Modeling of Disease Progression of Type 2 Diabetes Using Real‐World Data: Quantifying Competing Risks of Morbidity and Mortality

ABSTRACT

Type 2 diabetes (T2D) is a progressive metabolic disorder that could be an underlying cause of long‐term complications that increase mortality. The assessment of the probability of such events could be essential for mortality risk management. This work aimed to establish a framework for risk predictions of macrovascular complications (MVC) and diabetic kidney disease (DKD) in patients with T2D, using real‐world data from the Swedish National Diabetes Registry (NDR), in the presence of mortality as a competing risk. The study consisted of 41,517 patients with T2D registered in NDR between 2005 and 2013. At inclusion, patients were newly diagnosed (T2D < 1 year) and had no prior evidence of DKD or MVC. Using three‐quarters of the data, a five‐state multistate model was established to describe competing events of MVC, DKD, a combination thereof, and the terminal state, death. Two hypotheses were investigated: (1) the risk of MVC and DKD are mutually independent, and (2) mortality is independent of morbidities. At the end of the study, the majority of individuals remained in uncomplicated T2D; however, the probability of transition to complications and death increased over time. The mortality hazard depended on the presence of morbidities and was quantified as a life expectancy decreased by 5.0, 9.7, and 12.2 years for MVC, DKD, and the combined morbidity, respectively, compared to uncomplicated T2D. An established framework with a five‐state model incorporating competing events was shown to be a useful tool for comorbidities risk assessment in newly diagnosed patients with T2D.

Summary.

• What is the current knowledge on the topic?

  • ○
    Patients diagnosed with type 2 diabetes (T2D) have an elevated risk of developing complications as their disease progresses over time. Although pharmacometric approaches using multi‐state models have previously been used to describe disease progression in other areas, their application to T2D, especially using Swedish registry data, is still limited.
• What question did the study address?

  • ○
    The study characterized the progression of long‐term complications of T2D in patients from the Swedish National Diabetes Registry, accounting for competing events using a multi‐state model.
• What does this study add to our knowledge?

  • ○
    Although around 80% of individuals remain in uncomplicated T2D at the end of their observation period, the model confirmed considerable differences in mortality in the presence of comorbidities. Additionally, our study offered quantitative evidence for the development of microvascular complications, increasing the risk of macrovascular complications more than vice versa.
• How might this study change drug discovery, development, and/or therapeutics?

  • ○
    The developed multi‐state model with competing risks offers a framework for understanding and predicting long‐term complications and mortality in patients with T2D, which is a lifelong illness.

1. Introduction

Diabetes, affecting over 400 million people globally and constituting 90% of type 2 diabetes (T2D) cases [1], remains a prominent cause of death, ranking among the top 10 worldwide, with 1.5 million deaths attributed to it in 2019, according to WHO [2]. However, the reported number might underestimate the impact of T2D, as it could be an underlying cause for long‐term complications that contribute to increased mortality [3, 4]. Diabetes leads to both microvascular complications like diabetic kidney disease (DKD) and macrovascular complications (MVC), including cardiovascular, cerebrovascular, and peripheral arterial diseases [2]. Recent evidence indicates that the likelihood of developing these long‐term complications in patients with T2D may be influenced by the presence of additional risk factors [5].

T2D is a progressive metabolic disorder, and as such, progression is usually assessed with long‐term cohort studies. Longitudinal data widely collected during these studies are used to investigate relationships between patient characteristics, i.e., covariates, and an event of medical interest. Time‐to‐event (TTE) models can be used to analyze the time until such events of medical interest occur. With proper inclusion of covariates, a TTE model can give insight into why and when an event of interest is likely to occur. Parametric TTE models have the additional advantage of being able to predict future events in similar populations and include the impact of time‐variant covariates, including drug/treatment exposure, on the predictions [6].

As longitudinal studies include repeated measures to follow individuals over prolonged time, multiple events of interest could be recorded in an individual, e.g., cardiovascular events and death. The analysis in such studies is often conducted using multi‐state models. A multi‐state model (MSM) is a model for a continuous‐time stochastic process allowing individuals to transition through multiple states [7]. Unlike standard TTE methods, including the Kaplan–Meier estimators and Cox proportional hazards models, which are typically used for a single type of event analysis, MSMs are designed to handle multiple events of interest [8]. The MSM accounts for the probability of an event in an interval between medical visits (i.e., interval censoring) and allows simultaneous estimation of covariate effects on the different states. The typical outcome includes the type of event that occurred and the time of occurrence. The occurrence of an event signifies the transition from one state to another, and, therefore, MSM provides an appropriate modeling framework for event history data [9].

