performance of our proposed method on simulation data (Bias and MSE)

From: Synthesis of clinical prediction models under different sets of covariates with one individual patient data

	Case 1; Both X₁ and X₂ are continuous									Case 2; X₁ is continuous and X₂ is binary
		Correlation r=0				Correlation r=0.5				Correlation r=0				Correlation r=0.5
Covariance matrix imputed with IPD
		-2	-1	0	1	-2	-1	0	1	-2	-1	0	1	-2	-1	0	1
Bias	Proposed method
	α ₀	-0.002	0.024	0.030	0.000	0.028	0.029	0.043	0.052	0.025	0.022	0.013	-0.040	0.057	0.037	0.006	-0.006
	α ₁	-0.052	-0.022	-0.001	0.086	-0.049	-0.024	-0.011	0.083	-0.050	-0.015	-0.003	0.071	-0.064	-0.017	0.002	0.025
	α ₂	0.038	0.022	0.012	0.097	0.030	0.018	0.010	0.058	0.044	0.007	0.018	0.266	0.049	0.001	0.012	0.488
	M1: Full set only
	α ₀	0.011	0.010	-0.018	-0.365	0.009	-0.009	-0.029	-0.058	0.011	0.016	-0.004	-0.016	0.027	0.011	-0.007	-0.002
	α ₁	-0.009	0.003	0.011	0.061	0.001	0.002	0.000	0.082	-0.001	0.002	0.000	0.029	-0.006	0.001	-0.004	0.012
	α ₂	0.001	-0.009	-0.019	0.061	0.001	0.000	-0.015	0.023	0.008	-0.027	-0.006	0.124	0.027	-0.008	0.001	0.272
	M2: Mean imputation
	α ₀	2.166	1.551	-0.193	-1.275	1.197	0.724	-0.145	-0.590	2.930	2.116	0.048	-1.131	2.612	1.789	0.050	-0.841
	α ₁	-1.807	-0.818	-0.171	0.218	-1.921	-1.101	-0.415	-0.135	-1.334	-0.756	-0.082	0.203	-1.385	-0.800	-0.142	0.075
	α ₂	0.811	0.218	-0.034	0.226	1.543	0.940	0.109	-0.145	0.034	-0.138	-0.069	-0.460	1.292	0.778	0.010	-1.356
MSE	Proposed method
	α ₀	0.123	0.098	0.205	0.803	0.085	0.056	0.101	0.251	0.096	0.055	0.065	0.136	0.074	0.044	0.047	0.086
	α ₁	0.045	0.021	0.037	0.215	0.060	0.025	0.057	0.181	0.051	0.015	0.012	0.058	0.057	0.017	0.016	0.059
	α ₂	0.033	0.022	0.034	0.204	0.044	0.027	0.060	0.188	0.144	0.055	0.051	0.247	0.173	0.070	0.076	0.486
	M1: Full set only
	α ₀	0.248	0.208	0.453	7.960	0.160	0.131	0.274	0.707	0.195	0.116	0.142	0.300	0.169	0.099	0.108	0.197
	α ₁	0.068	0.033	0.068	0.620	0.075	0.033	0.094	0.398	0.096	0.027	0.025	0.112	0.099	0.030	0.028	0.112
	α ₂	0.038	0.032	0.093	0.591	0.045	0.034	0.118	0.570	0.162	0.077	0.103	2.165	0.190	0.095	0.120	4.883
	M2: Mean imputation
	α ₀	5.290	2.663	0.236	1.929	1.633	0.625	0.113	0.638	8.771	4.532	0.039	1.372	6.912	3.242	0.033	0.775
	α ₁	3.694	0.806	0.071	0.242	3.771	1.254	0.214	0.213	2.083	0.601	0.012	0.126	2.075	0.661	0.026	0.087
	α ₂	0.870	0.195	0.088	0.209	2.424	0.934	0.091	0.333	0.310	0.098	0.079	2.058	1.919	0.676	0.065	5.396
Convergence proportion (%)
		100	100	99.1	61.5	100	100	98.4	67.3	100	100	98.4	61.2	100	100	98.4	60.3
True Covariance matrix
		-2	-1	0	1	-2	-1	0	1	-2	-1	0	1	-2	-1	0	1
Bias	Proposed method
	α ₀	0.032	0.034	0.049	0.215	0.058	0.038	0.050	0.185	0.059	0.045	0.028	0.032	0.075	0.054	0.014	0.041
	α ₁	-0.118	-0.048	-0.005	0.099	-0.110	-0.046	-0.010	0.105	-0.116	-0.037	-0.004	0.072	-0.117	-0.036	0.003	0.036
	α ₂	0.070	0.055	0.052	0.104	0.055	0.049	0.058	0.096	0.082	0.036	0.039	0.250	0.072	0.023	0.037	0.462
MSE	Proposed method
	α ₀	0.111	0.089	0.196	0.690	0.077	0.053	0.094	0.204	0.091	0.054	0.065	0.123	0.071	0.043	0.046	0.080
	α ₁	0.050	0.021	0.034	0.161	0.061	0.024	0.050	0.125	0.057	0.015	0.012	0.050	0.062	0.017	0.015	0.051
	α ₂	0.031	0.022	0.032	0.146	0.039	0.026	0.053	0.136	0.133	0.049	0.049	0.215	0.145	0.060	0.069	0.417
Convergence proportion (%)
		100	100	99.1	61.5	100	100	98.4	67.3	100	100	98.4	61.2	100	100	98.4	60.3

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