Joint Modeling of Fasting Blood Sugar Changes and Cardiovascular Disease Progression in Type‐2 Diabetes Mellitus Patients: A Retrospective Cohort Study - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( Lock Locked padlock icon ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites. Search Log in Dashboard Publications Account settings Log out Search… Search NCBI Primary site navigation Search Logged in as: Dashboard Publications Account settings Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide PERMALINK Copy As a library, NLM provides access to scientific literature. 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Learn more: PMC Disclaimer | PMC Copyright Notice Health Sci Rep . 2026 Apr 14;9(4):e72327. doi: 10.1002/hsr2.72327 Search in PMC Search in PubMed View in NLM Catalog Add to search Joint Modeling of Fasting Blood Sugar Changes and Cardiovascular Disease Progression in Type‐2 Diabetes Mellitus Patients: A Retrospective Cohort Study Kassaye Getaneh Arge Kassaye Getaneh Arge 1 Department of Statistics, College of Natural and Computational Sciences, Samara University, Samara, Ethiopia Find articles by Kassaye Getaneh Arge 1 , Dereje Danbe Dereje Danbe 2 Department of Statistics, College of Natural and Computational Sciences, Hawassa University, Hawassa, Ethiopia Find articles by Dereje Danbe 2, ✉ Author information Article notes Copyright and License information 1 Department of Statistics, College of Natural and Computational Sciences, Samara University, Samara, Ethiopia 2 Department of Statistics, College of Natural and Computational Sciences, Hawassa University, Hawassa, Ethiopia * Correspondence: Dereje Danbe ( [email protected] ) ✉ Corresponding author. Revised 2026 Mar 19; Received 2024 Nov 26; Accepted 2026 Apr 6; Collection date 2026 Apr. © 2026 The Author(s). Health Science Reports published by Wiley Periodicals LLC. This is an open access article under the terms of the http://creativecommons.org/licenses/by-nc-nd/4.0/ License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made. PMC Copyright notice PMCID: PMC13079428 PMID: 41994610 ABSTRACT Background Type II diabetes mellitus is one of the major public health concerns causing a two‐ to four fold increased risk of developing cardiovascular disease (CVD) among patients in developing countries. The primary objective of this study was to assess how the rate of change in fasting blood sugar (FBS) determines CVD progression and to identify risk factors. Methods The hospital‐based retrospective cohort study data of 344 type‐II diabetic mellitus patients under follow‐up at Dessie Referral Hospital in the Amhara region, Northern Ethiopia, were used in the study. The linear mixed effects model was used to estimate the rate of change in FBS over time, and the time‐to‐event model was used to estimate time to CVD progression. We measure the relationship between temporal changes in FBS levels and time to CVD progression using a joint modeling approach. Results From total of the study participants, 51.2% were female, and 48.8% were male; of these, 52.6% were rural residents, and 47.4% were from urban areas. 51.16% of patients experienced CVD during the study period. Time to CVD progression had an inverse relation with the rate of change in FBS level ( α = −0.8232). Pulse rate, cholesterol level, and older age (80+) had a significant association with the change in FBS and time to CVD progression. Conclusion Accelerated rate of change in FBS, old age (80+), increased pulse rate, and a raised cholesterol level were the major risk factors of CVD progression. A slow rate of change in FBS elongates time to CVD progression. Keywords: cardio vascular disease, joint analysis, joint model, linear mixed effects model, longitudinal data analysis, survival analysis model, time‐to‐recovery, type II diabetes mellitus 1. Introduction Diabetes is a chronic disease characterized by elevated levels of blood glucose (or blood sugar), which causes serious damage to the heart, blood vessels, eyes, kidneys, and nerves [ 1 , 2 ]. It is a severe chronic illness that has world wide impact on people's life and general well‐being, and the families of those who suffer from it confront a significant financial dilemma [ 3 ]. Diabetes had an estimated prevalence of 9.3% (463 million) in 2019 and is projected to have 10.2% (578 million) in 2030 and 10.9% (700 million) in 2045 worldwide [ 4 ]. Approximately 285 million individuals worldwide suffer from type 1 and type 2 diabetes, the two most common forms of the illness [ 5 , 6 ]. Type II diabetes is the most common diabetes mellitus (DM), which occurs when the body becomes resistant to insulin or doesn't make enough insulin due to combined risk factors [ 7 ]. The prevalence of the disease has been increasing intensely over the past few decades in the world, with the highest rates of growth being observed in Sub‐Saharan Africa [ 8 , 9 , 10 , 11 ]. Adults with diabetes historically have a higher prevalence rate of cardiovascular diseases (CVD), which is a broad umbrella term used to describe all conditions affecting the heart and circulatory system [ 12 , 13 ]. Even before fasting plasma glucose levels rise to the point where a diabetes diagnosis can be made, there is a constant rise in the risk of CVD [ 14 ]. The effect of type II DM on CVD varies based on the specific cardiovascular outcome. Globally, CVD affects approximately 32.2% of all persons with type II DM, where coronary artery disease, stroke, hypertension, smoking, and obesity were the major contributors to the disease [ 15 , 16 , 17 ]. According to the national WHO STEPS survey in 2015, the prevalence of DM was 3.2% in Ethiopia, where the population at risk has shown a 100% increase from 1990 to 2017. Other studies in the country have also reported that the prevalence of diabetes mellitus ranges from 0.5% to 6.5% [ 18 , 19 , 20 , 21 , 22 ]. A systematic review conducted in Ethiopia reported that the prevalence of CVD ranges from 7.2% to 24% in the country [ 23 ]. According to other recent reports, the disease accounts for about 90% of all the DM cases and 9% of total deaths due to non‐communicable diseases [ 24 ]. Overall prevalence of CVD among type II DM patients in Ethiopia