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Original Article
Estimation of the onset time of diabetic complications in type 2 diabetes patients in Thailand: a survival analysis
Natthanicha Sauenramorcid, Jutatip Sillabutraorcid, Chukiat Viwatwongkasemorcid, Pratana Satitvipaweeorcid
Osong Public Health and Research Perspectives 2023;14(6):508-519.
DOI: https://doi.org/10.24171/j.phrp.2023.0084
Published online: November 23, 2023
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Department of Biostatistics, Faculty of Public Health, Mahidol University, Bangkok, Thailand

Corresponding author: Jutatip Sillabutra Department of Biostatistics, Faculty of Public Health, Mahidol University, Ratchawithi Road, Ratchathewi, Bangkok 10400, Thailand E-mail: jutatip.sil@mahidol.edu
• Received: March 31, 2023   • Revised: September 14, 2023   • Accepted: October 11, 2023

© 2023 Korea Disease Control and Prevention Agency.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

  • Objectives
    This study aimed to identify factors associated with the onset time of diabetic complications in patients with type 2 diabetes mellitus (T2DM) and determine the best-fitted survival model.
  • Methods
    A retrospective cohort study was conducted among T2DM patients enrolled from October 1, 2016 to July 15, 2020 at the National Health Security Office (NHSO). In total, 388 T2DM patients were included. Cox proportional-hazard and parametric models were used to identify factors related to the onset time of diabetic complications. The Akaike information criterion, Bayesian information criterion, and Cox-Snell residual were compared to determine the best-fitted survival model.
  • Results
    Thirty diabetic complication events were detected among the 388 patients (7.7%). A 90% survival rate for the onset time of diabetic complications was found at 33 months after the first T2DM diagnosis. According to multivariate analysis, a duration of T2DM ≥42 months (time ratio [TR], 0.56; 95% confidence interval [CI], 0.33–0.96; p=0.034), comorbid hypertension (TR, 0.30; 95% CI, 0.15–0.60; p=0.001), mildly to moderately reduced levels of the estimated glomerular filtration rate (eGFR) (TR, 0.43; 95% CI, 0.24–0.75; p=0.003) and an eGFR that was severely reduced or indicative of kidney failure (TR, 0.38; 95% CI, 0.16–0.88; p=0.025) were significantly associated with the onset time of diabetic complications (p<0.05).
  • Conclusion
    Patients with T2DM durations of more than 42 months, comorbid hypertension, and decreased eGFR were at risk of developing diabetic complications. The NHSO should be aware of these factors to establish a policy to prevent diabetic complications after the diagnosis of T2DM.
Diabetes refers to metabolic diseases characterized by hyperglycemia, which results from defects in insulin secretion, insulin action, or both [1]. As of 2021, the global prevalence of diabetes among individuals aged 20 to 79 was estimated to be 10.5% (95% confidence interval [CI], 8.3%–12.0%), and this figure is projected to rise to 12.2% (95% CI, 9.5%–14.0%) by 2045. In the Western Pacific region, the prevalence of diabetes was 11.9% (95% CI, 10.1%–13.5%), and it is expected to increase to 14.4% (95% CI, 12.1%–16.4%) by 2045 [2]. In Thailand, the prevalence of diabetes was estimated to be 9.7% among individuals aged 20 to 79 years in 2021 [3]. In 2019, the International Diabetes Federation Atlas reported that 4.2 million people died from diabetes, corresponding to approximately 11.3% of deaths from all causes [4].
Type 2 diabetes mellitus (T2DM) accounts for over 90% of all diabetes mellitus cases and is characterized by impaired insulin secretion from pancreatic islet β-cells, tissue insulin resistance, and an insufficient compensatory insulin secretion response [5]. In 2017, T2DM was prevalent in approximately 6.28% of the global population, corresponding to a rate of 6,059 cases per 100,000 individuals. This figure is projected to increase to 7,079 cases per 100,000 individuals by 2030 [6]. The incidence and prevalence of T2DM continue to rise, and uncontrolled blood glucose levels in patients can result in long-term complications.
