Table III.

BHS-2 study results (n=248). IADL dependency (range: 0–7) regressed on patient sex (1=male,0=female) and age (years); estimated coefficients (β̂) and standard errors (SE).

Validation Data Used?	Assumed β(0)	Method	λ2	${\rho }_{(\mathit{sp})}^{(0)}$	Sex		Age (Years)
					β̂	SE	β̂	SE
No	β(1)	Subject Only	—	—	1.14	0.52	0.10	0.02
	α(0)	Subject + Proxy	—	—	0.81	0.37	0.12	0.02
	β(1)	ML-Model 1	—	—	1.14	0.52	0.10	0.02
	β(1)	MI-Model 1	—	0.35	1.08	0.51	0.10	0.02
	β(1)	MI-Model 1	—	0.70	1.11	0.54	0.10	0.02
	α(0)	ML-Model 2	(0, 0)	—	0.81	0.38	0.12	0.02
	α(0)	MI-Model 2	(0, 0)	0.35	0.80	0.45	0.12	0.02
	α(0)	MI-Model 2	(0, 0)	0.70	0.83	0.41	0.12	0.02
	α(0)+λ2	ML-Model 2	(−0.26,0.01)	—	0.81	0.38	0.13	0.02
	α(0)+λ2	MI-Model 2	(−0.26,0.01)	0.35	0.82	0.47	0.13	0.02
	α(0)+λ2	MI-Model 2	(−0.26,0.01)	0.70	0.80	0.43	0.13	0.02
	α(0)+λ2	ML-Model 2	(−0.52,0.02)	—	0.82	0.38	0.14	0.02
	α(0)+λ2	MI-Model 2	(−0.52,0.02)	0.35	0.82	0.49	0.14	0.02
	α(0)+λ2	MI-Model 2	(−0.52,0.02)	0.70	0.84	0.45	0.14	0.02
	α(0)	ML-Model 3	(0, 0)	0.35	0.81	0.86	0.12	0.05
	α(0)	MI-Model 3	(0, 0)	0.35	0.83	0.80	0.12	0.04
	α(0)	ML-Model 3	(0, 0)	0.70	0.81	0.49	0.12	0.03
	α(0)	MI-Model 3	(0, 0)	0.70	0.80	0.47	0.12	0.02
	α(0)/γ	ML-Model 3	(0, 0)	0.35	3.34	1.38	0.33	0.10
	α(0)/γ	MI-Model 3	(0, 0)	0.35	3.26	1.14	0.33	0.06
	α(0)/γ	ML-Model 3	(0, 0)	0.70	1.41	0.55	0.17	0.03
	α(0)/γ	MI-Model 3	(0, 0)	0.70	1.40	0.55	0.17	0.03
	(α(0) −λ3)/γ	ML-Model 3	(−0.26,0.01)	0.35	0.81	0.86	0.13	0.05
	(α(0)−λ3)/γ	MI-Model 3	(−0.26,0.01)	0.35	0.90	0.83	0.13	0.04
	(α(0)−λ3)/γ	ML-Model 3	(−0.26,0.01)	0.70	0.81	0.50	0.13	0.03
	(α(0)−λ3)/γ	MI-Model 3	(−0.26,0.01)	0.70	0.84	0.49	0.13	0.02
	(α(0)−λ3)/γ	ML-Model 3	(−0.52,0.02)	0.35	0.82	0.86	0.14	0.05
	(α(0)−λ3)/γ	MI-Model 3	(−0.52,0.02)	0.35	0.76	0.79	0.14	0.04
	(α(0)−λ3)/γ	ML-Model 3	(−0.52,0.02)	0.70	0.82	0.50	0.14	0.03
	(α(0)−λ3)/γ	MI-Model 3	(−0.52,0.02)	0.70	0.85	0.49	0.14	0.03
Yes	α(0)+λ2	ML-Model V(2)	β̂1−α̂1	${\widehat{\rho }}_{(\mathit{sp})}^{(1)}$	1.14	0.47	0.14	0.02
	α(0)+λ2	MI-Model V(2)	β̂1−α̂1	${\widehat{\rho }}_{(\mathit{sp})}^{(1)}$	1.18	0.53	0.14	0.03
	(α(0)−λ3)/γ	ML-Model V(3)	β̂1−α̂1	${\widehat{\rho }}_{(\mathit{sp})}^{(1)}$	1.14	0.50	0.14	0.02
	(α(0)−λ3)/γ	MI-Model V(3)	β̂1−α̂1	${\widehat{\rho }}_{(\mathit{sp})}^{(1)}$	1.14	0.56	0.14	0.03

‘Subject Only’ refers to linear regression with only observed subject data, ‘Subject+Proxy’ refers to linear regression where proxy data substitute for missing subject data, ML=maximum likelihood, MI=multiple imputation. Models 2 and 3 without validation data: assume ${\rho }_{\left(\mathit{sp}\right)}^{\left(0\right)}=0.35\mathrm{or}0.70$, λ₂=(−0.26,0.01) or (−0.52,0.02). ${\rho }_{\left(\mathit{sp}\right)}^{\left(0\right)}$ and λ₂ used to derive λ₃. Models V(2) and V(3) with validation data: estimate ${\rho }_{\left(\mathit{sp}\right)}^{\left(0\right)}$ as ${\widehat{\rho }}_{\left(\mathit{sp}\right)}^{\left(1\right)}=0.87$, estimate λ₂ as β̂⁽¹⁾− α̂⁽¹⁾=(0.52,0.04), and use λ₂to derive λ₃.