Socio-Demographic and Clinical Characteristics of Glaucoma Patients
According to Table 1 below, 388 glaucoma patients who had visited Hawassa Referral Hospital at least once a month were followed up while they were blind. In the 388 glaucoma patients evaluated, 172 (44.33%) were lost or transferred out due to unidentified reasons, and the remaining 216 (55.67%) patients had finished their follow-up at the time of this study. In the Hawassa referral hospital, 105 (27.06%) of patients are between the ages of 18 and 43, 219 (56.45%) are between the ages of 44 and 69, and the remaining patients are over the age of 70. Whereas 163 (42.01%) of the patients were male and 225 (57.99%) of the patients were female. According to the type of glaucoma, 123 patients (31.70%) had POAG, 156 patients (40.21%) had PCAG, 79 patients (20.36%) had SOAG, and the remaining 30 patients (7.73) had SCAG.
Table 1
The Distribution of Important Socio-Demographic and Clinical Characteristics of Glaucoma Patients in Hawassa Referral hospital Hawassa, Ethiopia. (n = 388)
No
|
Covariates
|
Categories
|
Number
|
Percent
|
event
|
Present
|
censoring
|
Percent
|
1
|
Age
|
18–43
|
105
|
27.06
|
64
|
29.63
|
41
|
23.84
|
44–69
|
219
|
56.45
|
119
|
55.09
|
100
|
58.14
|
≥ 70
|
64
|
16.49
|
33
|
15.28
|
31
|
18.02
|
2
|
Sex
|
Female
|
225
|
57.99
|
130
|
60.19
|
95
|
55.23
|
Male
|
163
|
42.01
|
86
|
39.81
|
77
|
44.77
|
3
|
Educational level
|
Uneducated
|
104
|
26.80
|
55
|
25.46
|
49
|
28.49
|
primary education
|
158
|
40.72
|
95
|
43.98
|
63
|
36.63
|
Secondary and above
|
126
|
32.47
|
66
|
30.56
|
60
|
34.88
|
4
|
Marital status
|
Married
|
205
|
52.84
|
112
|
51.85
|
93
|
54.07
|
Widowed
|
32
|
8.25
|
21
|
9.72
|
11
|
6.40
|
Single
|
63
|
16.24
|
37
|
17.13
|
26
|
15.12
|
Divorced
|
88
|
22.68
|
46
|
21.30
|
42
|
24.42
|
5
|
Place of residence
|
Urban
|
170
|
43.81
|
102
|
47.22
|
68
|
39.53
|
Rural
|
218
|
56.19
|
114
|
52.78
|
104
|
60.47
|
6
|
Stage of glaucoma of the patient
|
Mild
|
61
|
15.72
|
34
|
15.74
|
27
|
15.70
|
Moderate
|
177
|
45.62
|
97
|
44.91
|
80
|
46.51
|
Advanced
|
114
|
29.38
|
66
|
30.56
|
48
|
27.91
|
Terminal
|
36
|
9.28
|
19
|
8.80
|
17
|
9.88
|
7
|
Type of glaucoma
|
POAG
|
123
|
31.70
|
65
|
30.09
|
58
|
33.72
|
PCAG
|
156
|
40.21
|
85
|
39.35
|
71
|
41.28
|
SOAG
|
79
|
20.36
|
47
|
21.76
|
32
|
18.60
|
SCAG
|
30
|
7.73
|
19
|
8.80
|
11
|
6.40
|
8
|
Family history of glaucoma
|
Yes
|
162
|
41.75
|
89
|
41.20
|
73
|
42.44
|
No
|
226
|
58.25
|
127
|
58.80
|
99
|
57.56
|
9
|
IOP
|
Normal
|
221
|
56.96
|
124
|
57.41
|
97
|
56.40
|
Not Normal
|
167
|
43.04
|
92
|
42.59
|
75
|
43.60
|
10
|
Blood pressure
|
Yes
|
206
|
53.09
|
117
|
54.17
|
89
|
51.74
|
|
No
|
182
|
46.91
|
99
|
45.83
|
83
|
48.26
|
11
|
Diabatic
|
Yes
|
193
|
49.74
|
106
|
49.07
|
87
|
50.58
|
No
|
195
|
50.26
|
110
|
50.93
|
85
|
49.42
|
12
|
CUP-disk ratio
|
\(\le 0.6\)
|
255
|
65.72
|
145
|
67.13
|
110
|
63.95
|
\(>\)0.6
|
133
|
34.28
|
71
|
32.87
|
62
|
36.05
|
13
|
Types of medication
|
Systemic
|
66
|
17.01
|
35
|
16.20
|
31
|
18.02
|
Topical
|
194
|
50.00
|
113
|
52.31
|
81
|
47.09
|
laser therapy
|
76
|
19.59
|
41
|
18.98
|
35
|
20.35
|
Surgical therapy
|
52
|
13.40
|
27
|
12.50
|
25
|
14.53
|
Kaplan Meier survival curve for different types of variables
Figure 1 shows us current the estimated survivorship function and the 95% CI that provide a convenient an expressive measure the overall pattern of the survival time.