was estimated to be 42.51% [ 25 ]. Several investigations have been conducted in Ethiopia to determine the main contributing factors and to estimate the frequency of fasting blood sugar (FBS) levels. Other studies were carried out to determine the mean time to CVD progression and related risk variables among type II DM patients undergoing treatment follow‐up [ 26 ]. The majority of these investigations, however, did not take into consideration how time‐varying variables affected the course of CVD. Other studies have been conducted in the country to estimate the association between the level of FBS and CVD progression. However, these studies have not yet estimated the effects of temporal changes in FBS levels on time to CVD progression. To the best of our knowledge, no study has examined the effect size of individual‐level changes in FBS levels on times to CVD progression. Therefore, the primary objective of this study was to estimate the magnitude and rate of change in FBS levels over time within and between type 2 diabetic patients undergoing treatment follow‐up using a joint modeling approach. This analysis seeks to shed light on the long‐term implications of varying FBS levels on cardiovascular outcomes. By gaining a clearer understanding of these dynamics, we aim to enhance clinical practices and refine management strategies for patients with type 2 diabetes who are at risk of CVD. 2. Methods 2.1. Study Area, Study Population, and Data Sources This study was conducted at Dessie Referral Hospital in the Amhara Region, Northern Ethiopia. Hospital‐based retrospective cohort data of type II diabetic mellitus patients enrolled in the treatment follow‐up between September 30, 2015, and August 30, 2016 employed in the study. Each patient was followed for 57 months. A total of 344 patients who had four or more follow‐up visits to the hospital, had complete medical and clinical records, and those who were not under critical health conditions during the data collection period were included in the study. In repeated‐measures analysis, it is common for the measurement occasions to be 3–10 or more, depending on the specific research question, the nature of the variables being studied, and the statistical model used [ 27 ]. To assess temporal changes in specific time patterns within and between the study subjects and to increase estimation precision and power [ 28 ], patients who had four or more measurement occasions were included in the study. 2.2. Variables in the Study Response variables : FBS level and time to CVD progression were response variables. Each patient had a minimum of 4 and a maximum of 19 measurements taken on the FBS level during the study period. Time to CVD progression among patients was defined as the time from the first hospital visit to the 57th‐month hospital visit. Predictor variables : Two types of predictors included in the study: continuous predictors (age, systolic blood pressure [SBP], diastolic blood pressure [DBP], and pulse rate [PuR]) and categorical covariates (smoking status, family history of diabetes, marital status, education level, sex, area of residence, and cholesterol level). 2.3. Methods of Data Analysis Both descriptive and inferential statistical methods were used to achieve the study's objectives. Descriptive analysis was conducted to present results as percentages, proportions, charts, and graphs. To estimate the level of significance and effect size of each predictor on the outcome variables, we used three methods of inferential analysis. Each of the models fitted to the data was compared for its fitting performance based on the model diagnostic test statistics. The FBS level within and between study subjects was estimated using mixed‐effects analysis method. Time‐to‐CVD progression and associated factors were estimated using survival analysis methods. The joint analysis was done to estimate the degree of association between the rate of change in FBS level over time and the time to CVD progression. 2.4. Longitudinal Data Analysis This method of analysis is widely used and a flexible approach to capture temporal changes within and between subjects over time. The rate of change in FBS level over time and associated risk factors was estimated using a mixed‐effects modeling framework. 2.5. Linear Mixed Effects Model (LMM) The LMM is one of the widely applied statistical methods of data analysis, specifically when the research interest is to account for within and between‐subject differences over time. This modeling framework accounts for natural heterogeneity in the population and handles missing observations in the dataset [ 28 ]. In the current study, we assumed that missing observations are dependent on the observed values, but they are not directly related to the values of the missing observations. The LMM estimates the model parameters accounting for individual‐level variation (random effect) and the source of heterogeneity in FBS levels (fixed effects). Repeated measurements of FBS level are represented as Y i which corresponds to a n i × 1 response variable of the i th subject and X ip corresponds to p th predictor for i th subject. The elements of n of X i predictors can be time‐varying or time‐invariant. Y ij = X β + Z i b i + ε ij , i = 1 , 2 , … … . , N , j = 1 , 2 , 3 , … , n , (1) Var ( b i ) = D = D 11 D 12 D 21 D 22 , D 11 = var ( b 0 i ) , D 22 = var ( b 1 i ) ; b i ~ N ( 0 , D ) ; ε i ~ N ( 0 , σ 2 I ( n i ) ) , where, Y i is the n i dimensional response vector for subject i, for 1 ≤ i ≤ N ; N is the number of subjects, X i and Z i are n i × p and n i × q dimensional matrices of time invariant and time variant covariates, respectively; β is a p‐ dimensional vector containing the fixed effects, b i is a q ‐dimensional vector of random effects and ϵ i is an n i ‐ dimensional vector of errors components, D is q × q variance‐covariance matrix of cofficients of random effects. The fixed‐effect parameter in the model represents the average change in FBS level for a unit change in a predictor. 