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. Author manuscript; available in PMC: 2011 Dec 25.

Published in final edited form as: J Gerontol A Biol Sci Med Sci. 2006 Dec;61(12):1253–1261. doi: 10.1093/gerona/61.12.1253

Table 3.

Estimates of β, σ_f², and σ_p² When the Fixed Covariates Are Uncorrelated With Frailty

	Model
Parameter	Proportional Hazards	Shared Frailty	Correlated Frailty
	β = 2.0, σ_p² = 0.5
β	1.600 (0.052)	1.707 (0.053)	1.930 (0.076)
$S D (\hat{β})$	0.044 (1.2e-4)	0.048 (1.2e-4)	0.054 (1.9e-4)
σ _f ²	–	0.119 (0.034)	–
σ _p ²	–	–	0.412 (0.094)
	β = 2.0, σ_p² = 1.0
β	1.378 (0.050)	1.521 (0.051)	1.846 (0.077)
$S D (\hat{β})$	0.040 (1.0e-4)	0.044 (1.1e-4)	0.053 (1.9e-4)
σ _f ²	–	0.189 (0.046)	–
σ _p ²	–	–	0.712 (0.129)
	β = 0.7, σ_p² = 0.5
β	0.556 (0.032)	0.593 (0.034)	0.669 (0.042)
$S D (\hat{β})$	0.029 (5.9e-5)	0.031 (6.1e-5)	0.035 (9.5e-5)
σ _f ²	–	0.110 (0.036)	–
σ _p ²	–	–	0.390 (0.105)
	β = 0.7, σ_p² = 1.0
β	0.477 (0.031)	0.527 (0.033)	0.634 (0.043)
$S D (\hat{β})$	0.028 (5.5e-5)	0.030 (5.7e-5)	0.036 (1.0e-4)
σ _f ²	–	0.173 (0.047)	–
σ _p ²	–	–	0.652 (0.137)
	β = 0.1, σ_p² = 0.5
β	0.079 (0.028)	0.084 (0.030)	0.094 (0.033)
$S D (\hat{β})$	0.028 (6.2e-5)	0.029 (6.3e-5)	0.032 (9.6e-5)
σ _f ²	–	0.103 (0.039)	–
σ _f ²	–	–	0.363 (0.120)
	β = 0.1, σ_f² = 1.0
β	0.068 (0.027)	0.075 (0.029)	0.089 (0.034)
$S D (\hat{β})$	0.027 (5.6e-5)	0.028 (5.9e-5)	0.034 (9.8e-5)
σ _f ²	–	0.165 (0.050)	–
σ _p ²	–	–	0.604 (0.148)

Note: Empirical expected values and standard deviations (SD) of parameter estimates were based on 1000 simulations.