An observational study conducted across 28 countries in Asia, Africa, South America, and Europe found that 50% of patients with T2DM experienced microvascular complications, while 27% experienced macrovascular complications [7]. A prospective study of Thai T2DM patients revealed a prevalence of 38.3% for diabetic nephropathy, 23.7% for retinopathy, and over 15% for foot problems [8]. Numerous studies have highlighted significant factors contributing to diabetic complications in T2DM patients. These include age, sex, body mass index (BMI), smoking habits, family history of diabetes, duration of diabetes, ethnic group, hyperglycemia, hypertension, and hypercholesterolemia [912]. Additionally, several studies have found that screening for foot and eye issues could delay the onset of diabetes-related complications [1315].
Survival analysis is a statistical method employed to examine the time leading up to a failure event or the conclusion of a study, and it can be instrumental in identifying risk factors [16]. Regression models, such as Cox proportional hazard (PH) and parametric models, can be used to estimate the time until the occurrence of a failure event [17].
The primary assumption of the PH model is that the hazard ratio is constant over time. In contrast, parametric models are capable of modeling survival times, even when the PH assumption is not met, due to their assumption of a specific distribution for the outcome variable [18,19]. This study focused on parametric models, including Weibull and log-normal accelerated failure time (AFT). The characteristics of the hazard function for these 2 models are as follows: (1) the Weibull model can either increase or decrease with increasing survival time, and (2) the log-normal model can increase, decrease, or invert [20]. These models are also suitable for fitting diabetes data.
This study compared the performance of Cox PH, Weibull, and log-normal AFT models to identify factors associated with the onset time of diabetic complications in patients with T2DM. The best-fitted survival model was also determined.
This study was structured as a retrospective cohort study. We collected secondary data from diabetes patients, spanning from October 1, 2016 to July 15, 2020, from the National Health Security Office (NHSO) database. We selected patients who were first diagnosed with T2DM between October 1, 2016, and September 30, 2017. Patients with incomplete laboratory data, such as fasting blood glucose (FBG), hemoglobin A1c (HbA1c), total triglycerides (TG), low-density lipoprotein cholesterol (LDL-C), and estimated glomerular filtration rate (eGFR), were excluded. Additionally, we excluded patients who had a history of health issues related to complications. The final dataset for analysis consisted of 388 records from T2DM patients with complete data.
Using the survival analysis formula [21], it was established that the data collected in this study constituted a suitable sample size.
With the alpha error set to 95% and a power of 90%, a hazard ratio of 0.726 for developing neuropathy for patients with and without hypertension [22], the minimum sample size was determined to be 329.
Data from the NHSO database, comprising 388 entries, were analyzed. The variables considered included sex, age, age at T2DM diagnosis, duration of T2DM, BMI, comorbidity with hypertension, foot and retina examinations, FBG, HbA1c, TG, LDL-C, eGFR, and diabetic complications such as nephropathy, retinopathy, neuropathy, and peripheral vascular disease.
The onset time of diabetic complications was defined as the duration, in months, between the diagnosis of T2DM and the development of complications. Clinical complications such as nephropathy, retinopathy, neuropathy, and peripheral vascular disease were diagnosed by a physician and documented in the NHSO database. Patients were categorized into 2 groups: those with diabetic complication events and those with censored data.
The other variables were defined as independent variables. Sex was categorized into 2 groups: male and female. Age was categorized into 3 groups: ≤49 years, 50 to 59 years, and ≥60 years [23]. Age at the diagnosis of T2DM was categorized into 2 groups: <35 years and ≥35 years. The duration of T2DM was categorized into 2 groups: <42 months and ≥42 months. BMI was categorized into 4 groups according to the Asian criteria: underweight (<18.5 kg/m2), normal (18.5–22.9 kg/m2), overweight (23–24.9 kg/m2), and obese (≥25 kg/m2) [24]. Comorbid hypertension was dichotomized as yes and no. Whether foot examinations or retina examinations had been performed was also categorized into 2 groups: yes and no. FBG was categorized into 2 groups: <130 mg/dL and ≥130 mg/dL. HbA1c was categorized into 2 groups: <7% and ≥7%. TG was also dichotomized as <150 mg/dL and ≥150 mg/dL. LDL-C was categorized into 2 groups: <100 mg/dL and ≥100 mg/dL. eGFR was categorized into 3 groups: normal to mild decline (>60 mL/min/1.73 m2), mild to moderate decline (30–59 mL/min/1.73 m2), and severe decline to kidney failure (<30 mL/min/1.73 m2) [2527].
