3.1. Patients Characteristic
Out of the 509 patients with COVID-19 included in this study, 29.86% (152) of them were cured while the rest 70.14% (357) were censored. In this case, all censored instances considered to be right-censored, which means they either died or didn’t recover and were still undergoing treatment by March 24, 2020. The average time of a patient stay in the hospital was 7.86±6.46 days. In addition, 60.12% (306) of patients were male, while 39.88% (203) were female. The average age of male patients was 42.86 (±16.46) years, while for female patients its was 43.48(±16.85) years.
Table 2: Demographic characteristics of the COVID-19 cases in Singapore
Characteristics
|
N (%)
|
Mean
|
SD
|
Age (year)
|
Male
|
306 (60.12)
|
42.86
|
16.46
|
Female
|
203 (39.88)
|
43.48
|
16.85
|
Total
|
509 (100)
|
43.11
|
16.60
|
Time (day)
|
Male
|
306 (60.12)
|
7.83
|
6.72
|
Female
|
203 (39.88)
|
7.90
|
6.07
|
Total
|
509 (100)
|
7.86
|
6.46
|
Age (year)
|
Singaporean
|
369 (72.50)
|
43.47
|
17.04
|
Others
|
140 (27.50)
|
42.16
|
15.42
|
Total
|
509 (100)
|
43.11
|
16.60
|
Time (day)
|
Singaporean
|
369 (72.50)
|
7.48
|
6.33
|
Others
|
140 (27.50)
|
8.84
|
6.71
|
Total
|
509 (100)
|
7.86
|
6.46
|
The BIC criterion for the Normal and Logistic models were 1248.55 and 1239.55, respectively, which are the highest among all parametric models. For the Exponential model, the BIC criterion was 620.31. Moreover, the BIC criterion for the Log-Normal, Generalized Gamma, and Weibull models were 491.32, 489.23, and 489.13, respectively. The Log-Logistic model had the lowest BIC with the value of 481.90, which infer that this model has a better fit to this data (Table 2). Based on the plot of predicted probabilities against recovery time using Log-Logistic distribution, it's clearly inferred that the Log-Logistic regression model had a better fit to the data (Figure 1).
Table 3: Comparison of the BIC between Parametric Models
Model
|
Number of Parameters
|
BIC
|
Exponential
|
4
|
620.31
|
Weibull
|
5
|
489.13
|
Logistic
|
5
|
1239.55
|
Log-Logistic
|
5
|
481.90
|
Normal
|
5
|
1248.55
|
Log-Normal
|
5
|
491.32
|
Generalized Gamma
|
5
|
489.23
|
3.2. Log-Logistic Accelerated Failure Time (AFT) Model
(See Log-Logistic Accelerated Failure Time (AFT) Model in the Supplementary Files)
3.4. Modeling the Recovery Time using Log-Logistic Distribution
Based on the multiple Log-Logistic regression model, after adjusting other factors, the hazard ratio of age is 1.01 (95% CI: 1.01, 1.01), which is statistically significant at the level of 5%. Similarly, the hazard ratio of nationality was 0.76 and significant (95% CI: 0.64, 0.91). The only insignificant factor was the gender of patients (HR = 0.91, 95% CI: 0.78, 1.07).
Table 4: Diagnostic Factors of the COVID-19 Cases Using Multiple Log-Logistic Regression Model
Parameters
|
HR
|
Chi-Square
|
P-value
|
95% CI HR
|
Intercept
|
9.26
|
277.71
|
0.00
|
7.13
|
12.03
|
Age
|
1.01
|
10.66
|
0.00
|
1.00
|
1.01
|
Gender
|
|
|
|
|
|
Female
|
0.91
|
1.22
|
0.27
|
0.78
|
1.07
|
Male (Reference)
|
|
|
|
|
|
Nationality
|
|
|
|
|
|
Singaporean
|
0.76
|
9.21
|
0.00
|
0.64
|
0.91
|
Non-Singaporean (Reference)
|
|
|
|
|
|