A crucial issue in event history analysis is the presence of competing risks. A competing risk is an event which occurrence precludes the occurrence or modifies the probability of another event happening [10]. For instance, considering a primary outcome of cardiovascular death, death due to non‐cardiovascular causes would be a competing event, as patients who die of non‐cardiovascular causes are no longer at risk of cardiovascular death [11]. Competing risk methodology is progressively applied to mortality risk assessments to obtain accurate probabilities of death stratified by certain causes [12] or addresses scenarios where patients may face multiple competing outcomes, such as further disease progression, alongside the possibility of mortality. The widely used approaches for competing risks are the cause‐specific and the subdistribution relative hazard [13]. In the cause‐specific approach, the instantaneous rate of the event of interest is modeled, treating competing events as censored. It is particularly suited for understanding the underlying cause‐specific event dynamics. In contrast, the subdistribution hazard focuses on the cumulative incidence of the event, incorporating the influence of competing risks explicitly [13]. A limitation of this approach is that, for certain covariate patterns, the sum of the cause‐specific cumulative incidence functions can exceed one [14]. Although both methods have their applications, the cause‐specific hazard approach is often preferred in multi‐state models, especially when the goal is to describe the transitions between different disease states due to the complications and to provide a clearer interpretation of how individual factors influence the hazard of progressing to different states [15].

Previous studies have utilized standard and MSM methodology to explore various aspects of T2D and vascular complications, as separate outcomes or considering their interplay. These studies include, but are not limited to, investigations into the progression of micro‐ [16] and macrovascular [17] morbidities at different stages; T2D progression concerning micro‐ and macrovascular complications, although lacking the combined state that is likely to occur in reality [18]; and the burden of multimorbidity among T2D populations [19, 20, 21]. Existing evidence shows that patients with T2D face increased risks of cardiovascular disease, renal failure, and other complications, contributing to elevated morbidity and mortality rates [22]. However, these studies typically treat events independently, potentially overlooking the interplay between competing risks of comorbidities and mortality. The MSM approach integrated with competing risk analysis can enhance the understanding of T2D disease progression by employing a comprehensive modeling framework that quantifies competing risks of morbidity and mortality using real‐world data. This allows for more accurate risk stratification and can inform targeted interventions, potentially improving patient care and management strategies in T2D [23, 24].

This work aimed to establish a framework for risk predictions of macrovascular complications (MVC) and diabetic kidney disease (DKD) in patients with T2D, using real‐world data from the Swedish National Diabetes Registry (NDR) [25].

2. Methods

2.1. Clinical Data

The database used to develop the framework originated from the Swedish National Diabetes Register (NDR). The NDR was initiated in 1996 and has been previously described in details [26, 27]. It includes information on risk factors, complications of diabetes, and medication. The regional ethical review board has approved this study (Dnr 2013/399).

Considerable revisions of targets for diabetes care were implemented in Sweden in 1999. To ensure a high degree of implementation of these new targets, we defined the population of interest as patients included in the NDR from 2005 to 2013. Additionally, patients were adults (≥ 18 years), diagnosed with T2D ≤ 1 year earlier, had at least one record of key covariates during the observation period, and did not show signs of MVC or DKD at inclusion. The first recording in NDR is defined as time = 0, occurring up to a maximum of 1 year from the date of diagnosis. We defined an MVC event as a patient having an ischemic heart or a cerebrovascular disease, including a transient ischemic attack and stroke; these diseases were recorded by the NDR. The definition of a DKD event was based on the Renal Association Guide [28]; patients with GFR < 29 mL/min/1.73 m², GFR 30–44 mL/min/1.73 m² complicated by micro‐ or macroalbuminuria, or GFR 45–59 mL/min/1.73 m² complicated by macroalbuminuria were defined to have a DKD event. Once the criteria for an MVC or DKD event were met, a patient was considered to have experienced this event until another event occurred or until the end of the study.

