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

Table 1

Analyses of the AIDS data under different models.

Model	Method		𝛽0	𝛽1	𝛼0	𝛼1	𝜎
Cox model	Two-stage	Estimate	—	0.315	−0.233	1.345	0.605
		SE	—	0.208	0.113	0.154	—
		𝑃 value	—	0.129	0.040	<0.001	—
		BSE	—	0.237	—	—	—
Cox model	Joint model	Estimate	—	0.648	−0.201	1.342	0.603
		SE	—	0.234	0.135	0.162	—
		𝑃 value	—	0.006	0.137	<0.001	—
AFT model	Joint model	Estimate	0.168	−0.487	−0.237	1.341	0.604
		SE	0.260	0.289	0.125	0.156	—
		𝑃 value	0.517	0.091	0.059	<0.001	—

SE: standard error; BSE: bootstrap standard error. The 𝑃 values are from the Wald tests for testing if the corresponding parameters are zero or not.