Table 5.

The comparison of results for effects of treatment and cigarette smoking on visual acuity (letters) change over time in the CAPT study (n = 1052 subjects, 11846 eye visits).

Effect	Time (mons)	Naïve model (ignore inter-ye correlation and longitudinal correlations)		Fixed effects†		Mixed effects§ (Random visit) 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
Visit			<0.0001		<0.0001		<0.0001		<0.0001		<0.0001		<0.0001
	0	(ref)		(ref)		(ref)		(ref)		(ref)		(ref)
	12	−0.78 (0.65)	0.65	−0.88 (0.80)	0.27	−0.88 (0.77)	0.25	−0.86 (1.12)	0.44	−0.86 (0.61)	0.16	−0.78 (0.62)	0.21
	24	−4.27 (1.73)	0.01	−4.63 (1.08)	<0.0001	−4.63 (1.08)	<0.0001	−4.64(1.14)	<0.0001	−4.62 (1.06)	<0.0001	−4.27 (1.11)	0.0001
	36	−6.42 (1.73)	0.0002	−6.79 (1.34)	<0.0001	−6.78 (1.37)	<0.0001	−6.69 (1.14)	<0.0001	−6.68 (1.36)	<0.0001	−6.42 (1.39)	<0.0001
	48	−7.89 (1.76)	<0.0001	−8.50 (1.60)	<0.0001	−8.51 (1.65)	<0.0001	−8.23 (1.16)	<0.0001	−8.19 (1.49)	<0.0001	−7.89 (1.55)	<0.0001
	60	−13.2 (1.77)	<0.0001	−13.5 (1.89)	<0.0001	−13.6 (1.94)	<0.0001	−13.5 (1.17)	<0.0001	−13.5 (1.99)	<0.0001	−13.2 (2.06)	<0.0001
Laser vs. no treatment			0.19		0.01		0.03		0.06		0.03		0.03
	0	0.03 (0.55)	0.96	0.04 (0.23)	0.86	0.03 (0.18)	0.89	0.03 (0.46)	0.96	0.03 (0.18)	0.89	0.03 (0.18)	0.89
	12	0.30 (0.55)	0.59	0.28 (0.34)	0.41	0.28 (0.31)	0.38	0.29 (0.46)	0.54	0.30 (0.31)	0.34	0.30 (0.31)	0.34
	24	1.05 (0.56)	0.06	0.98 (0.43)	0.02	0.98 (0.40)	0.02	1.03 (0.47)	0.03	1.05 (0.40)	0.009	1.05 (0.40)	0.009
	36	1.10 (0.57)	0.054	1.02 (0.52)	0.049	1.04 (0.48)	0.03	1.06 (0.48)	0.03	1.10 (0.49)	0.02	1.10 (0.49)	0.02
	48	0.59 (0.58)	0.31	0.72 (0.60)	0.23	0.73 (0.56)	0.19	0.61 (0.48)	0.21	0.59 (0.56)	0.30	0.59 (0.56)	0.30
	60	−0.19 (0.58)	0.75	−0.25 (0.70)	0.72	−0.25 (0.66)	0.71	−0.21 (0.49)	0.67	−0.19 (0.67)	0.78	−0.19 (0.67)	0.78
Current smoking vs. former/no smoking			0.14		0.003		0.003		0.002		0.01		0.01
	0	1.49 (1.20)	0.21	1.48 (0.63)	0.02	1.49 (0.73)	0.04	1.49 (1.34)	0.27	1.49 (0.65)	0.02	1.49 (0.65)	0.02
	12	2.17 (1.23)	0.08	2.11 (0.96)	0.03	2.11 (1.02)	0.04	2.13 (1.37)	0.12	2.13 (0.81)	0.009	2.17 (0.82)	0.008
	24	0.26 (1.26)	0.84	−0.01 (1.21)	0.99	0.02 (1.27)	0.99	−0.01 (1.38)	0.99	0.01 (1.25)	1.00	0.26 (1.27)	0.84
	36	0.32 (1.25)	0.80	0.19 (1.47)	0.90	0.25 (1.56)	0.87	0.23 (1.38)	0.87	0.24 (1.54)	0.88	0.32 (1.55)	0.84
	48	0.30 (1.20)	0.81	0.29 (1.72)	0.86	0.33 (1.83)	0.86	0.34 (1.40)	0.81	0.35 (1.65)	0.83	0.30 (1.69)	0.86
	60	−2.90 (1.31)	0.03	−2.61 (2.00)	0.19	−2.64(2.12)	0.21	−2.81 (1.41)	0.046	−2.81 (2.11)	0.18	−2.90 (2.17)	0.18
−2lnL		93,445		81,293		81,083		87520
AIC		93,447		81,339		81,191		87526
QIC										11867		11868
QICu										11864		11864
Covariance parameters		1		24		43		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 for both the intercept and the Visit parameter.

^£Generalized estimating equation (GEE) model.

^ΔTime was modelled as categorical with 6 levels (i.e., months 0,12, 24, 36,48, 60) due to the non-linear decline in visual acuity.