Scientific Reports

Table 3 Simulation results of \(\gamma _1\), \(\gamma _2\) under MNAR mechanism, reporting the estimated bias, mean squared error (MSE), and 95% confidence interval coverage in percentage (Coverage), along with corresponding Monte Carlo standard errors (MCSE) of estimate (Est).

From: A two-stage joint model approach to handle incomplete time dependent markers in survival data through inverse probability weight and multiple imputation

		n=100
		cc		locf		twos		mi		wmi
		Est	MCSE	Est	MCSE	Est	MCSE	Est	MCSE	Est	MCSE
\(\gamma _1\)	Bias	0.062	0.128	0.111	0.109	-0.011	0.096	0.084	0.091	0.170	0.058
	MSE	0.016	0.002	0.012	0.002	0.009	0.001	0.008	0.001	0.004	0.001
	Coverage	93.0	2.551	94.0	2.375	90.0	3.000	100.0	0.000	96.0	1.960
\(\gamma _2\)	Bias	-0.825	0.737	7.946	0.723	-0.481	0.557	-0.566	0.622	0.033	0.501
	MSE	0.545	0.091	1.149	0.137	0.309	0.049	0.386	0.050	0.249	0.035
	Coverage	96.0	1.960	77.0	4.208	95.0	2.179	96.0	2.200	93.0	2.551
		n=200
\(\gamma _1\)	Bias	0.031	0.126	0.033	0.120	0.010	0.093	0.026	0.062	0.061	0.055
	MSE	0.016	0.003	0.014	0.002	0.009	0.001	0.004	0.001	0.003	0.000
	Coverage	96.0	1.960	96.0	1.950	91.0	2.862	96.0	1.960	98.0	1.400
\(\gamma _2\)	Bias	0.446	0.790	1.195	0.824	-0.508	0.541	-0.322	0.428	7.005	0.470
	MSE	0.620	0.094	0.687	0.078	0.293	0.048	0.183	0.023	0.710	0.079
	Coverage	94.0	2.375	96.0	2.040	95.0	2.179	96.0	1.960	85.0	2.877
		n=300
\(\gamma _1\)	Bias	0.063	0.125	0.019	0.083	0.071	0.084	0.176	0.058	0.027	0.057
	MSE	0.015	0.003	0.007	0.001	0.007	0.001	0.004	0.001	0.003	0.000
	Coverage	95.0	2.179	90.0	3.000	92.0	2.713	96.0	1.960	97.0	1.977
\(\gamma _2\)	Bias	0.413	0.783	0.343	0.523	6.392	0.583	0.002	0.509	0.451	0.487
	MSE	0.609	0.095	0.272	0.042	0.745	0.091	0.257	0.036	0.237	0.029
	Coverage	93.0	2.551	97.0	1.706	71.0	4.538	92.0	2.713	97.0	1.560

All reported estimates are scaled by a factor of 100; the true parameter value equals (table value)/100 and 0.000 denotes \(<0.0001\).

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