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. Author manuscript; available in PMC: 2021 May 26.
Published in final edited form as: Ophthalmic Epidemiol. 2020 Aug 2;28(1):3–20. doi: 10.1080/09286586.2020.1786590

Table 9.

The comparison of results from various models for evaluating the factors association with visual acuity among randomly selected 200 participants in eyes with AMD category 3 at baseline in AREDS Study (N = 200 subjects, 314 eyes, 1799 eyes visits).

Naïve Model
(ignore inter-ye correlation and longitudinal correlations)
 Fixed effects†
 Mixed effects§
(Random intercept and slope)
 Mixed effects
(Random intercept)
 GEE£
(Compound symmetry)
 GEE£
(Working independence)
Effect   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 83.4 (0.93) <0.0001 83.0 (0.63) <0.0001 83.2 (0.79) <0.0001 83.5 (1.19) <0.0001 83.7 (0.75) <0.0001 83.4 (0.83) <0.0001
Treatment Group   0.44   0.11   0.19   0.65   0.23   0.44
Placebo    (ref)    (ref)    (ref)    (ref)    (ref)    (ref)
Antioxidants only   0.48 (1.24)   0.70   1.10 (0.85)   0.19   1.39 (1.06)   0.19   0.79 (1.60)   0.62   1.03 (1.08)   0.34   0.48 (1.17)   0.68
Zinc only   1.88 (1.23)   0.13   1.87 (0.84)   0.03   2.14 (1.06)   0.04   1.91 (1.59)   0.23   1.92 (0.94)   0.04   1.88 (0.99)   0.06
Antioxidants+zinc   1.28 (1.24)   0.30   1.68 (0.84)   0.048   1.75 (1.06)   0.10   1.46 (1.60)   0.36   1.52 91.08)   0.16   1.28 (1.14)   0.26
Time (Year) −1.33 (0.32) <0.0001 −1.14 (0.42)   0.007 −1.27 (0.44)   0.004 −1.32 (0.24) <0.0001 −1.31 (0.35)   0.0002 −1.33 (0.37)   0.0004
Age (per year) −0.32 (0.08)   0.0001 −0.35 (0.06) <0.0001 −0.32 (0.07) <0.0001 −0.31 (0.11)   0.004 −0.31 (0.08)   0.0001 −0.32 (0.08) <0.0001
Hypertension: yes vs. No −1.33 (0.93)   0.15 −0.79 (0.63)   0.21 −0.93 (0.80)   0.24 −1.25 (1.20)   0.30 −1.34 (0.85)   0.12 −1.33 (0.89)   0.13
Current Smoking: Yes vs. no   2.11 (1.79)   0.24   1.23 (1.21)   0.31   2.18 (1.52)   0.15   2.78 (2.29)   0.23   2.78 (2.12)   0.19   2.11 (2.17)   0.33
Age*time −0.09 (0.03)   0.002 −0.09 (0.04)   0.01 −0.09 (0.04)   0.03 −0.09 (0.02) <0.0001 −0.09 (0.04)   0.02 −0.09 (0.04)   0.03
Current smoking * time −1.04(0.63)   0.10 −0.86 (0.79)   0.28 −1.03 (0.82)   0.21 −1.34 (0.47)   0.004 −1.33 (1.13)   0.24 −1.04(1.21)   0.39
Hypertension*time   0.65 (0.32)   0.04   0.27 (0.41)   0.51   0.21 (0.43)   0.63   0.44 (0.23)   0.06   0.45 (0.35)   0.20   0.65 (0.37)   0.08
Treatment group*time   0.31   0.39   0.55   0.12   0.62   0.59
Placebo    (ref)    (ref)    (ref)    (ref)    (ref)    (ref)
Antioxidants only −0.18 (0.43)   0.68 −0.74 (0.56)   0.19 −0.58 (0.58)   0.32 −0.29 (0.32)   0.37 −0.28 (0.53)   0.59 −0.18 (0.56)   0.75
Zinc only −0.58 (0.42)   0.16 −0.66 (0.54)   0.23 −0.52 (0.57)   0.36 −0.55 (0.31)   0.07 −0.55 (0.56)   0.32 −0.58 (0.58)   0.31
Antioxidants+zinc   0.16 (0.43)   0.71 −0.05 (0.55)   0.93   0.08 (0.58)   0.90   0.11 (0.31)   0.72   0.11 (0.47)   0.81   0.16 (0.49)   0.74
−2lnL  12809  11358  11546  12212
AIC  12811  11403  11559  12218
QIC  1766  1777
QICu  1714  1714
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.

Δ

Using 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).