Demographic information was gathered from NDR, including biological sex, age, and age at T2D diagnosis (Tables 1 and 2). The selected individuals were then cross‐referenced with the Cause of Death register to retrieve the date of death.

TABLE 1.

Baseline characteristics of the study population, originating from the Swedish National Diabetes Register; a total of 41,517 patients with T2D.

	Mean	Median	Range	CV%
Age (years)	61.6	62.0	18.5–99.6	19.5
Age at diabetes onset (years)	61.1	62.0	18.0–99.0	19.7
Duration of diabetes (years)	3.2	3.1	0.01–9.6	67.7
BMI (kg/m2)	30.5	29.8	14.2–50.0	17.3
HbA1c (mmol/mol)	52.5	48.0	26.0–144.0	29.7
Cholesterol (mmol/L)	5.3	5.2	2.0–14.0	21.1
Triglycerides (mmol/L)	2.0	1.7	0.30–16.0	64.8
HDL (mmol/L)	1.3	1.2	0.3–4.0	31.2
LDL (mmol/L)	3.2	3.1	0.4–8.7	30.4
sBP (mmHg)	137	135	80–250	12.1
dBP (mmHg)	80	80	40–130	12.1
Sex (Men/Women)	22,715/18,802		(54.7%/45.3%)

Abbreviations: BMI, body mass index; CV%, coefficient of variation; dBP, diastolic blood pressure; HbA1c, hemoglobin A1c; HDL, high‐density lipoproteins; LDL, low‐density lipoproteins; sBP, systolic blood pressure.

TABLE 2.

Statistics of events, i.e., diabetic kidney disease (DKD), macrovascular complications (MVC), and deaths in the study population of patients with newly diagnosed T2D.

	Entire dataset, N (%)	Training dataset, N (%)	Evaluation dataset, N (%)
Uncomplicated T2D	34,970 (84.2)	26,155 (84.2)	8815 (84.4)
Deaths	1950 (5.6)	1454 (5.6)	496 (5.6)
Macrovascular complications (MVC)	3878 (9.3)	2936 (9.5)	942 (9.0)
Cerebrovascular disease	1507	1134	373
Ischemic heart disease	2886	2184	702
Deaths	330 (8.5)	241 (8.2)	89 (9.5)
Diabetic kidney disease (DKD)	664 (1.6)	492 (1.6)	172 (1.6)
Deaths	112 (17.1)	83 (17.1)	29 (17.1)
MVC and DKD	3878 (9.3)	2936 (9.5)	942 (9.0)
Deaths	49 (21.5)	34 (20.0)	15 (25.9)
Total death	2439 (5.9)	1811 (5.8)	627 (6.0)

Note: DKD was defined as GFR < 29 mL/min/1.73 m² or GFR between 30 and 44 mL/min/1.73 m² complicated by micro‐ or macroalbuminuria or GFR between 45 and 59 mL/min/1.73 m² complicated by macroalbuminuria. MVC was defined as an event of cerebrovascular disease (CVD) or ischemic heart disease (IDH).

Left censoring of data was addressed by including only newly diagnosed patients (first registration in NDR within a year from the date of diagnosis) with T2D without prior evidence of complications (Figure S4). As the exact date of the MVC and the DKD events were unknown, these events are subject to interval censoring. Interval censoring, as well as right censoring, were handled by the method as described below in the model structure and development section. Individuals where the date of death was unknown were excluded. Right‐censoring was mainly administrative censoring, as the observation period ended. The Kaplan–Meier plots of comorbidities and death are found in the Figure S3.

This study population consisted of 41,517 patients, with 290,434 observations (Figure 1). For the analysis, data was split into a training dataset with 31,077 patients (i.e., 75% of the data) on which the framework was developed and a validation dataset with 10,440 patients (i.e., 25% of the data) used for validation of the framework.

FIGURE 1.

The flowchart represents the step‐by‐step criteria for the patients and the number of patients being included in the current data analysis.

2.2. Model Structure and Development

The framework for risk predictions of comorbidities (i.e., MVC and DKD events) and mortality used an acyclic multi‐state model with five states, as depicted in Figure 2. The initial state, state 1, represents patients with uncomplicated T2D, i.e., without signs of comorbidities. All patients enter in this state. A patient can progress to state 2, MVC, or state 3, DKD. These states are competing as the transition to the combined state, state 4, occurs through either state 2 or 3. From any of these states (states 1–4), at any time point, a transition to the absorptive state 5 (death) could happen.

