Analysis of Longitudinal and Survival Data: Joint Modeling, Inference Methods, and Issues

Table 2

Comparison of the two-stage Method and the joint likelihood method via a simulation study.

Method	Parameter	𝛽1	𝛼0	𝛼1	𝜎	𝐴11	𝐴22
	True value	0.6	−0.2	1.3	0.6	0.5	0.3
Two-stage	Est	0.183	−0.183	1.303	0.598	0.501	0.353
	ESE	0.216	0.111	0.164	0.025	0.114	0.209
	ASE	0.201	0.111	0.164	—	—	—
	BSE	0.250	—	—	—	—	—
	Bias	−0.417	0.017	0.003	−0.002	−0.001	0.053
	MSE	0.221	0.013	0.027	0.0007	0.013	0.046
	CR	42.8	95.6	94.4	—	—	—
Joint model	Est	0.6004	−0.175	1.296	0.598	0.492	0.321
	ESE	0.256	0.103	0.161	0.020	0.092	0.156
	ASE	0.249	0.099	0.163	—	—	—
	Bias	0.0004	0.025	−0.004	−0.002	−0.008	0.021
	MSE	0.066	0.011	0.026	0.0004	0.008	0.025
	CR	95.6	95.8	95.2	—	—	—