Scientific Reports

Table 1 Simulation results of \(\gamma _1\), \(\gamma _2\) under MCAR 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	0.089	0.128	0.064	0.124	0.020	0.083	0.082	0.090	0.174	0.055
	MSE	0.016	0.002	0.015	0.003	0.007	0.001	0.008	0.001	0.003	0.000
	Coverage	94.0	2.375	95.0	1.940	90.0	3.000	93.0	2.551	96.0	1.960
\(\gamma _2\)	Bias	-0.913	0.745	0.570	0.777	0.352	0.522	-0.578	0.622	8.062	0.482
	MSE	0.557	0.092	0.601	0.094	0.271	0.042	0.387	0.051	0.880	0.083
	Coverage	95.0	2.179	97.0	1.900	97.0	1.706	90.0	3.000	80.0	3.984
		n=200
\(\gamma _1\)	Bias	0.060	0.128	0.033	0.122	0.030	0.088	0.030	0.062	0.167	0.058
	MSE	0.016	0.002	0.015	0.002	0.008	0.001	0.004	0.001	0.004	0.001
	Coverage	93.0	2.551	93.0	2.551	92.0	2.713	95.0	2.179	97.0	2.120
\(\gamma _2\)	Bias	-0.828	0.735	1.188	0.824	8.445	0.503	-0.363	0.425	0.059	0.498
	MSE	0.542	0.091	0.686	0.080	0.963	0.093	0.180	0.021	0.246	0.034
	Coverage	96.0	1.960	95.0	2.179	61.0	4.877	96.0	1.960	98.0	2.110
		n=300
\(\gamma _1\)	Bias	-0.003	0.118	0.021	0.084	0.011	0.094	0.026	0.062	0.028	0.056
	MSE	0.014	0.002	0.007	0.001	0.009	0.001	0.004	0.001	0.003	0.000
	Coverage	93.0	2.551	89.0	3.129	96.0	2.110	95.0	2.179	98.0	1.400
\(\gamma _2\)	Bias	9.447	0.734	0.326	0.518	-0.502	0.544	-0.316	0.427	0.450	0.483
	MSE	1.426	0.164	0.267	0.041	0.296	0.048	0.182	0.023	0.233	0.029
	Coverage	74.0	4.386	97.0	1.706	97.0	2.050	97.0	1.706	93.0	2.551

The actual values of the entries in the tables are like: true value = (table value)/100 and 0.000 denotes \(<0.0001\).

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