FIGURE 2.

Graphical representation of the framework of disease progression in type 2 diabetes. The framework consists of a five‐state model: State 1—uncomplicated T2D (green square), state 2—macrovascular complications (MVC; orange square), state 3—diabetes kidney disease (DKD; blue square), state 4—MVC and DKD (purple square) and state 5—death (gray circle, absorbing state). All patients start from state 1 (S1) and can either stay in S1 until the end of the observation period, or develop one of the comorbidities, i.e. MVC (S2) or DKD (S3) or die (S5). If they develop one of the comorbidities (S2 or S3), they can stay in this state until the end of the observation period, develop the other comorbidity, progress to the combined state (S4), or die (S5). In state 4, patients can stay until the end of the observation period or die (S5).

In this study, the competing risks of developing state 2 (MVC) and state 3 (DKD) were assumed to occur to the combined state 4 through a preceding transition into either state 2 or 3. The terminal process of death censors the non‐terminal processes of developing any comorbidity, while death is non‐censored until the end of the study. This is called semi‐competing risk, as censoring is non‐mutual between states [29].

The change in a state probability was expressed in terms of differential equations (Equations (1), (2), (3), (4), (5)), where the mass transfer between states corresponds to the change in the distribution of the probability of states over time.

$$\raisebox{1ex}{$\mathrm{d}{P}_1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.=-P_1·\left({\lambda }_{12}+{\lambda }_{13}+{\lambda }_{15}\right)$$ (1)

$$\raisebox{1ex}{$\mathrm{d}{P}_2$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.=P_1·{\lambda }_{12}-P_2·\left({\lambda }_{24}+{\lambda }_{25}\right)$$ (2)

$$\raisebox{1ex}{$\mathrm{d}{P}_3$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.=P_1·{\lambda }_{13}-P_3·\left({\lambda }_{34}+{\lambda }_{35}\right)$$ (3)

$$\raisebox{1ex}{$\mathrm{d}{P}_4$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.=P_2·{\lambda }_{24}+P_3·{\lambda }_{34}-P_4·{\lambda }_{45}$$ (4)

$$\raisebox{1ex}{$\mathrm{d}{P}_5$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.=P_1·{\lambda }_{15}+P_2·{\lambda }_{25}+P_3·{\lambda }_{35}+P_4·{\lambda }_{45}$$ (5)

where P _S is the probability of state S at time t (time is continuous) and λ _SR is the cause‐specific hazard used to describe the transition intensities between current state S and next state R. As mentioned, all patients were assumed to start in state 1 (uncomplicated T2D), with the full probability (100%) being assigned to state 1. While patients experience an event, the full probability (i.e., 100%) is transferred to that observed state, and the subsequent time permits the transfer of probability to the remaining allowed transitions, without the possibility of transit back to a previous state. Transitions to states 2, 3, and 4, accounted for interval censoring, while transitions to state 5 were recorded at the date of death.

2.3. Terminal Transitions

For transition intensities to death (state 5), the Gompertz‐Makeham equation [30] was used, estimating an age shift for each state‐specific transition (Equation 6).

$${\lambda }_{S5}={\alpha }_{15}+{\beta }_{15}·e^{{\kappa }_{15}\left(\mathit{age}\left(t\right)+{\mathit{\text{MtAS}}}_{S5}\right)}$$ (6)

where 𝜆 _S5 represented the mortality hazard from state 1 (𝜆 ₁₅ ), state 2 (𝜆 ₂₅ ), state 3 (𝜆 ₃₅ ), and state 4 (𝜆 ₄₅ ). α ₁₅ , 𝛽 ₁₅ , and 𝜅 ₁₅ are the intercept, the scale, and the shape parameters, respectively; all sex‐specific. Instead of estimating separate parameters for each state, the differences in mortality hazard for different states were expressed as shifts in biological age, MtAS _S5 , setting the uncomplicated T2D as the reference, i.e., MtAS ₁₅ was fixed to 0. Mortality age‐shifts, for transitions 2 → 5, 3 → 5, and 4 → 5 were estimated in the model.

Several modifications to the terminal transitions were explored, such as the addition of the duration of disease as a step function or a linear model with or without an intercept.