2.6. Time to Event Analysis The mean time to CVD progression was estimated using a time‐to‐event analysis. Despite the many parametric methods used to analyze time‐to‐event data, one method can be chosen over another due to a number of reasons [ 29 ]. One of the reasons that could lead researchers to choose one method of analysis over another is the nature of the study and the characteristics of the variable of interest. Parametric Proportional Hazard (PH) models are one of the commonly applied methods of time‐to‐event data analysis when covariates are assumed to affect the hazard in the form of multiplication. To estimate the effect size of different predictors on the variable of interest, a Cox regression model can be used. However, when the PH's assumption does not hold, we say the effect of the covariate is time‐varying [ 30 ]. 2.7. Accelerated Failure Time (AFT) Unlike the PH model, the AFT model states that the effects of covariates on the variable of interest are time‐varying. Similar to the PH model, the AFT model describes the relationship between time‐to‐event probabilities and degrees of association with covariates [ 31 ]. There are different classes of AFT models used for time‐to‐event data analysis. Commonly proposed models include the exponential AFT model, the Weibull AFT model, the log‐logistic AFT model, the log‐normal AFT model, and the gamma AFT model. These models are named for the distribution of time to event (T) rather than the distribution of the error term ( ϵ i ) or log(T). We applied all the AFT class models to the data in the current study and compared their fitting performance. 2.8. Model Selection: Time‐to‐Event Analysis The graphical methods were used to check if a parametric model applied to the data fits well. When the time to event data follows an exponential distribution, a plot of log [ log ( s ( t ) ) ] versus log ( t ) can yield a straight line with a slope of 1. If the plots are parallel but not straight, then the PH assumption holds, but not for the Weibull case. If the lines for two groups are straight but not parallel, the Weibull assumption is supported, but the PH and AFT assumptions don't hold. The log‐logistic assumption can be graphically evaluated by plotting log [ ( 1 − s ( t ) ) / s ( t ) ] versus log ( t ) . For the log normal distribution, a plot of ϕ − 1 [ 1 − S ( t ) ] versus log (t) should be linear. However, all these plots are based on the assumption that the sample is drawn from a homogeneous population, implying that no covariates are taken into account. So these graphical diagnostic approaches are not very reliable in practice. Thus, there are other commonly used methods to check the fitness of the model, such as information criteria (Akaike information criterion and Bayesian information criterion). 2.9. Joint Analysis of Longitudinal and Time‐to‐Event Data Many clinical trials generate both longitudinal (repeated measures) and survival (time‐to‐event) data. In DM disease, patients were measured for fasting glucose levels and diagnosed with CVD progression at each hospital visit. Time to CVD progression may be associated with the degree of change in FBS over time. In this case, the association between the rate of change and time to CVD progression can arise in two ways: one involves common explanatory variables, while the other involves stochastic dependence among random effects unique to each subject. When an association between the two processes exists, less biased and more efficient inferences can be obtained by using a joint model [ 32 ] to draw unbiased statistical inferences [ 33 ]. In general, the joint modeling approach considered in this study has two components: longitudinal and time‐to‐event sub‐model components. 2.10. Longitudinal Sub‐Model In joint modeling approaches, longitudinal data are delineated by a conventional linear mixed model by assuming homogeneity between the subject variances. However, such a homogeneity assumption is automatically precluded when temporal assessments made on the same individuals are expected to be correlated. Thus, we have combined both approaches using the joint model to relate the variability of sugar level within the subjects over time and time to CVD progression. The FBS level trajectory described by both the conventional linear fixed and the LMM accounts for subject‐specific variances [ 31 ]. Y i = µ i ( t ij ) + w 1 i ( t ij ) + ε i ; i = 1 ; 2 , … , n , (2) Y i = X 1 i T ( t ij ) β 1 + Z i T ( t ij ) b i + ε i ; i = 1 ; 2 , … , n , where y is an n i dimensional vector of observed responses, β 1 is n i * p dimensional vector of fixed effects coefficients, b i is a q dimensional vector of random effects coefficients, X 1 i T ( t ij ) β 1 is a matrix of (p size) fixed effects associated with time‐varying covariates; Z i T ( t ij ) b i is a matrix of size n * q random effects covariates and ε i is an n i dimensional vector of error term having a Gaussian distribution. In this model, µ i ( t ij ) = X 1 i T ( t ij ) β 1 is the mean response, and w 1 i ( t ij ) = Z i T ( t ij ) b i is the random effects or subject‐specific variances, that is, the within‐group errors, ε i , may not have homogeneous variances. The term w 1 i ( t ij ) can be viewed as the true individual‐level trajectories after being adjusted for the overall mean trajectory and other fixed effects. The random effects covariates, Z 1 i , are usually a subset of the fixed effects covariates, X 1 i . 2.11. Time to Event Sub‐Model The time to event sub‐model is given by: h i ( t | m i ( t ij ) ) = h 0 ( t ) exp X 2 i T ( t ij ) β 2 + α m i ( t ij ) , (3) where h 0 ( t ) is piecewise constant, α = measures the association between longitudinal and survival sub‐model, m i ( t ij ) is a linear mixed model, and β 2 is cofficient for survival sub‐model covariates. The longitudinal model proposed by Laird and Ware [ 33 ] assumes each patient is receiving random intercept, linear, and quadratic slope terms. The parameter α in the time to event model (Equation 3 ) measures the association between the two sub‐models induced by the random intercepts, linear slope, and quadratic slope. All model parameter estimations were based on ML methods using the R statistical package, version 4.5.2, and all statistical tests were conducted at the 5% level of significance. 