Introduction

The increasing proportion of people suffering from chronic diseases is peculiarly worrying as these conditions constrain activities of daily living, necessitate ongoing medical attention and hence, are associated with considerably higher costs and healthcare expenses [1]. Disease management activities have been shown to reduce the risk of acute complications and premature mortality caused by chronic diseases [2]. Though, effective responses require accurate estimates of current and future chronic disease burden to tailor health care planning and resource allocation [3]. Worldwide, diabetes mellitus is one of the most frequent chronic diseases, and thus, is a disease with high public health relevance [1, 2, 4]. Current type 2 diabetes (T2D) prevalence is estimated with 7.4% among men and 7.0% among women in Germany aged 40 years or older [4, 5]. Besides severe late complications, diabetes mellitus leads to significantly higher mortality and is associated with 1.5 to 4.4 times higher health-care costs compared to people without diabetes [1].

Projection models are powerful tools to estimate future case numbers of a disease in order to inform decision-makers and cost-bearers in the health care system. Consequently, further developing and spreading the knowledge about accurate projection methods is essential to counteract the ever-worsening disease situation. However, different models may vary in their outcomes and closeness to reality [6]. Nonetheless, to our best knowledge, there is no scientific work that systematically compares these different projections methods for the context of chronic diseases. Therefore, the aim of this work is to fill this gap and to introduce, describe, and critically discuss each of the methods individually and in comparison.

In general, projection methods are limited by the availability of epidemiological and demographic data. Consequently, it is common to project and compare several scenarios that reflect on possible future trends in these areas [3, 4, 6–8]. Besides, the choice of the method can considerably affect projection results. In the context of chronic diseases, there are several methodological approaches that have been advocated for case number projections. For example, most reports are based on a ‘status quo approach’ [6] which relies on a simple application of the current prevalence to population projections. This procedure has been used for instance in the contexts of pulmonology [9], Parkinson’s disease [10] and diabetes [11] among others. Probably due to its simplicity, this method is most popular in projection contexts. However, approaches that aim to incorporate for example underlying disease-specific transition rates, i.e., incidence and mortality, seem more appropriate as they better capture the complex nature of chronic diseases [12]. Therefore, some studies rely on multistate models that incorporate and relate disease-specific transition rates. In this regard, multistate models are widely used in infectious and chronic disease epidemiology [13–15]. For example, Milan and Fetzer [6], Brinks et al. [8, 16] and Waldeyer et al. [3] used time-discrete Markov models in the context of dementia, lupus and diabetes. Another approach is used by Carstensen et al. [7] who used a Poisson regression to model disease-specific transition rates of diabetes. Thereof, they extrapolate the future trends of the rates by extending the trends observed in the past. A relatively novel approach is reported by Tönnies et al. [4], who use a partial differential equation to project future diabetes prevalence in Germany. There remains, however, considerable debate about the methodological approach.

In the present article, we give an overview of possible methods and underlying data used for future case number projections in the context of chronic conditions. For this purpose, we will examine three projection methods in more detail. We discuss how to employ each of the approaches in a practical application to project sex- and age-specific case numbers of people with diagnosed T2D for Germany between 2010 and 2040.

Methods

In the following section, we describe different models for projecting chronic disease case numbers. All methods were implemented using the free software R, v.4.1.0 (The R Foundation for Statistical Computing).

We focus on three different approaches to project chronic disease case numbers. Previous studies have mostly used a very simple approach, commonly referred to as status quo method [6]. Due to its popularity, we include this procedure in our work, speaking of it as method 1). This approach solely relies on the age- and sex-specific prevalence from a base year, which is then applied to population projections. Other epidemiological factors, such as the incidence, are only incorporated implicitly in the prevalence. Thus, this method ignores the fact that prevalence is a consequence of incidence and mortality. Hence, it might be too simplistic to accurately mirror reality. The alternative methods 2) and 3) rely on demographic components as well as on various disease-specific information on prevalence, incidence, and mortality rates as input factors. Method 2) is aligned with the work of Tönnies et al. [4], who takes advantages of the theory of multistate models in chronic disease epidemiology and an associated partial differential equation (PDE). With method 3) we present a novel projection method, which consists of a two-dimensional system of PDEs. The theoretical background for the PDEs used with method 2) and 3) originates in the illness-death model (IDM) as depicted in Fig 1. The IDM is a multistate model that represents continuous-time stochastic processes. Thereby, it allows individuals to move between a finite number of states [17, 18]. The classical IDM consists of three states, i.e., "healthy" (number of healthy people aged a at time t H(t, a)) with regards to the disease of interest, the disease state "ill" (number of ill people I(t, a)) and the death state, i.e., "dead" (D). It is assumed that at birth all individuals start in the healthy state. From there on, they can either be diagnosed with a chronic disease like T2D and then die at some point in time, or they can transition directly to death state (without contracting diabetes). The arrows indicate the transition rates between the states which depend on age and time. Since diabetes is a chronic condition, we assume that there is no remission from the chronic condition back to the healthy state. The transition rates are given by the incidence rate IR(t, a) the mortality of the non-diseased m₀(t, a) and the mortality of diseased people m₁(t, a), which are all sex-specific functions of calendar time t and age a. In epidemiological contexts, calendar time t is also denoted by period.