Model Estimation
The Kaplan-Meier (KM) technique is a nonparametric survival probability estimator for observations of both censored data and events of interest [28]. The KM estimator of a survival function S(t)=P(Tt) is given by
S^(t)=i=1k(1dini)
Where di is the observed number of events at time ti and ni is number of individuals at risk at time ti.
The Cox PH model is the most widely used multivariate statistical model for survival analysis [29]. The Cox PH is a semi-parametric model, where the baseline hazard can be described as follows:
hi(t|x)=h0(t)exp(βx)
Where h0(t) is the baseline hazard function and Xi is a vector of covariates and β is a vector of parameters for effect of the predictors.
Two types of graphical techniques are used to evaluate the PH assumption. The first is the ln(-ln(s(t))) plot, where parallel curves indicate that the PH hypothesis has not been violated. The second technique involves the KM and predicted survival plot. If the observed and predicted survival curves are closely aligned, it suggests that the PH assumption has not been violated. After fitting a Cox model, we can also test using Schoenfeld residuals. In this case, there was no evidence to suggest that the PH assumption was violated (p>0.05) [30].
An alternative to the Cox model is a parametric survival model, which assumes a specific form for the survival distribution. The models most frequently used are the Weibull and log-normal models. The AFT model posits that the effect of covariates multiplies with survival time [31]. In this study, we used the Weibull and log-normal AFT models for evaluation within the parametric model. The distribution of time to event, represented as T, as a function of a single covariate, is expressed as follows:
log(T)=β0+β1x+σε
Where β1 is the coefficient for corresponding covariate, ε follows the extreme minimum value distribution G(0, σ), and σ is the shape parameter [32].
Data Analysis
All data were cleaned to ensure completeness and consistency. The variables were categorized based on the criteria used to determine the reference group, as derived from the literature review, and were then exported to STATA statistical software ver. 17.0 (STATA Corp.). Descriptive statistics were employed to outline the characteristics of the sample. The KM method was used to estimate the survival experience of patients across different groups, represent median time, and estimate percentiles across various time scales [33]. The log-rank test was utilized to compare survival times between subgroups within each variable. Factors associated with diabetic complication events were examined using univariate and multivariate analysis, based on the Cox PH, Weibull, and log-normal AFT models, in order to identify the most fitting model. The best-fitted survival model was determined by comparing the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The model with the lowest AIC and BIC values was selected. The Cox-Snell residuals were used to assess the overall fit of the model.
Ethics Approval
All procedures conducted in the studies received ethical approval from the Faculty of Public Health, Mahidol University, Thailand (No: MUPH 45/2021). The Committee for Human Research Ethics granted an exemption for this research under protocol number MUPH 45/2021. The research complied with the non-disclosure agreement with the National Health Security Office.
Characteristics of Study Participants
Of the 388 newly diagnosed T2DM patients, 250 (64.4%) were women. The average age of the patients was 61±12 years, with ages ranging from 18 to 94 years. The majority of patients (n=376, 96.9%), were diagnosed with T2DM at or after the age of 35 and had been living with T2DM for less than 42 months, accounting for 319 (82.2%) of the patients. Half of the patients (n=195, 50.3%), were classified as obese. Most patients (n=357, 92.0%), did not have comorbid hypertension. The number of patients who had not undergone foot and retinal examinations was 296 (76.3%) and 323 (83.2%), respectively. More than half of the patients (n=236, 60.8%), had an FBG level of 130 mg/dL or higher, and 244 (62.9%) had an HbA1c level of 7% or higher. Furthermore, 205 (52.8%) had TG levels of 150 mg/dL or higher. Three-quarters of the patients (n=292, 75.3%), had LDL-C levels of 100 mg/dL or higher. The majority of patients (n=290, 74.7%), had normal to mildly decreased eGFR (>60 mL/min/1.73 m2) (Table 1).