2.12. Ethical Clearance and Consent of Participation The authors confirm that the research presented in this article met the ethical guidelines and received ethical clearance from Hawassa University, College of Medicine and Health Sciences, Institutional Review Board (Ref. No: IRB/834/12). Written consent was obtained from the Dessie Hospital medical board and the study participants. All the methods were performed in accordance with the relevant guidelines and regulations. 3. Results and Discussions 3.1. Descriptive Statistics From a total of 344 type‐II DM patients in the study, 176 (51.16%) were female, and 168 (48.84%) were male; of which, 163 (47.38%) were urban residents, while 181 (52.62%) were from rural areas. Among study participants, 17.70%, 51.16%, and 18.31% had no education, attended primary and high school, and had more than high school educational status, respectively. About 28% of participants had a history of previous complications, and 36.63% were alcohol users. During the study period, 44.88% of females and 57.73% of males had experienced CVD at 56.1 and 47.7 median months of follow‐up, respectively. Patients those who had a median of 75 mmHg SBP and 158 mmHg DBP experience CVD (Table 1 ). Table 1. Socio‐demographic and clinical characteristics of study participants (categorical covariates). Covariates Category Summary No. of patients ( n (%)) Developed CVD ( n (%)) Median Sex Female 176 (51.16%) 79 (44.88%) 56.1 Male 168 (48.84%) 97 (57.73%) 47.9 Residence Rural 181 (52.62%) 82 (45.3%) 56.2 Urban 163 (47.38%) 94 (57.66%) 53.2 Family history of diabetes mellitus disease (DMD) Negative 183 (53.20%) 90 (49.18%) 56.2 Positive 161 (46.80%) 86 (53.41%) 56 Marital status Divorced 27 (7.85%) 13 (48.14%) 55.2 Married 302 (87.80%) 156 (51.65%) 56.0 Single 15 (4.35%) 7 (46.66%) 55.18 Education level None educated 61 (17.73%) 33 (54.09%) 53.1 Primary school 176 (51.16%) 94 (53.4%) 55.1 Secondary school 63 (18.31%) 30 (47.61%) 56.2 Higher education 44 (12.80%) 19 (43.18%) 56.2 Alcohol use No 218 (63.37%) 111 (50.91%) 56.2 Yes 126 (36.63%) 65 (51.58%) 56.0 Previous complication No 248 (72.09%) 106 (42.74%) 56.9 Yes 96 (27.91) 70 (72.91%) 26.2 Open in a new tab As treatment follow‐up time increase the log of FBS level decreases (Figure 1 ). The mean FBS level was high (271.2 Hg/dL) at the baseline (month = 0). However, as the follow‐up time increases, both the mean and the standard deviation of the FBS level decrease. In the first 27 months of follow‐up, the level of FBS decreases, and then an increasing trend observed starting from Month 30, and then begins to drop after Month 33 (Figure 2 ). Figure 1. Open in a new tab Mean and subject‐specific log fasting blood sugar (FBS) level of 344 study participants over follow‐up time. Figure 2. Open in a new tab Mean and standard deviation of fasting blood sugar (FBS) level of 344 study participants measured over follow‐up time. The mean age of study subjects was 55.04 years, with a minimum and maximum age of 30 and 84 years, respectively. The PuR, SBP, and DBP of the participants were 119.85, 80.51, and 153.37, respectively (Table 2 ). Table 2. Summary statistics of demographic and clinical characteristics of study participants (continuous variables). Variable Minimum 1st Quartile Median Mean 3rd Quartile Maximum Standard deviation Age 30 44 55 55.04 65.25 84 12.66 PuR 63 99 118 119.85 135 198 27.7 SBP 58 69 75 80.51 90 147 14.6 DBP 98 138 157 153.37 168 201 22.61 Open in a new tab Abbreviations: DBP, diastolic blood pressure; PuR, pulse rate; SBP, systolic blood pressure. 3.2. Linear Mixed Effects Analysis The LMM was used to estimate the sources of variation in FBS level within and between subjects over the follow‐up period. The Shapiro–Wilk and Kolmogorov‐Smirnov tests indicate that the normality assumption does not hold. As a result, we transformed the original data into a logarithmic form (log FBS), and the results of LMM presented in Table 3 . Table 3. Linear mixed effects analysis of logFSB level and associated factors. Variables Category Estimate Standard error t value Lower Upper p value Fixed effects Intercept 4.376 0.0549 79.64 4.268 4.483 < 0.001 Observation time Continuous −0.004 0.0002 −14.55 −0.005 −0.003 < 0.001 Area of residence Rural (Ref) — — — — — — Urban 0.059 0.0167 3.556 0.027 0.092 < 0.001 Smoking status No (Ref) — — — — — — Yes −0.052 0.0246 −2.125 −0.101 −0.003 0.03 Age group 30–39 (Ref) — — — — — — 40–49 0.018 0.0293 0.634 −0.039 0.076 0.53 50–59 0.054 0.0317 1.708 −0.008 0.116 0.09 60–69 0.064 0.0289 2.228 0.008 0.121 0.03 70–79 0.084 0.0358 2.352 0.014 0.155 0.02 80+ 0.077 0.1147 0.673 −0.148 0.303 0.001 Systolic blood pressure (SBP) Continuous 0.005 0.0004 11.87 0.004 0.005 < 0.001 Diastolic blood pressure (DBP) Continuous 0.001 0.0002 6.996 0.0009 0.002 < 0.001 Pulse rate Continuous −0.000 0.0002 −0.98 −0.001 0.000 0.33 Cholesterol level Normal (Ref) — — — — — — Raised 0.424 0.0083 50.95 0.408 0.440 < 0.001 Random effects Standard deviation Standard deviation ( β 0 i ) 0.246 0.2211 0.2736 Standard deviation ( β 1 i ) 0.003 0.0024 0.0041 Correlation ( β 0 i , β 1 i ) −0.96 −0.9960 −0.605 Residual ( ϵ i ) 0.267 0.2590 0.2745 Open in a new tab The variance for both the random intercept and slope was greater than zero, indicating heterogeneity in FBS levels across the study subjects at baseline. A strong negative correlation between random slope and random intercept indicates an inverse relationship between baseline FBS level and follow‐up time. This shows that as treatment time increases, the rate of change in log FBS levels significantly drops (Table 3 ). For a 1‐month increase in treatment time, the log of the FBS level decreases by a factor of 0.004 ( p = 0.001, 95% CI : −0.005, −0.003). The rate of change in logFBS level among rural residents was 0.059 times higher than that of urban residents. Smoker patients had a 0.052 times increased risk of higher fasting sugar level compared to non‐smokers. The FBS level in patients who were 60 years and above was significantly higher than patients who were below 40 years. The FBS level had a significant association with SBP, DBP, and cholesterol level. For a unit rise in SBP and DBP, log FBS level increased by a factor of 0.005 ( p ≤ 0.001, 95% CI: 0.004, 0.005) and 0.001 ( p ≤ 0.001, 95% CI: 0.0009, 0.002), respectively. Patients who had raised cholesterol level had 0.424 times increased logFBS level ( p = 0.001, 95% CI: 0.408, 0.440) compared to those who had normal cholesterol (Table 3 ). 