Table 3.

Results of fitting frailty models to the OPTIMA Veterans Cohort

Strategy 1	Shared frailty model		Joint frailty model		Proposed joint model
	HR (95% CI)	p-value	HR (95% CI)	p-value	HR (95% CI)	p-value
Recurrent ADE	1.11 (0.79, 1.56)	0.554	1.08 (0.64, 1.81)	0.771	1.05 (0.64, 1.72)	0.850
Death	NA	NA	1.04 (0.55, 1.95)	0.903	1.06 (0.62, 1.80)	0.830
Veteran-level Cluster	Estimate (SE)	p-value	Estimate (SE)	p-value	Estimate (SE)	p-value
Heterogeneity	0.46 (0.20)	0.024	1.49 (0.16)	<0.001	1.48 (0.16)	<0.001
Association with death	NA	NA	1.17 (0.20)	<0.001	0.97 (0.15)	<0.001
VAMC-level Cluster	Estimate (SE)	p-value	Estimate (SE)	p-value	Estimate (SE)	p-value
Heterogeneity	NA	NA	NA	NA	0.08 (0.23)	0.737
Association with death	NA	NA	NA	NA	0.67 (0.44)	0.878
Strategy 2	Shared frailty model		Joint frailty model		Proposed joint model
	HR (95% CI)	p-value	HR (95% CI)	p-value	HR (95% CI)	p-value
Recurrent ADE	1.01 (0.72, 1.42)	0.936	0.95 (0.57, 1.59)	0.845	0.92 (0.56, 1.51)	0.748
Death	NA	NA	1.20 (0.63, 2.27)	0.586	1.15 (0.68, 1.95)	0.610
Veteran-level Cluster	Estimate (SE)	p-value	Estimate (SE)	p-value	Estimate (SE)	p-value
Heterogeneity	0.46 (0.21)	0.026	1.48 (0.16)	<0.001	1.48 (0.16)	<0.001
Association with death	NA	NA	1.19 (0.21)	<0.001	0.97 (0.15)	<0.001
VAMC-level Cluster	Estimate (SE)	p-value	Estimate (SE)	p-value	Estimate (SE)	p-value
Heterogeneity	NA	NA	NA	NA	0.08 (0.23)	0.719
Association with death	NA	NA	NA	NA	0.67 (0.43)	0.877

NA: Not Applicable; ART = antiretroviral treatment, HR = hazard ratio, CI = confidence interval, ADE = AIDS defining event; Shared frailty model is analyzed without level-2 clustering; joint frailty model is analyzed without level-2 clustering; Strategy 1 = intensive antiretroviral treatment (ART) vs. standard ART; Strategy 2 = ART treatment interruption vs. no interruption