Overall Survival to the Onset of Diabetic Complications in T2DM Patients by the KM Method
Patients with T2DM were followed for a median period of 37 months, ranging from 4 to 43 months. Throughout the study, the incidence rate of diabetic complications was 2.5 cases (95% CI, 0.17–0.36) per 1,000 person-months. The incidence rates for specific complications such as retinopathy, peripheral vascular disease, nephropathy, and neuropathy were 6.35 (95% CI, 3.17–12.70), 4.76 (95% CI, 0.67–33.81), 4.19 (95% CI, 2.71–6.50), and 3.13 (95% CI, 0.44–22.18) cases per 100 person-months, respectively.
By the conclusion of the study, the number of patients experiencing diabetic complication events was below the 50th percentile—that is, the median onset time for diabetic complications could not be determined. It was observed that after 33 months, patients with T2DM had a survival probability of 0.90, indicating a survival rate of 90% until the study’s end (Figure 1). The cumulative probabilities of experiencing diabetic complications among T2DM patients at 12, 24, and 36 months were 0.0131, 0.0492, and 0.1010, respectively.
Predictors of Diabetic Complications in T2DM Patients
The log-rank test revealed factors significantly related to the onset time of diabetic complications in patients with T2DM. These factors included the duration of T2DM, comorbidity with hypertension, and eGFR (p<0.05). Other factors, however, were found to be insignificant (Table 2).
The results of the univariate analysis for the Cox PH, Weibull, and log-normal AFT models are presented in Table 3. In all 3 models, variables such as age, duration of T2DM, comorbid hypertension, HbA1c, LDL-C, and eGFR were found to be significant (p<0.10).
Multivariate analysis utilizing the Cox PH, Weibull, and log-normal AFT models revealed that the duration of T2DM, the presence of hypertension, and eGFR values were significant predictors of the onset time for diabetic complications in T2DM patients (p<0.05) (Table 4).
The results of the univariate and multivariate analyses did not differ between the Cox PH, Weibull, and log-normal AFT models. However, the AIC and BIC values of these models suggested that the log-normal AFT model was the most suitable for explaining the onset time of diabetic complications in patients with T2DM (Table 5). Similarly, the Cox-Snell residuals from the 3 models indicated that the log-normal AFT model closely aligned, with a straight line at a 45° angle (Figure 2).
This study’s findings revealed that the KM method could not estimate the median time of diabetic complications.
The 90% survival rate for the onset time of diabetic complications in patients with T2DM was observed at 33 months of follow-up. This is consistent with a study conducted in southern Lithuania, which reported a survival rate of 93% at 2 years, decreasing to 41% over 13 years of living with diabetes [34]. A study in Northwest Ethiopia [35] found that the median time to develop microvascular complications was 30 months, and in Iran [36], the median time until retinopathy was 58 months. A multivariate analysis of the model for the onset time of diabetic complications in T2DM patients revealed that a duration of T2DM exceeding 42 months, the presence of comorbid hypertension, and eGFR levels (ranging from mildly to moderately decreased and severely decreased to kidney failure) were identified as factors associated with diabetic complications (p<0.05).
The duration of T2DM was significantly associated with diabetic complications (p=0.001), a finding that aligns with other studies [3740]. Among patients with diabetic complications, the median duration of T2DM was approximately 3 years, a figure lower than that reported by Zoungas et al. [41]. They discovered that a diabetes duration of 5 years or longer was linked to an increased risk of both macrovascular and microvascular complications. Our results indicated a shorter survival time for diabetic complications in patients with a T2DM duration of 42 months or longer, compared to those with a duration of less than 42 months, by about 44%. A similar study conducted in Northwest Ethiopia [42] found that a duration of less than 4 years was a significant predictor of diabetic neuropathy in patients with T2DM.