2.4. Non‐Terminal Transitions

Several alternatives for describing the transition intensities between non‐terminal states were investigated during the model development. Initially, cause‐specific constant hazards were used to describe the transition intensities between states 1, 2, 3, and 4, implemented as the reciprocal to allow the mean transit time (MTT) through a state to be estimated (Equation 7)

$${\lambda }_{\mathit{SR}}=1/{\mathit{MTT}}_{\mathit{SR}}$$ (7)

where MTT _SR is the mean transit time for the transition from state S to state R.

In addition, age‐dependent transition intensity without or with a constant age‐independent contribution (i.e., Gompertz and Gompertz‐Makeham equation, respectively; Equations 8 and 9) were investigated.

$${\lambda }_{\mathit{SR}}\left(t\right)={\beta }_{\mathit{SR}}·e^{{\kappa }_{\mathit{SR}}·\mathit{age}\left(t\right)}$$ (8)

$${\lambda }_{\mathit{SR}}\left(t\right)={\alpha }_{\mathit{SR}}+{\beta }_{\mathit{SR}}·e^{{\kappa }_{\mathit{SR}}·\mathit{age}\left(t\right)}$$ (9)

where α _SR , 𝛽 _SR , and 𝜅 _SR are the intercept, the scale, and the shape parameters for transitions from state S to state R, respectively, estimated in the model. For the low‐frequency transitions (i.e., 3 → 4 and 2 → 4), a more complex transition intensity was only investigated if that complexity was deemed important for the more frequent transitions (i.e., 1 → 2 and 1 → 3). The impact of sex on the non‐terminal states was also explored.

2.5. Software and Statistical Considerations

Data management and exploration of the data, visual predictive checks (VPCs), and data‐splitting were performed using R v.3.5.1 [31]. Model fitting, simulations, and statistical testing were performed in NONMEM V7.4.3 [32] with PsN [33]. Parameters were estimated with the FO method and ADVAN 13 as the differential equation solver.

Throughout the model building, internal evaluation through VPCs and statistical testing with the likelihood ratio test (LRT) were performed. The LRT was used to compare the fits of nested models, where the difference in objective function values (OFVs) is assumed to be χ ²‐distributed with the degree of freedom being the number of differing parameters between competing models. To perform the model building with a focus on predictive performance, 3‐fold cross‐validation was performed, stratifying to ensure that every subset of data included individuals with all possible transitions. The statistical significance level used was 1%.

The VPC involved simulating 100 samples from the model and then comparing the median of the observed data with the 95% confidence interval of the median of the simulated data. The final model was also evaluated using a validation dataset. Parameters from the training dataset were applied, and 100 samples were simulated, comparing the observed median with the 95% confidence interval of the simulated median. While performing the simulations, non‐random censoring (i.e., death) was addressed by adding yearly observation records of patients who died during the study, extending their longitudinal data until the date of administrative censoring. Neglecting to extend these patients' shorter data series would incorrectly limit simulated individuals' observation period, causing biased simulations. Data records for individuals who died in the simulated population were truncated at the time of death [34]. All other dropouts were considered completely at random, as they originated from administrative censoring and thus simulated according to the realized design.

3. Results

The model selection process, highlighting the OFVs and cross‐validation OFVs for the key runs, is summarized in Table 3.

TABLE 3.

Cross‐validation of the key model runs performed during the model development and selection.

Model selection
		Cross‐validation		Estimation
Type of model	Run N	OFV	dOFV	OFV	dOFV	Reference model	N of estimates	Comment
Mortality	1	55,667	0	55,661	0	NA	8	Constant HZ
Mortality	2	54,323	−1344	54,294	−1367	1	13	GM
Mortality	3	54,112	−211	54,097	−197	2	14	GM + DP (shift)
Mortality a	4	53,802	−521	53,770	−524	2	14	GM + DP (slope*time)
Mortality	5	53,789	−534	53,770	−524	2	15	GM + DP (slope*time + shift)
Morbidity	6	52,954	−848	52,932	−838	4	15	BMM + G on S1 → S2, same k for men and women
Morbidity	7	52,851	−103	52,826	−106	6	16	BMM + G on S1 → S2, different k for men and women
Morbidity	8	53,279	−523	53,261	−509	4	15	BMM + G on S1 → S3, same k for men and women
Morbidity	9	52,357	−494	52,327	−499	7	17	BMM + G on S1 → S2, different k + G on S1 → S3, same k

Abbreviations: BMM, best mortality model; DP, disease progression; G, Gompertz; GM, Gompertz‐Makeham; HZ, hazard; k, shape parameter in Gompertz and Gompertz‐Makeham equations.