3.3. Time to CVD Progression The standard Cox regression model with baseline measurements does not hold the PH assumption. Thus, we applied different parametric families of time‐to‐event models and compared their fitting performance. The log‐normal AFT model best fitted the data and estimation results presented in Table 4 . The FBS level at the baseline ( p = 0.0012, 95% CI: −0.0013, −0.0003), smoking status (95% CI: −0.3226, −0.0288, p = 0.019), history of previous complications (95% CI: −0.6325 to −0.4030, p < 0.001), PuR (95% CI: −0.0038 to −0.0002, p = 0.03), and sex (95% CI: −0.2814 to −0.0795, p < 0.001) had statistically significant associations with time to CVD progression. Patients who had higher FBS levels at baseline had 0.99 times accelerated time to CVD progression compared to those who had normal FBS levels at baseline. Patients those who were smokers had 0.84 (0.8388) times accelerated time to CVD progression compared to non‐smokers. The time to CVD progression for patients with higher PuRs was 0.997 times higher than for those with lower PuRs. Patients who had a previous history of complications had 0.59 times accelerated time to CVD progression compared to those who had no previous history of complications, holding other covariates constant in the model. Age, educational status, and cholesterol level had no statistically significant association with time to CVD progression when other covariates in the model held constant (Table 4 ). Table 4. Log‐normal accelerated failure time (AFT) analysis of time to CVD progression and associated covariates. Covariates Category β SE ( β ) ϕ 95% CI p value Intercept — 5.0028 0.1938 148.839 4.6229, 5.3827 < 0.001 Sex Female (ref) — — — — — Male −0.1804 0.0515 0.8348 −0.2814, −0.0795 < 0.001 Smoking status No (ref) — — — — — Yes −0.1757 0.0749 0.8388 −0.3226, −0.0288 0.02 Age group 30–39 (ref) — — — — — 40–49 −0.1066 0.0933 0.8988 −0.2896, 0.0764 0.25 50–59 −0.0729 0.0998 0.9296 −0.2685, 0.1226 0.46 60–69 −0.1134 0.0909 0.8927 −0.2916, 0.0648 0.21 70–79 0.0275 0.1149 1.0279 −0.1976, 0.2527 0.81 80+ −0.3277 0.3126 0.7205 −0.9406, 0.2850 0.29 Pulse rate Continues −0.0026 0.0009 0.997 −0.0038, −0.0002 0.03 Baseline FBS Continues −0.0008 0.0002 0.999 −0.0013, −0.0003 0.001 Previous complication No (ref) — — — — — Yes −0.5178 0.0585 0.59 −0.6325, −0.4030 < 0.001 Education level No education −0.1831 0.09 0.83 −0.3673, 0.0009 0.05 Primary education −0.1535 0.08 0.86 −0.3113, 0.0042 0.06 Secondary education −0.07 0.09 0.93 −0.2551, 0.1161 0.46 Higher education (ref) — — — — — Cholesterol level Normal (ref) — — — — — Raised −0.0115 0.0809 0.99 −0.1702, 0.1471 0.88 Log(scale) −0.8998 0.058 < 0.001 Open in a new tab Note: ref, reference category. 3.4. Joint Analysis In the previous sections, we aimed to estimate the rate of change in FBS levels during the follow‐up period and the time to cardiovascular (CVD) progression. The aim of the separate analyses was to estimate the rate of change in FBS levels both within and between subjects. These approaches examine associated covariates and key determinants related to the progression of CVD. However, separate approaches do not show whether the rate of change in FBS significantly contributes to time to CVD progression. In the next section, we estimated the association between temporal changes in FBS and time to CVD progression. The joint analysis was done using the Weibull AFT model as presented in Table 5 . Table 5. The Weibull‐Accelerated Faller Time (AFT) analysis of temporal change in fasting blood sugar (FBS) and time to CVD progression. Variables Category Joint Weibull AFT model Longitudinal sub‐component Survival sub‐component Estimate Standard error p value Estimate Standard error p value Intercept 4.9795 0.0438 0 .000 6.366 0.529 < 0.001 Observation time −0.0561 0.0045 0.0 00 — — — Sex Female (ref.) — — — — — — Male 0.0183 0.0182 0.3159 −0.118 0.045 0.01 Residence Rural (ref.) — — — — — — urban 0.0483 0.0189 0.0108 −0.054 0.044 0.22 Smoking No (ref.) — — — — — — Yes −0.0427 0.0261 0.1021 −0.226 0.069 0.001 Family history No (ref.) — — — — — — Yes 0.0002 0.0266 0.9927 0.152 0.069 0.03 Age 30–39 (ref.) — — — — — — 40–49 0.0091 0.0277 0.7421 −0.117 0.084 0.16 50–59 0.0508 0.0317 0.1097 −0.044 0.087 0.61 60–69 0.0551 0.0303 0.0689 −0.079 0.081 0.33 70–79 0.0837 0.03571 0.0343 0.056 0.095 0.56 80+ 0.0857 0.0396 0.0169 −0.396 0.229 0.04 Systolic blood pressure 0.0050 0.0005 0.0001 — — — Diastolic blood pressure 0.0014 0.0002 0.0001 — — — Pulse rate 0.0001 0.0002 0.0429 −0.0021 0.0008 0.01 Cholesterol level Normal (ref.) — — — — — — Raised 0.4280 0.0096 0 .0001 −0.288 0.090 0.001 Previous complications No (ref.) — — — — — — Yes 0.0192 0.0261 0.4610 −0.354 0.049 < 0.001 Education level None −0.0385 0.0306 0.2092 −0.171 0.084 0.04 Primary −0.0025 0.0252 0.9218 −0.123 0.072 0.08 Secondary 0.0006 0.0320 0.9849 −0.064 0.084 0.44 Higher (ref.) — — — — — — Random effects component for mixed linear model ( β 0 i ) 0.262 ( β 1 i ) 0.056 Cor. ( β 0 i , β 1 i ) −0.902 Residual ( ϵ i ) 0.258 Association parameter ( α ) −0.8232 0.1065 < 0.001 Log(scale) parameter for the joint time to event model 1.2898 0.0642 < 0.001 Open in a new tab Abbreviations: cor., correlation; ref., reference category. The first component consists of longitudinal analysis of temporal change in FBS and associated covariates. The survival subcomponent estimates the determinants of time to CVD progression. The joint analysis shows that there was a strong and inverse relationship between changes in FBS level and time to CVD progression (association parameter, α = −0.8232). Longitudinal sub‐model analysis shows that sex, place of residence, smoking status, age (70+), SBP, DBP, PuR, cholesterol level, history of previous complications, and follow‐up time (ObsT) had a significant association with the rate of change in FBS. On the other hand, survival‐subcomponent analysis shows that sex, smoking status, PuR, cholesterol level, education level, history of previous complications, and age (80+) had a significant association