The findings suggest that patients with comorbid T2DM and hypertension are at a heightened risk of diabetic complications. This aligns with research conducted in Ethiopia [43,44], Indonesia [45], and Taiwan, which also found an increased risk of major diabetic foot complications and cardiovascular events in T2DM patients with hypertension [46]. The study revealed that the time from onset to diabetic complications in T2DM patients with hypertension is estimated to be 70% shorter than in patients without hypertension. This could be due to hyperglycemia causing a systemic increase in blood pressure by expanding the volume of circulating fluid. Additionally, the progression of vascular remodeling can increase peripheral artery resistance, contributing to hypertension [47]. Therefore, T2DM patients with hypertension tend to develop diabetic complications more rapidly than those without hypertension (p<0.001).
A reduction in the GFR signifies a decrease in hyperfiltration, a process that initiates diabetic nephropathy [48]. This study found that the level of eGFR is a significant factor in diabetic complications (p<0.05), a result that aligns with other studies conducted in China and Japan. The influence of undiagnosed diabetes mellitus was also assessed, identifying the eGFR as a risk factor for the development of diabetic kidney disease [4951]. The estimated survival time for patients with T2DM and eGFR levels ranging from mildly to moderately decreased to kidney failure (G3a to G5) is shorter than that of patients with a normal eGFR and those with a mildly decreased eGFR, at 57% and 62% respectively. Consequently, a decreased eGFR can lead to the rapid progression of diabetic nephropathy and cardiovascular diseases [52,53].
The AIC and BIC values were utilized to compare models and identify the best-fitted survival model [36,5456], and a Cox-Snell residual plot was used to assess whether the overall model fit the data [20,57,58] for semi-parametric and parametric models. This study found that the log-normal AFT model had the lowest AIC and BIC values. Additionally, in the Cox-Snell residual plot, the lines were closely aligned with a straight line at a 45° angle. Consequently, the log-normal AFT model was determined to be the best-fitted survival model for explaining the onset time of diabetic complications in patients with T2DM, compared to other models. Parametric models provide more informative and precise estimates when the distribution is accurately specified, as compared to the Cox model [32,59].
This study adhered to recommendations for data handling to estimate and reduce right-censored data in a precise manner. Diabetes mellitus is a chronic disease influenced by individuals’ behavior. Therefore, behavioral factors (smoking and alcohol drinking) and other comorbid factors should be added in future studies to identify risk factors for the onset time of diabetic complications.
This study found that the duration of T2DM, the presence of hypertension, and the eGFR were factors associated with the onset of diabetic complications in patients with T2DM. It is crucial for the NHSO to consider these factors, as identified by the most suitable survival model, in order to formulate and implement policies aimed at preventing the development of diabetic complications.
The log-normal AFT model proved to be more effective and suitable for our type 2 diabetes dataset than the Cox PH model. Based on the AIC and BIC values, as well as the Cox-Snell residual plot, the log-normal AFT parametric model was identified as the best-fitting survival model. This model most accurately explains the onset time of diabetic complications in patients with T2DM.
• Within 33 months, the survival rate for the onset of diabetic complications in patients with type 2 diabetes mellitus (T2DM) was 90%.
• The duration of T2DM, comorbid hypertension, and estimated glomerular filtration rate were identified as factors associated with the onset time of diabetic complications in patients with T2DM.
• A log-normal accelerated failure time (AFT) model was more effective and appropriate to our type 2 diabetes dataset than a Cox proportional-hazard model.
• The log-normal AFT model was the best-fitted survival model to explain the onset time of diabetic complications in patients with T2DM.