^a Best model for mortality (BMM).

3.1. Terminal Transitions

All mortality transitions were best described using the Gompertz‐Makeham equation. An additional linear relationship with time since diagnosis was also included on the mortality, as a T2D progression (T2DP, Equations 10 and 11):

$$T2\mathit{DP}=\mathit{\text{SLOPE}}·t$$ (10)

$${\lambda }_{S5}={\alpha }_{15}+{\beta }_{15}·e^{{\kappa }_{15}\left(\mathit{age}\left(t\right)+{\mathit{\text{MtAS}}}_{S5}+T2\mathit{DP}\right)}$$ (11)

The mortality was found to be dependent on morbidities, and the mortality hazard from MVC, DKD, and the combined morbidity, relative to patients with uncomplicated T2D, corresponded to the hazard of a person 5.0 years, 9.7 years, and 12.2 years older, respectively.

3.2. Non‐Terminal Transitions

To describe the hazard of the disease progression from uncomplicated T2D to MVC and DKD, the Gompertz formula fitted the data best (Equation 8). This model captured the tendency to escalate the transition intensity with increasing age (Figure S1).

Conceptually, transitions 1 → 2 and 3 → 4 imply the onset of MVC, and thus, the transition intensity could potentially share parameters. Similarly, transitions 1 → 3 and 2 → 4 imply the onset of DKD. To test this hypothesis, the same equations were used for transitions 1 → 2 and 3 → 4 as well as for transitions 1 → 3 and 2 → 4, estimating only a difference in hazard as a morbidity age‐shift (MbAS) (Equations 12 and 13). All Gompertz parameters (𝛽_SR and κ _SR) were shared for the corresponding morbidity transition (1 → 2 with 3 → 4 and 1 → 3 with 2 → 4).

$${\lambda }_{24}\left(t\right)={\beta }_{13}·e^{{\kappa }_{13}\left(\mathit{age}\left(t\right)+{\mathit{\text{MbAS}}}_{24}\right)}$$ (12)

$${\lambda }_{34}\left(t\right)={\beta }_{12}·e^{{\kappa }_{12}\left(\mathit{age}\left(t\right)+{\mathit{\text{MbAS}}}_{34}\right)}$$ (13)

where MbAS ₂₄ and MbAS ₃₄ are the morbidity age‐shifts, which are estimated parameters, shifting the biological age to a higher value and thus, a higher hazard. The hazard of DKD, with prior MVC, was estimated to be equivalent to the hazard of DKD for a 6.6‐year older patient without pre‐existing MVC. The corresponding estimate for MVC, with pre‐existing DKD, was 3.6 years. These models were both statistically better than constant transition intensity (ΔOFV = −61 and ΔOFV = −8). However, due to model instability, the constant transition intensity (Equation 7) was retained in the final model.

An interactive data visualization for the framework is found at https://hanna‐kunina.shinyapps.io/MSMM/.

The final model described the semi‐competing terminal process of death and the two competing non‐terminal processes of developing MVC and DKD during the study period of 9 years since diagnosis of T2D. According to the VPC of the final model of both internal (Figure S1) and external data (Figure 3), the medians of the observed and simulated data showed the same trend, and the median of the observed data was well within the 95% prediction interval (PI) of the model simulations. Final model parameter estimates with their uncertainties are presented in Table 4. The parameters were determined with high certainty, with a majority of the estimated parameters' relative standard error (RSE) not exceeding 25%.

FIGURE 3.

External validation showing the proportion of patient observations in each state versus time since diagnosis. Gray shaded areas represent the 95th prediction interval of model simulations and the median of the observed data is displayed as black open circles connected with splines.

TABLE 4.

Final model parameter estimates with point‐estimates (Estimate) and corresponding relative standard errors (RSE).

