Scientific Reports

Table 2 Simulation results of model parameter \(\gamma _1\), \(\gamma _2\) under MAR 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	0.097	0.121	0.040	0.123	0.024	0.083	0.086	0.090	0.169	0.058
	MSE	0.015	0.002	0.015	0.002	0.007	0.001	0.008	0.001	0.004	0.001
	Coverage	95.0	2.179	93.0	2.551	97.0	2.040	93.0	2.551	96.0	1.960
\(\gamma _2\)	Bias	9.414	0.750	1.311	0.820	0.312	0.521	-0.569	0.621	0.036	0.501
	MSE	1.444	0.138	0.682	0.081	0.270	0.041	0.385	0.051	0.249	0.035
	Coverage	65.0	4.770	95.0	2.179	96.0	3.100	90.0	3.000	93.0	2.551
		n=200
\(\gamma _1\)	Bias	0.046	0.128	0.037	0.121	0.010	0.094	-0.015	0.058	0.036	0.056
	MSE	0.016	0.002	0.015	0.002	0.009	0.001	0.003	0.000	0.003	0.000
	Coverage	97.0	2.150	93.0	2.551	91.0	2.862	93.0	2.551	98.0	1.400
\(\gamma _2\)	Bias	-0.869	0.739	1.169	0.819	-0.496	0.542	10.034	0.406	0.546	0.475
	MSE	0.548	0.091	0.678	0.079	0.294	0.048	1.170	0.091	0.226	0.028
	Coverage	96.0	2.156	95.0	2.179	95.0	2.179	32.0	4.665	94.0	2.375
		n=300
\(\gamma _1\)	bias	0.064	0.124	0.043	0.075	0.100	0.092	0.018	0.062	0.031	0.056
	MSE	0.015	0.003	0.006	0.001	0.008	0.001	0.004	0.001	0.003	0.000
	Coverage	95.0	2.179	94.0	2.375	92.0	2.713	100.0	0.000	98.0	1.400
\(\gamma _2\)	Bias	0.419	0.783	10.049	0.481	-0.529	0.631	-0.291	0.429	0.458	0.483
	MSE	0.609	0.095	1.239	0.097	0.397	0.051	0.183	0.024	0.233	0.029
	Coverage	93.0	2.551	44.0	4.964	90.0	3.000	97.0	2.010	93.0	2.551

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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