Ethics Approval

This study was approved by the Institutional Review Board of the Faculty of Public Health, Mahidol University, Thailand (No: MUPH 45/2021) and performed in accordance with the principles of the Declaration of Helsinki. The informed consent was waived because of the retrospective nature of this study.

Conflicts of Interest

The authors have no conflicts of interest to declare.

Funding

None.

Availability of Data

The datasets are not publicly available due to privacy or ethical restrictions according to the data sharing agreement with the National Health Security Office.

Authors’ Contributions

Conceptualization: all authors; Data curation: NS, JS; Formal analysis: NS, JS; Investigation: NS, JS; Methodology: all authors; Project administration: NS, JS; Supervision: JS, CV, PS; Validation: JS, CV, PS; Visualization: NS; Writing–original draft: NS, JS; Writing–review & editing: all authors. All authors read and approved the final manuscript.

Acknowledgements
This research work was supported by type 2 diabetes data from the National Health Security Office (NHSO).
Figure 1.
Overall Kaplan-Meier survival curve of 388 type 2 diabetes patients.
j-phrp-2023-0084f1.jpg
Figure 2.
Cox-Snell residual plots for assessing the goodness of fit of (A) the Cox proportional hazards (PH) model, (B) the Weibull accelerated failure time (AFT) model, and (C) the log-normal AFT model.
j-phrp-2023-0084f2.jpg
j-phrp-2023-0084f3.jpg
Table 1.
Characteristics of T2DM patients in 2020
Characteristic No. of diabetic complications (n=30) No. of censored data points (n=358) Total (n=388)
Sex
 Male 11 127 138 (35.6)
 Female 19 231 250 (64.4)
Age (y)
 ≤49 2 56 58 (14.9)
 50–59 10 92 102 (26.3)
 ≥60 18 210 228 (58.8)
Age at the diagnosis of T2DM (y)
 <35 1 11 12 (3.1)
 ≥35 29 347 376 (96.9)
Duration of T2DM (mo)
 <42 17 302 319 (82.2)
 ≥42 13 56 69 (17.8)
Body mass index
 Underweight 1 12 13 (3.4)
 Normal 11 90 101 (26.0)
 Overweight 4 75 79 (20.4)
 Obese 14 181 195 (50.3)
Comorbid hypertension
 No 23 334 357 (92.0)
 Yes 7 24 31 (8.0)
Foot examination
 No 21 275 296 (76.3)
 Yes 9 83 92 (23.7)
Retina examination
 No 25 298 323 (83.2)
 Yes 5 60 65 (16.8)
FBG (mg/dL)
 <130 9 143 152 (39.2)
 ≥130 21 215 236 (60.8)
HbA1c (%)
 <7 14 130 144 (37.1)
 ≥7 16 228 244 (62.9)
TG (mg/dL)
 <150 16 167 183 (47.2)
 ≥150 14 191 205 (52.8)
LDL-C (mg/dL)
 <100 6 90 96 (24.7)
 ≥100 24 268 292 (75.3)
eGFR (mL/min/1.73 m2)
 Normal to mild decrease (>60) 16 274 290 (74.7)
 Mild to moderate decrease (30–59) 10 68 78 (20.1)
 Severe decrease to kidney failure (<30) 4 16 20 (5.2)

Data are presented as n or n (%).

T2DM, type 2 diabetes mellitus; FBG, fasting blood glucose; HbA1c, hemoglobin A1c; TG, triglycerides; LDL-C, low-density lipoprotein cholesterol; eGFR, estimated glomerular filtration rate.

Table 2.
Comparison of the survival probability for the onset time of diabetic complications in T2DM patients using the Kaplan-Meier and log-rank tests
Variable Survival probability at 36 months (95% CI) Log-rank test
X2 p
Sex 0.03 0.868
 Male 0.90 (0.83–0.94)
 Female 0.91 (0.85–0.94)
Age (y) 2.10 0.349
 ≤49 0.96 (0.84–0.99)
 50–59 0.88 (0.79–0.94)
 ≥60 0.90 (0.84–0.94)
Age at the diagnosis of T2DM (y) 0.00 0.952
 <35 0.92 (0.54–0.99)
 ≥35 0.90 (0.86–0.93)
Duration of T2DM (mo) 6.81 0.009*
 <42 0.92 (0.88–0.95)
 ≥42 0.82 (0.71–0.90)
Body mass index 2.25 0.523
 Underweight 0.90 (0.47–0.99)
 Normal 0.86 (0.76–0.92)
 Overweight 0.94 (0.83–0.98)
 Obese 0.91 (0.85–0.95)
Comorbid hypertension 13.19 <0.001*
 No 0.92 (0.88–0.95)
 Yes 0.70 (0.46–0.85)
Foot examination 0.39 0.535
 No 0.90 (0.86–0.97)
 Yes 0.90 (0.81–0.95)
Retina examination 0.01 0.904
 No 0.90 (0.86–0.93)
 Yes 0.91 (0.79–0.96)
FBG (mg/dL) 1.31 0.253
 <130 0.93 (0.87–0.97)
 ≥130 0.88 (0.83–0.92)
HbA1c (%) 1.42 0.234
 <7 0.88 (0.81–0.93)
 ≥7 0.92 (0.87–0.95)
TG (mg/dL) 0.89 0.345
 <150 0.89 (0.82–0.93)
 ≥150 0.92 (0.86–0.95)
LDL-C (mg/dL) 0.12 0.734
 <100 0.92 (0.82–0.96)
 ≥100 0.90 (0.85–0.93)
eGFR (mL/min/1.73 m2) 10.18 0.006*
 Normal to mild decrease (>60) 0.93 (0.89–0.96)
 Mild to moderate decrease (30–59) 0.83 (0.70–0.91)
 Severe decrease to kidney failure (<30) 0.77 (0.49–0.91)

T2DM, type 2 diabetes mellitus; CI, confidence interval; FBG, fasting blood glucose; HbA1c, hemoglobin A1c; TG, triglycerides; LDL-C, low-density lipoprotein cholesterol; eGFR, estimated glomerular filtration rate.