Final model parameter estimates
Parameter description	Abbreviation	Estimate	RSE (%)
Slope in the natural disease progression (−)	SLOPE	3.44	5.49
Mortality age shift of state 2 relative to state 1 (Years)	MtAS25	5.0	19.0
Mortality age shift of state 3 relative to state 1, (Years)	MtAS35	9.68	17.6
Mortality age shift of state 4 relative to state 1 (Years)	MtAS45	12.2	15.74
Transition intensity from state 2 → 4, as reciprocal of MTT (Years−1)	1/MTT24	0.016	11.01
Transition intensity from state 3 → 4, as reciprocal of MTT (Years−1)	1/MTT34	0.066	15.43
Scale parameter (women) of mortality (Years−1)	κ f	0.086	4.43
Scale parameter (men) of mortality (Years−1)	κ m	0.082	3.99
Intercept (women) of mortality (−)	αf	0.00051	107.9
Intercept (men) of mortality (−)	αm	0.00115	50.9
Shape parameter (women) of mortality (−)	βf	13.4⋅10−6	35.5
Shape parameter (men) of mortality (−)	βm	24.9⋅10−6	29.4
Shape parameter for transition 1 → 2 (−)	β12	0.00125	8.48
Scale parameter (women) for transition 1 → 2 (Years−1)	κ 12,f	0.047	2.69
Scale parameter (men) for transition 1 → 2 (Years−1)	κ 12,m	0.0524	2.44
Scale parameter for transition 1 → 3 (Years−1)	κ 13	0.089	0.36
Shape parameter for transition 1 → 3 (−)	β13	14⋅10−6	1.36

4. Discussion

In this study, a multistate model of T2D disease progression was developed that predicts the competing risks of the first occurrence of micro‐ and macrovascular complications and death. The final model described death rates of a Swedish cohort of patients with newly diagnosed T2D and the risks of developing comorbidities during the study period, in both the data used to develop the model and more importantly, in the validation data.

During the observation period, the patients were followed, and we found that the probability of occupying the initial state, i.e., uncomplicated diabetes, was continuously decreasing, showing tendencies of patients moving to the subsequent states. At the same time, the state occupational probabilities of intermediate states and death, for the most part, continuously increased following concerning time. The majority (approximately 80%) of patients remained in uncomplicated T2D from the start to the end of the study period.

Approximately 10% of patients have developed vascular complications, with MVC being more common than DKD. The risk of developing vascular complications was higher among men than women, and the rate of developing MVC increased more rapidly with age in men. The occupational probability of the MVC state was higher than that of the DKD state; however, patients in the DKD state had a higher risk of death. The risk of transitioning to the semi‐competing death state was higher for the combined MVC + DKD state than for either state individually, with the rate of transition to the MVC + DKD state from the DKD state being higher than from the MVC state. Thus, comorbidities reduce the expected lifespan to a significant extent, and even more when present together.

These findings support the main results of the work conducted by Höskuldsdóttir et al., applied to a larger cohort from the NDR [35]. Although the high incidence of MVC may indicate a need to improve treatment for prevention, the model identified a mortality risk of DKD and MVC + DKD that was much higher than for MVC alone, as the mortality age for MVC, DKD, and MVC + DKD was estimated to be 5 years, 9.7 years, and 12.2 years older than the population with uncomplicated T2D (Figure S5). From a mortality point of view, it may thus be more efficient to focus on reducing the risk of DKD.

The mortality age for the combined MVC + DKD state was estimated to be higher than having MVC or DKD alone, compared to uncomplicated T2D. This suggests an interaction between the comorbidities, as the effect on life expectancy from having both is less than simply additive, indicating that one comorbidity may influence the development or management of the other. The rate of DKD development was estimated to be equivalent to that of a 6.6‐year older patient for patients being in the MVC state compared to those in the T2D state. Similarly, the rate of MVC development was estimated to be equivalent to that of a 3.6‐year older patient for patients being in the DKD state compared to those in the T2D state.

When transitioning to the death state, men had a higher age‐independent risk of death and a higher initial age‐dependent mortality rate compared to women, although mortality rates over time were similar for both sexes (Table 4). These findings applied to all transitions to the death state due to shared parameters. However, future research can investigate sex‐specific constants for mortality transitions to evaluate their impact on each developed comorbidity and uncomplicated T2D individually.

