Table 7.

The comparison of results from various models for evaluating the factors association with visual acuity among eyes with AMD category 3 at baseline in AREDS Study (N = 1463 subjects, 2334 eyes, 13277 eye visits).

Effect	Naïve Model (ignore inter-ye correlation and longitudinal correlations)		Fixed effects†		Mixed effects§ (Random intercept and slope) Δ		Mixed effects§ (Random intercept)		GEE£ (Compound symmetry)		GEE£ (Working independence)
	Beta (SE)	P-value	Beta (SE)	P-value	Beta (SE)	P-value	Beta (SE)	P-value	Beta (SE)	P-value	Beta (SE)	P-value
Intercept	85.0 (0.35)	<0.0001	84.7 (0.23)	<0.0001	85.0 (0.29)	<0.0001	85.2 (0.46)	<0.0001	85.4 (0.29)	<0.0001	85.0 (0.30)	<0.0001
Treatment Group		0.46		0.21		0.20		0.60		0.15		0.30
Placebo	(ref)		(ref)		(ref)		(ref)		(ref)		(ref)
Antioxidants only	0.02 (0.46)	0.96	0.04 (0.30)	0.90	0.30 (0.38)	0.42	0.17 (0.60)	0.77	0.26 (0.39)	0.51	0.02 (0.40)	0.96
Zinc only	−0.12 (0.46)	0.80	−0.17 (0.30)	0.58	−0.10 (0.38)	0.79	−0.18 (0.60)	0.77	−0.23 (0.39)	0.52	−0.12 (0.39)	0.76
Antioxidants+zinc	−0.63 (0.46)	0.17	−0.53 (0.30)	0.08	−0.51 (0.38)	0.18	−0.60 (0.60)	0.31	−0.59 (0.38)	0.13	−0.63 (0.39)	0.11
Time (Year)	−1.46 (0.12)	<0.0001	−1.39 (0.15)	<0.0001	−1.40 (0.15)	<0.0001	−1.47 (0.08)	<0.0001	−1.46 (0.16)	<0.0001	−1.46 (0.16)	<0.0001
Age (per year)	−0.34 (0.03)	<0.0001	−0.34 (0.02)	<0.0001	−0.34 (0.03)	<0.0001	−0.34 (0.04)	<0.0001	−0.34 (0.03)	<0.0001	−0.34 (0.03)	<0.0001
Hypertension: yes vs. No	−0.59 (0.34)	0.08	−0.39 (0.22)	0.07	−0.48 (0.28)	0.08	−0.55 (0.44)	0.21	−0.59 (0.29)	0.04	−0.59 (0.29)	0.04
Current Smoking: Yes vs. no	−1.99 (0.62)	0.002	−1.80 (0.40)	<0.0001	−1.71 (0.51)	0.0008	−1.67 (0.81)	0.04	−1.50 (0.57)	0.01	−1.99 (0.57)	0.0005
Age*time	−0.08 (0.01)	<0.0001	−0.08 (0.01)	<0.0001	−0.08 (0.01)	<0.0001	−0.08 (0.01)	<0.0001	−0.08 (0.01)	<0.0001	−0.08 (0.02)	<0.0001
Current smoking * time	−0.52 (0.22)	0.02	−0.55 (0.27)	0.04	−0.48 (0.27)	0.08	−0.55 (0.15)	0.0003	−0.55 (0.28)	0.054	−0.52 (0.29)	0.07
Hypertension*time	0.05 (0.11)	0.64	−0.05 (0.14)	0.73	−0.07 (0.15)	0.61	−0.01 (0.08)	0.88	−0.01 (0.15)	0.94	0.05 (0.16)	0.73
Treatment group*time		0.92		0.73		0.75		0.55		0.87		0.96
Placebo	(ref)		(ref)		(ref)		(ref)		(ref)		(ref)
Antioxidants only	−0.03 (0.16)	0.87	−0.16 (0.20)	0.41	−0.15 (0.20)	0.45	−0.06 (0.11)	0.57	−0.06 (0.20)	0.76	−0.03 (0.21)	0.91
Zinc only	−0.01 (0.16)	0.95	−0.02 (0.19)	0.90	−0.03 (0.20)	0.88	−0.01 (0.11)	0.98	−0.01 (0.22)	0.99	−0.01 (0.23)	0.97
Antioxidants+zinc	0.07 (0.16)	0.63	−0.05 (0.20)	0.80	0.06 (0.20)	0.76	0.09 (0.11)	0.39	0.09 (0.21)	0.65	0.08 (0.21)	0.72
−2lnL	96518		84836		85634		91241
AIC	96520		84882		85646		91247
QIC									12814		12825
QICu									12760		12760
Covariance parameters	1		24		5		3		2		0

^†Fixed effects model using SAS PROC MIXED with the REPEATED OPTION with a UN@UN correlation structure.

^§Mixed effects model using SAS PROC MIXED with the RANDOM OPTION with random effects for subject and eye within subject.

^ΔUsing random intercept and slope for the subject level, and random intercept for the eye level.

^£Generalized estimating equation (GEE) model.

Note: Age is normalized using mean age (i.e., age-69).