* p<0.05.

Table 3.
Comparison of the results of Cox PH, Weibull AFT and log-normal AFT models in the univariate analysis for the onset time of diabetic complications in T2DM patients
Characteristic Cox PH Weibull AFT Log-normal AFT
Sex
 Male Ref.
 Female 0.959 0.907 0.946
Age (y)
 ≤49 Ref.
 50–59 0.052* 0.065* 0.045*
 ≥60 0.121 0.132 0.092*
Age at the diagnosis of T2DM (y)
 <35 Ref.
 ≥35 0.134 0.153 0.166
Duration of T2DM (mo)
 <42 Ref.
 ≥42 0.003* 0.010* 0.029*
Body mass index
 Underweight Ref.
 Normal 0.666 0.655 0.959
 Overweight 0.725 0.736 0.414
 Obese 0.599 0.595 0.445
Comorbid hypertension
 No Ref.
 Yes <0.001* 0.001* <0.001*
Foot examination
 No Ref.
 Yes 0.101 0.114 0.363
Retina examination
 No Ref.
 Yes 0.128 0.131 0.391
FBG (mg/dL)
 <130 Ref.
 ≥130 0.382 0.394 0.627
HbA1c (%)
 <7 Ref.
 ≥7 0.091* 0.099* 0.182
TG (mg/dL)
 <150 Ref.
 ≥150 0.458 0.493 0.691
LDL-C (mg/dL)
 <100 Ref.
 ≥100 0.098* 0.103 0.215
eGFR (mL/min/1.73 m2)
 Normal to mild decrease (>60) Ref.
 Mild to moderate decrease (30–59) 0.002* 0.005* 0.002*
 Severe decrease to kidney failure (<30) 0.007* 0.014* 0.031*

PH, proportional hazards; AFT, accelerated failure time; ref., reference group; T2DM, type 2 diabetes mellitus; ref., reference; FBG, fasting blood glucose; HbA1c, hemoglobin A1c; TG, triglycerides; LDL-C, low-density lipoprotein cholesterol; eGFR, estimated glomerular filtration rate.

* p<0.10.

Table 4.
Comparison of the final fitted Cox PH, Weibull AFT and log-normal AFT models in the multivariate analysis for the onset time of diabetic complications in T2DM patients (p<0.05)
Variable Model
Cox PH
Weibull AFT
Log-normal AFT
B HR p B TR p B TR p
Intercept 7.3 1,480.53 <0.001 7.564 1,926.99 <0.001
Duration of T2DM (mo)
 <42 Ref.
 ≥42 0.961 2.61 0.012 –0.575 0.56 0.030 –0.575 0.56 0.034
Comorbid hypertension
 No Ref.
 Yes 1.619 5.05 <0.001 –1.014 0.36 0.002 –1.192 0.30 0.001
eGFR
 Normal to mild decrease Ref.
 Mild to moderate 1.266 3.55 0.003 –0.798 0.45 0.006 –0.850 0.43 0.003
 Severe to kidney failure 1.468 4.34 0.009 –0.895 0.41 0.021 –0.962 0.38 0.025

PH, proportional hazards; AFT, accelerated failure time; T2DM, type 2 diabetes mellitus; HR, hazard ratio; TR, time ratio; ref., reference; eGFR, estimated glomerular filtration rate.

Table 5.
Comparison of model fit based on the AIC and BIC
Model df LL AIC BIC
Cox PH 4 –155.25 318.51 334.35
Weibull AFT 6 –105.87 223.79 247.48
Log-normal AFT 6 –103.72 219.44 243.21

AIC, Akaike information criterion; BIC, Bayesian information criterion; df, degrees of freedom; LL, log-likelihood; PH, proportional hazards; AFT, accelerated failure time.

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