with time to CVD progression. PuR, cholesterol level, and age (80+) were significantly associated with both temporal changes in FBS levels and time to CVD progression. The association parameter is significantly different from zero, indicating that a decline in FBS levels over time decreases the risk of rapid CVD progression. Cholesterol level had a positive and significant association with the change in FBS level. Patients with elevated cholesterol levels had 0.428 times higher log of FBS levels and 0.288 times slower time to CVD progression than patients with normal cholesterol levels, while other covariates in the model held constant. In patients 80 years and older, the logFBS level was 0.057 times higher, but the time to CVD progression was 0.396 times slower in patients below 80 years of age. For a unit increase in PuR, the rate of change in logFBS increased by a factor of 0.0001, but time to CVD progression was 0.0021 times decelerated (Table 5 ). 4. Discussions The current study was intended to estimate the magnitude of temporal change in FBS and its association with time to CVD progression among type II DM patients. Both joint and separate modeling approaches were used to identify factors contributing to the change in FBS and time to CVD progression. Different time‐variant and time‐invariant covariates were incorporated in the analysis to estimate the degree of association between the variables of interest. This study revealed that urban residents had higher FBS levels but a decelerated time to CVD progression compared to rural residents. Another study reported similar findings [ 33 ]. This may be due to lifestyle factors, unhealthy diet, stress, and/or poor exercise habits. Patients who had no formal education showed accelerated time to CVD progression compared to those who had a higher educational level. The similar findings by [ 34 ] revealed that education level had a significant association with the risk of developing CVD. This might be due to the fact that educated people had better awareness of disease and associated risk factors. And also, patients who had higher educational status might follow all the prescriptions from their physicians and take all the treatment measures properly. Patients with fast‐changing FBS levels had a significantly increased risk of progressing CVD. Similar findings reported by the study conducted in Asia [ 27 ]. This study revealed that higher levels of FBS among type I or type II DM patients could lead to the risk of several cardiovascular disorders. Patients who were 80 years and older had increased FBS levels but a decelerated time to CVD progression compared to those who were below 80 years of age. Other studies have also reported that when the age of patients increases, their blood vessels become inflexible, and this may make blood flow harder through blood vessels [ 27 , 34 ]. Patients with a raised PuR had a significantly higher risk of increased FBS level, where the risk of fast CVD progression decreased. This points out that there was an inverse relationship between the amount of PuR and the time to CVD progression. A study conducted in China [ 38 ] using data collected from middle‐aged and older Chinese patients confirmed that both continuous increase and decrease in baseline PuR had increased risk of CVD complications. An increase in heart rate reflects increased sympathetic activity through the development of subclinical underlying cardiovascular events, while a decrease in PuR reflects improving cardiac function, physical fitness, and lower sympathetic tone. Female patients had an elongated time to CVD progression compared to males, but FBS levels in males decreased compared to females. However, other findings from a systematic review and meta‐analysis conducted in Ethiopia [ 35 ] reported that gender had no significant association with the prevalence of CVD. To minimize bias caused by the endogenous nature of fasting blood glucose, the current study employed a joint modeling approach to repeated measurements of fasting blood glucose levels among type‐II DM patients. The strength of this study lies in its ability to estimate the degree of relationship between FBS level and time to CVD progression by identifying potential risk factors. However, other important predictors such as proteinuria, hyperlipidemia, physical inactivity, body mass index, and occupation variability, which are strong predictors of CVD events [ 36 , 37 , 38 ], were not included in the current study. Moreover, this study used a retrospective study design where the secondary data were collected from a single‐hospital setting. This might affect the estimation power of the statistical methods for identifying potential risk factors. Thus, we suggest further study accommodating for measurement bias, including unmeasured confounder variables in the study, and accounting for the effects of loss to follow‐up. 5. Conclusions and Recommendations This study aimed to estimate the relationship between changes in FBS levels and time to CVD progression by identifying potential risk factors. The joint modeling approach performs better at fitting the data than a separate modeling framework. Time to CVD progression depends significantly on the rate of change in FBS levels. Place of residence, male sex, older age (70+), SBP, DBP, PuR, and cholesterol level were major risk factors of change in FBS level, while female sex, smoking status, PuR, cholesterol level, education status, previous complications, and older age (80+) were potential risk factors of time to CVD progression among type II DM patients. In general, smoking cigarettes, sex, cholesterol level, older age, family history of similar disease complications, and area of residence significantly contribute to increased FBS level and accelerated time to CVD progression. Thus, controlling temporal changes (variability) in FBS at the individual level requires multi‐factorial interventions, such as reducing rising cholesterol levels, regular check‐ups for diastolic and SBP, PuR, and other associated risk factors. Physicians should recommend regular and continuous medical follow‐up for those at risk of treatment follow‐up at each hospital visit. Stakeholders should implement