In comparison to primary open angle, secondary open angle, and secondary close angle glaucoma, primary close angle glaucoma has a longer survival time, according to Fig. 2's Kaplan Meier curve.
Kaplan-Meier estimates of the survivor functions among different categories of the factors.
Table 2 demonstrates that the log rank was attained in order to assess the importance of the observed variation in the Kaplan-Meier estimations of the survivor functions among various covariate categories. For each categorical covariate, a Kaplan Meier analysis should be performed in a survival study. The variables can be candidate covariates for the multivariable statistical analysis if they are significant at a 25% significant level.
Table 2
Variables
|
Categories
|
event
|
%
|
Censored
|
%
|
Log rank test
|
Chi-square
|
p-value
|
Age
|
18–43
|
64
|
29.63
|
41
|
23.84
|
3.17
|
0.2046
|
44–69
|
119
|
55.09
|
100
|
58.14
|
\(>\)70
|
33
|
15.28
|
31
|
18.02
|
Sex
|
Female
|
130
|
60.19
|
95
|
55.23
|
0.25
|
0.6162
|
Male
|
86
|
39.81
|
77
|
44.77
|
Educational level
|
Uneducated
|
55
|
25.46
|
49
|
28.49
|
1.29
|
0.5250
|
primary education
|
95
|
43.98
|
63
|
36.63
|
Secondary and above
|
66
|
30.56
|
60
|
34.88
|
Marital status
|
Married
|
112
|
51.85
|
93
|
54.07
|
1.45
|
0.6941
|
Widowed
|
21
|
9.72
|
11
|
6.40
|
Single
|
37
|
17.13
|
26
|
15.12
|
Divorced
|
46
|
21.30
|
42
|
24.42
|
Place of residence
|
Urban
|
102
|
47.22
|
68
|
39.53
|
1.30
|
0.2440
|
Rural
|
114
|
52.78
|
104
|
60.47
|
Stage of glaucoma
|
Mild
|
34
|
15.74
|
27
|
15.70
|
0.87
|
0.8338
|
Moderate
|
97
|
44.91
|
80
|
46.51
|
Advanced
|
66
|
30.56
|
48
|
27.91
|
Terminal
|
19
|
8.80
|
17
|
9.88
|
Type of glaucoma
|
POAG
|
65
|
30.09
|
58
|
33.72
|
8.80
|
0.0321
|
PCAG
|
85
|
39.35
|
71
|
41.28
|
SOAG
|
47
|
21.76
|
32
|
18.60
|
SCAG
|
19
|
8.80
|
11
|
6.40
|
Family history
|
Yes
|
89
|
41.20
|
73
|
42.44
|
0.21
|
0.6451
|
No
|
127
|
58.80
|
99
|
57.56
|
IOP
|
Normal
|
124
|
57.41
|
97
|
56.40
|
0.42
|
0.5145
|
Not normal
|
92
|
42.59
|
75
|
43.60
|
Blood pressure
|
Yes
|
117
|
54.17
|
89
|
51.74
|
0.00
|
0.9599
|
No
|
99
|
45.83
|
83
|
48.26
|
Diabatic
|
Yes
|
106
|
49.07
|
87
|
50.58
|
0.80
|
0.3723
|
No
|
110
|
50.93
|
85
|
49.42
|
CUP-disk ratio
|
\(\le 0.6\)
|
145
|
67.13
|
110
|
63.95
|
5.98
|
0.0145
|
\(>\)0.6
|
71
|
32.87
|
62
|
36.05
|
Types of medication
|
Systemic
|
35
|
16.20
|
31
|
18.02
|
11.13
|
0.0110
|
Topical
|
113
|
52.31
|
81
|
47.09
|
laser therapy
|
41
|
18.98
|
35
|
20.35
|
Surgical therapy
|
27
|
12.50
|
25
|
14.53
|
Table 3
Tests of the proportional hazard assumption by using global test.