During the model development, the need for an increased transition probability to the terminal state shortly after the T2D diagnosis was identified to adequately describe the data and avoid model misfit (Figure 3 and Figure S2). Since patients with evidence of either MVC or DKD at diagnosis (i.e., study initiation) were excluded from the study, the increased mortality shortly after inclusion can be explained by several interconnected factors. First and foremost, as T2D is a “silent disease,” the patients may have initiated health contact due to other health issues, and T2D diagnosis is a secondary consequence of the healthcare interaction. These patients, who are ill from other diseases, might be at higher risk of death, and the model, with the current implementation, does not separate on death cause. Moreover, a delayed diagnosis due to missed early signs of T2D may result in individuals entering the healthcare system (and, therefore, NDR) at a stage where significant damage to the body has already manifested, although not as MVC or DKD, leading to a substantial number of patients developing complications, followed by death quickly after diagnosis (Figure S2). This behavior suggests a potential depletion‐of‐susceptible bias. Since the susceptible patients tend to have earlier outcome effects, their prevalence decreases over time. Consequently, the participant pool becomes skewed toward individuals who are more resilient or responsive to interventions over time, potentially causing a slowdown in the overall death rate.

The dataset for the simulations was extended for those individuals who died before the end of the observation period with one observation per year until the date of the administrative censoring. This was done to avoid simulation bias, as death is a non‐random dropout [34]. Assuming that observations were only made once yearly simplifies real‐world complexities where observation frequency varies greatly. Creating simulation data that even better mirrors the inherent heterogeneity in realized design, with a variable sampling frequency based on the realized sampling frequency, might allow for a more nuanced exploration of different scenarios of model fit. This alternative was not explored, and consequently, some simulation bias remains.

Several limitations of this study warrant attention. A significant number of incidents may go unreported for various reasons, such as lack of awareness, infrequent hospital visits, or reporting errors, even though the events of interest may have already occurred. Additionally, we included stroke and ischemic heart disease as evidence of cardiovascular disease, although they are soft endpoints. This, together with the relatively short observation period—primarily defined by updates in clinical guidelines and the introduction of GLP‐1 analogs and SLGT‐2 inhibitors—may not allow for the full capture of long‐term comorbidities, increasing the risk of underestimating MVC and DKD incidence. Moreover, T2D is a long‐term progressive disorder, so the characteristics of the study population might vary across different inclusion periods. Cohort effects, such as improvements in diabetes care or awareness over time, could contribute to variations in mortality rates among different cohorts within the study, so the cohort parameters derived in the current study should be evaluated in a different cohort in the future. Lastly, no individual patient characteristics other than age and biological sex were considered as covariates in the final multi‐state model. Furthermore, only high‐level information regarding therapeutic interventions was available for the analysis, e.g., oral antidiabetic treatment, but not the specific drug, which complicates the evaluation of the effects of various treatment strategies on patients' outcomes. However, most of the drug effects should be captured by the longitudinal changes observed in biomarkers such as HbA1c, blood pressure, and low/high‐density lipoproteins, which are primarily influenced by therapeutic interventions. Therefore, future investigations will focus on exploring baseline and time‐varying relationships with biomarkers, as well as conducting integrated composite assessments of these biomarkers.

Overall, T2D, being a highly heterogeneous disease in its progression, requires special considerations while calculating the risks of developing complications. The developed multi‐state model can serve as a solid baseline for describing the long‐term progression of T2D, focusing on the transition risks of comorbidities and mortality among newly diagnosed patients. This model can be naturally extended to incorporate additional covariates and competing risk outcomes, offering a flexible framework for further refinement as more data are included. The calculated risks of micro‐ and macrovascular complications using the developed multi‐state model, when linked to the individual patient characteristics, can be used in a more comprehensive estimation of the burden of T2D [36].

5. Conclusion

A multi‐state model for competing risks analysis of T2D long‐term complications was successfully developed. The model was built using cross‐validation and a separate validation dataset to ensure that the predictive performance of the model transfers to new data. This model can adequately describe the disease progression of long‐term complications in the newly diagnosed Swedish T2D patient population, focusing on the development of vascular complications and mortality. Future work involves the assessment of treatment impact on the risk of comorbidities and mortality through changes in individual covariates.

Author Contributions

H.K., S.F., and M.C.K. wrote the manuscript. M.C.K. designed the research. H.K. performed the research. H.K. and M.C.K. analyzed the data.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Data S1.

Data S2.