multiple mass screening campaigns and focus on intervention strategies based on identified risk factors to minimize the burden of type II DM disease which is the main source of CVD. Author Contributions Kassaye Getaneh: conceptualization, writing – original draft, methodology, visualization, data curation, investigation, formal analysis. Dereje Danbe: methodology, data curation, writing – review and editing. Both authors have read and approved the final version of the manuscript. All authors have read and approved the final version of the manuscript and have full access to all of the data in this study and take complete responsibility for the integrity of the data and the accuracy of the data analysis. Funding The authors have nothing to report. Conflicts of Interest The authors declare no conflicts of interest. Transparency Statement The lead author, Dereje Danbe, affirms that this manuscript is an honest, accurate, and transparent account of the study being reported; that no important aspects of the study have been omitted; and that any discrepancies from the study as planned (and, if relevant, registered) have been explained. Acknowledgments This study was conducted at Dessie Referral Hospital in the Amhara Region, Northern Ethiopia. We, the authors, are very thankful to the data management team and study participant patients under follow‐up for their willingness to provide us with the data used in the study. Data Availability Statement Data available on request due to privacy/ethical restrictions. References 1. WHO , Diabetes (2023), https://www.who.int/health-topics/diabetes#tab=tab_1 . 2. Cavalcante D. F. B., Brizon V. S. C., Probst L. F., Meneghim M. C., Pereira A. C., and Ambrosano G. M. B., “Did the Family Health Strategy Have an Impact on Indicators of Hospitalizations for Stroke and Heart Failure? Longitudinal Study in Brazil: 1998–2013,” PLoS One 13, no. 6 (2018): e0198428. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 3. Ud Din S. R., Saeed S., Khan S. U., Kiani F. A., Alsuhaibani A. M., and Zhong M., “Bioactive Compounds (BACs): A Novel Approach to Treat and Prevent Cardiovascular Diseases,” Current Problems in Cardiology 48, no. 7 (July 2023): 101664, 10.1016/j.cpcardiol.2023.101664. [ DOI ] [ PubMed ] [ Google Scholar ] 4. Abbas A., Raza A., Ullah M., et al., “A Comprehensive Review: Epidemiological Strategies, Catheterization and Biomarkers Used as a Bioweapon in Diagnosis and Management of Cardio Vascular Diseases,” Current Problems in Cardiology 48, no. 7 (July 2023): 101661, 10.1016/j.cpcardiol.2023.101661. [ DOI ] [ PubMed ] [ Google Scholar ] 5. Whiting D. R., Guariguata L., Weil C., and Shaw J., “IDF Diabetes Atlas: Global Estimates of the Prevalence of Diabetes for 2011 and 2030,” Diabetes Research and Clinical Practice 94, no. 3 (December 2011): 311–321, 10.1016/j.diabres.2011.10.029. [ DOI ] [ PubMed ] [ Google Scholar ] 6. Ogurtsova K., da Rocha Fernandes J. D., Huang Y., et al., “IDF Diabetes Atlas: Global Estimates for the Prevalence of Diabetes for 2015 and 2040,” Diabetes Research and Clinical Practice 128 (June 2017): 40–50, 10.1016/j.diabres.2017.03.024. [ DOI ] [ PubMed ] [ Google Scholar ] 7. Tuomi T., Santoro N., Caprio S., Cai M., Weng J., and Groop L., “The Many Faces of Diabetes: A Disease With Increasing Heterogeneity,” Lancet 383, no. 9922 (March 2014): 1084–1094, 10.1016/S0140-6736(13)62219-9. [ DOI ] [ PubMed ] [ Google Scholar ] 8. Ioannidis J. P. A., “Integration of Evidence From Multiple Meta‐Analyses: A Primer on Umbrella Reviews, Treatment Networks and Multiple Treatments Meta‐Analyses,” Canadian Medical Association Journal 181, no. 8 (October 2009): 488–493, 10.1503/cmaj.081086. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 9. Bandello F., Querques G., and Loewenstein A., Medical Retina: Update (Karger Medical and Scientific Publishers, 2017). [ Google Scholar ] 10. Mensah G. A., “Descriptive Epidemiology of Cardiovascular Risk Factors and Diabetes in Sub‐Saharan Africa,” Progress in Cardiovascular Diseases 56, no. 3 (November/December 2013): 240–250, 10.1016/j.pcad.2013.10.014. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 11. Keates A. K., Mocumbi A. O., Ntsekhe M., Sliwa K., and Stewart S., “Cardiovascular Disease in Africa: Epidemiological Profile and Challenges,” Nature Reviews Cardiology 14, no. 5 (May 2017): 273–293, 10.1038/nrcardio.2017.19. [ DOI ] [ PubMed ] [ Google Scholar ] 12. Emerging Risk Factors Collaboration, Sarwar N., Gao P., et al., “Diabetes Mellitus, Fasting Blood Glucose Concentration, and Risk of Vascular Disease: A Collaborative Meta‐Analysis of 102 Prospective Studies,” Lancet 375, no. 9733 (June 2010): 2215–2222, 10.1016/S0140-6736(10)60484-9, Erratum in: H. L. Hillage, Lancet 376, no. 9745 (2010): 958. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 13. Einarson T. R., Acs A., Ludwig C., and Panton U. H., “Prevalence of Cardiovascular Disease in Type 2 Diabetes: A Systematic Literature Review of Scientific Evidence From Across the World in 2007–2017,” Cardiovascular Diabetology 17, no. 1 (2018): 83, 10.1186/s12933-018-0728-6. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 14. Singh G. M., Danaei G., Farzadfar F., et al., “Global Burden of Metabolic Risk Factors of Chronic Diseases Collaborating Group; Asia‐Pacific Cohort Studies Collaboration (APCSC); Diabetes Epidemiology: Collaborative Analysis of Diagnostic Criteria in Europe (DECODE); Emerging Risk Factor Collaboration (ERFC); Prospective Studies Collaboration (PSC). The Age‐Specific Quantitative Effects of Metabolic Risk Factors on Cardiovascular Diseases and Diabetes: A Pooled Analysis,” PLoS One 8, no. 7 (July 2013): e65174, 10.1371/journal.pone.0065174. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 15. Kazeminia M., Salari N., and Mohammadi M., “Prevalence of Cardiovascular Disease in Patients With Type 2 Diabetes Mellitus in Iran: A Systematic Review and Meta‐Analysis,” Journal of Diabetes Research 2020 (September 2020): 3069867, 10.1155/2020/3069867. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 16. Gebreyes Y. F., Goshu D. Y., Geletew T. K., et al., “Prevalence of High Bloodpressure, Hyperglycemia, Dyslipidemia, Metabolic Syndrome and Their Determinants in Ethiopia: Evidences From the National NCDs STEPS Survey, 2015,” PLoS One 13, no. 5 (May 2018): e0194819, 10.1371/journal.pone.0194819. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 17. Zekewos A., Loha E., Egeno T., Wubshet K., and Merga Z., “Prevalence of Diabetes Mellitus and Associated Factors in Southern Ethiopia: A Community Based Study,” Ethiopian Journal of Health Sciences 28, no. 4 (July 2018): 451–460, 10.4314/ejhs.v28i4.11. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 18. Gizaw M., Harries A. D., Ade S., et al., “Diabetes Mellitus in Addis Ababa, Ethiopia: Admissions, Complications and Outcomes in a Large Referral Hospital,” Public Health Action 5, no. 1 (March 2015): 74–78, 10.5588/pha.14.0107. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 19. Abebe S. M., Berhane Y., Worku A., and Assefa A., “Diabetes Mellitus in North West Ethiopia: A Community Based Study,” BMC Public Health 14 (January 2014): 97, 10.1186/1471-2458-14-97. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 20. Habtewold T. D., Tsega W. D., and Wale B. Y., “Diabetes Mellitus in Outpatients in Debre Berhan Referral Hospital, Ethiopia,” Journal of Diabetes Research 2016 (2016): 3571368, 10.1155/2016/3571368. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 21. Tesfaye T., Shikur B., Shimels T., and Firdu N., “Prevalence and Factors Associated With Diabetes Mellitus and Impaired Fasting Glucose Level Among Members of Federal Police Commission Residing in Addis Ababa, Ethiopia,” BMC Endocrine Disorders 16, no. 1 (November 2016): 68, 10.1186/s12902-016-0150-6. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 22. Abebe S. M., Andargie G., Shimeka A., et al., “The Prevalence of Non‐Communicable Diseases in Northwest Ethiopia: Survey of Dabat Health and Demographic Surveillance System,” BMJ Open 7, no. 10 (October 2017): e015496, 10.1136/bmjopen-2016-015496. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 23. Angaw D. A., Ali R., Tadele A., and Shumet S., “The Prevalence of Cardiovascular Disease in Ethiopia: A Systematic Review and Meta‐Analysis of Institutional and Community‐Based Studies,” BMC Cardiovascular Disorders 21, no. 1 (January 2021): 37, 10.1186/s12872-020-01828-z. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 24. World Health Organization , Global Status Report on Noncommunicable Diseases 2014 (World Health Organization, 2014), https://iris.who.int/handle/10665/148114 . 25. Regassa L. D., Tola A., and Ayele Y., “Prevalence of Cardiovascular Disease and Associated Factors Among Type 2 Diabetes Patients in Selected Hospitals of Harari Region, Eastern Ethiopia,” Frontiers in Public Health 8 (February 2021): 532719, 10.3389/fpubh.2020.532719. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 26. Gesese M., “Survival Analysis of Time to Cardiovascular Disease Complication of Hypertensive Patients at Felege Hiwot Referal Hospital in Bahir‐Dar, Ethiopia: A Retrospective Cohort Study,” Archives of Current Research International 10, no. 3 (2017): 1–9, 10.9734/ACRI/2017/36017. [ DOI ] [ Google Scholar ] 27. Hecht M. and Zitzmann S., “Sample Size Recommendations for Continuous‐Time Models: Compensating Shorter Time Series With Larger Numbers of Persons and Vice Versa,” Structural Equation Modeling: A Multidisciplinary Journal 28, no. 2 (2020): 229–236, 10.1080/10705511.2020.1779069. [ DOI ] [ Google Scholar ] 28. Zeger S. L. and Liang K. Y., “An Overview of Methods for the Analysis of Longitudinal Data,” Statistics in Medicine 11, no. 14–15 (January 1992): 1825–1839. [ DOI ] [ PubMed ] [ Google Scholar ] 29. Abdulahi A. M., Aguade A. E., and Yohannis H. K., “Longitudinal Modeling of Fasting Blood Sugar With Diabetes: A Case Study of Adama Hospital Medical College, Ethiopia,” Health Science Reports 5, no. 6 (November 2022): e951, 10.1002/hsr2.951. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 30. Lim H. S., “Brief Introduction to Parametric Time to Event Model,” Translational and Clinical Pharmacology 29, no. 1 (March 2021): 1–5, 10.12793/tcp.2021.29.e7. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 31. Wulfsohn M. S. and Tsiatis A. A., “A Joint Model for Survival and Longitudinal Data Measured With Error,” Biometrics 53, no. 1 (March 1997): 330–339. [ PubMed ] [ Google Scholar ] 32. Sterling T. R., Lyles C. M., Vlahov D., Astemborski J., Margolick J. B., and Quinn T. C., “Sex Differences in Longitudinal Human Immunodeficiency Virus Type 1 RNA Levels Among Seroconverters,” Journal of Infectious Diseases 180, no. 3 (September 1999): 666–672, 10.1086/314967. [ DOI ] [ PubMed ] [ Google Scholar ] 33. Laird N. M. and Ware J. H., “Random‐Effects Models for Longitudinal Data,” Biometrics 38, no. 4 (December 1982): 963–974. [ PubMed ] [ Google Scholar ] 34. Seedat Y., Ali A., and Ferdinand K. C., “Hypertension and Cardiovascular Disease in the Sub‐Saharan African Context,” Annals of Translational Medicine 6, no. 15 (August 2018): 297, 10.21037/atm.2018.06.45. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 35. Vazir A., Claggett B., Cheng S., et al., “Association of Resting Heart Rate and Temporal Changes in Heart Rate With Outcomes in Participants of the Atherosclerosis Risk in Communities Study,” JAMA Cardiology 3, no. 3 (March 2018): 200–206, 10.1001/jamacardio.2017.4974. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 36. Zhang Z., Reinikainen J., Adeleke K. A., Pieterse M. E., and Groothuis‐Oudshoorn C. G. M., “Time‐Varying Covariates and Coefficients in Cox Regression Models,” Annals of Translational Medicine 6, no. 7 (April 2018): 121, 10.21037/atm.2018.02.12. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 37. Guo X. and Carlin B. P., “Separate and Joint Modeling of Longitudinal and Event Time Data Using Standard Computer Packages,” American Statistician 58, no. 1 (2004): 16–24, 10.1198/0003130042854. [ DOI ] [ Google Scholar ] 38. Tian J., Yuan Y., Shen M., et al., “Association of Resting Heart Rate and Its Change With Incident Cardiovascular Events in the Middle‐Aged and Older Chinese,” Scientific Reports 9, no. 1 (April 2019): 6556, 10.1038/s41598-019-43045-5. [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. 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