variables
|
Categorical
|
rho
|
Chi-square
|
df
|
p-value
|
Age
|
18–43 (ref)
|
|
|
1
|
|
44–69
|
0.17342
|
4.92
|
1
|
0.0265
|
\(> 70\)
|
0.27576
|
11.60
|
1
|
0.0007
|
Place of residence
|
Rural (ref)
|
|
|
1
|
|
Urban
|
0.05231
|
0.46
|
1
|
0.4957
|
Type of glaucoma
|
POAG (ref)
|
|
|
1
|
|
PCAG
|
-0.14233
|
3.69
|
1
|
0.0547
|
SOAG
|
-0.01547
|
0.04
|
1
|
0.8359
|
SCAG
|
0.05764
|
0.57
|
1
|
0.4497
|
CUP-disk ratio
|
\(\le 0.6\)(ref)
|
|
|
1
|
|
\(>\)0.6
|
0.02961
|
0.15
|
1
|
0.6992
|
Types of medication
|
Systemic (ref)
|
|
|
1
|
|
Topical
|
-0.04133
|
0.29
|
1
|
0.5934
|
laser therapy
|
-0.04106
|
0.29
|
1
|
0.5900
|
Surgical therapy
|
-0.10631
|
2.11
|
1
|
0.1465
|
Global Test
|
19.71
|
10
|
0.0321
|
We confirmed or accepted the PH assumption when we noticed from the above table that the p-values of the five covariates, whereas residency, glaucoma type, CUP-disk ratio, and type of medicine were statically not significant at 5% alpha level of significance. However, just one covariate age was statistically significant at 5% alpha levels; as a result, we either stratified by age or used an AFT model to reject the PH assumption. The graphical technique is also verified using the value of the global test, which is less than 5% levels of significant. Plots of the scaled Schoenfeld residuals against the survival time for each covariate are displayed graphically. The Schoenfeld residuals plot reveals that the slop is zero and that the covariates' random distribution included residency, glaucoma type, CUP-disk ratio, and kind of medicine. But because the smoothed curve is not horizontal and age visibly grew or exceeded over time, the global test did not satisfy the PH assumption. We applied the parametric accelerated failure time model in this instance.
Model Comparison
Table 4: displays the log likelihood, AIC, and BIC values for the fit of the five most frequently used parametric models and the cox proportional hazard model. The AIC and BIC values with the least values were Gamma AFT, as seen in the table above. Because of this, the gamma AFT model in the Hawassa referral hospital has the best fit model for the response of time to blindness.
Table 4
Comparison of the parametric model by using Akaike’s information criterion, Bayesian information criterion and log-likelihood.
model
|
Df
|
log-likelihood
|
AIC value
|
BIC value
|
Exponential
|
11
|
-325.26864
|
672.5373
|
716.1083
|
Weibull
|
12
|
-241.1239
|
506.2478
|
553.7799
|
Log-normal
|
12
|
-228.06298
|
480.126
|
527.658
|
Log-logistic
|
12
|
-231.71548
|
487.431
|
534.963
|
Gamma AFT
|
13
|
-226.51117
|
479.0223
|
530.5154
|
Multivariable analysis
The idea that a group of factors, each of which is only weakly related to the outcome, could become a significant predictor of the outcome when combined is disregarded by the univariable analytic technique. All factors that were determined to be significant at the 0.25 level of significance in the log rank or univariable analysis are included in the multivariable analysis.
The Table 5 shows that 95% confidence interval (CI) and the variable age, place of residence and types of medication were statistically significance at 5% levels of alpha. In this case as the age of the patient for keeping other covariates constant, the age survival time of glaucoma patient whose age between (44–69), 1.232091 times more likely than the glaucoma patient whose age between (18–43), the patient age > 70 the glaucoma 1.325534 times than compare with the age between 18–43.
Table 5
Multivariable for Gamma AFT model results
Covariates
|
Category
|
Gamma regression for AFT
|
Tm. Ratio
|
Std. Err.
|
P>|z|
|
[95% Conf. Interval]
|
Age
|
18–43(ref)
|
|
|
|
|
44–69
|
1.232091
|
.1013636
|
0.011
|
1.048611 1.447674
|
\(> 70\)
|
1.325534
|
.1657193
|
0.024
|
1.037464 1.693592
|
Place of residence
|
Rural(ref)
|
|
|
|
|
Urban
|
1.147198
|
.0747917
|
0.035
|
1.009588 1.303565
|
Type of glaucoma
|
POAG (ref)
|
|
|
|
|
PCAG
|
.957694
|
.0746927
|
0.579
|
.8219391 1.115871
|
SOAG
|
1.095927
|
.1033003
|
0.331
|
.9110639 1.318301
|
SCAG
|
1.519226
|
.2157134
|
0.003
|
1.150167 2.006705
|
CUP-disk ratio
|
\(\le 0.6\)(ref)
|
.
|
.
|
.
|
.
|
\(>\)0.6
|
1.036853
|
.085358
|
0.660
|
.8823537 1.218405
|
Types of medication
|
Systemic (ref)
|
.
|
.
|
.
|
.
|
Topical
|
1.275537
|
.1121765
|
0.006
|
1.07358 1.515484
|
laser therapy
|
1.25966
|
.1377205
|
0.035
|
1.016694 1.560689
|
Surgical therapy
|
.9857047
|
.118008
|
0.904
|
.7795455 1.246385
|
Types of medication: for keeping the other covariates constant, the survival time of time to blind for Topical medication 1.275537 times than Systemic and laser therapy medication 1.25966 times than systemic medication.