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Fig 1. Illness-death model.

All people in a population are in one of the three states: Healthy, Diseased, or Dead. It is assumed that at birth, all people start in the healthy state. Depending on time t and age a of each respective person, they will then transition to another state which is described by the IR, m₀, and m₁.

https://doi.org/10.1371/journal.pone.0264739.g001

The following sections describe each of the three methods as sketched in Fig 2 and the required input data in more detail. Aggregated data about prevalence and incidence of the chronic condition of interest, as well as on the mortality of the general population and the excess mortality are sufficient, i.e., none of the methods require individual subject data.

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Fig 2. Overview of methods for future disease case projection.

Illustrated in Fig 2A, method 1) uses the age-specific prevalence in base year t₀ which is applied to the population projections. Fig 2B depicts method 2). Using the theoretical background of the IDM, the age-specific prevalence for each year is derived by solving the PDE which requires input on the transition rates, namely the IR, m₀ and m₁. Method 3), as sketched in Fig 2C, calibrates m₀ and m₁ in the base year t₀ from the population projections. IR, m₀ and m₁ are inputs for the PDE which directly returns age-specific T2D case numbers for each year. Summing over all ages yields the total number of T2D cases for each year from 2010 to 2040 for each method.

https://doi.org/10.1371/journal.pone.0264739.g002

Results

Based on the age-specific prevalence in 2010, we projected the age-specific case numbers for T2D in the German male population between 2010 and 2040 using the above-mentioned approaches. Remember that we assume a constant age-specific prevalence with method 1), i.e., we apply the prevalence from 2010 to our population projections. We further assumed that also the IR remains constant over time for method 2) and 3) in the main analysis. However, we consider temporal trends in the MRR for method 2) and 3) which affects, amongst others, the prevalence. Since for Germany, information on long-term trends in the latter are limited, we use speculative time-related developments. Current evidence undermines that the mortality rate among people with T2D is likely to decrease faster than among healthy people due to progresses in medical care [21]. Therefore, it seems plausible to assume a reduction in the MRR [28]. For simplicity, we restrict the main analysis to a baseline scenario for method 2) and 3) which thus comprises a constant IR and a decrease in the MRR of 2% per year. We reflect on rather likely, as well as on relatively extreme scenarios for the MRR and IR in the sensitivity analyses discussed in the supporting information.

Fig 3 depicts the number of projected male T2D cases in Germany between 2010 and 2040 using the three different approaches. All the proposed methods suggest that the number of people with diabetes continues to grow in Germany. However, the projected number of male T2D cases differs substantially across the three methods. It is clearly visible that over time the difference between the projected values from each of the three methods enlarges. Since only the population composition changes over time, method 1) shows only slightly increasing future case numbers. In contrast, methods 2) and 3) also take into account the incidence and mortality, which influence the prevalence and number of cases. This, in addition to the demographic aging, is above all the reason for the higher number of projected T2D cases for these methods compared to method 1).

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Fig 3. T2D case projection results.

Projected male T2D cases in Germany for variant B1L2M1 of the population projections of the German FSO between 2010 and 2040. The population projection variant is based on constant birth rates, increases in life expectancy and a net migration of 147 000 people. Method 1) assumes constant age-specific prevalence, method 2) and method 3) build on constant incidence rate and 2%-decrease in the MRR.

https://doi.org/10.1371/journal.pone.0264739.g003

Table 1 displays the projected T2D case numbers among men in Germany in millions and the relative changes from 2010 compared to 2040 in percent. With method 1), we find an increase of male T2D case numbers by 0.8 million. This equals a total of almost 3.6 million T2D cases among males in Germany in 2040 (+29%). When presuming that the MRR decreases by 2% per year while the IR is assumed to remain constant, the number of cases is projected to increase by about 3.0 million (+104%) and 3.3 million (+116%) for method 2) and method 3), respectively. Apparently, the results show an obvious gap between method 1) and the other two methods. Interestingly, the difference between the projected case numbers of the latter methods is minor: During the entire time horizon of the projection until 2035, the future number of T2D cases for method 2) is slightly higher than the number projected by method 3). Thereafter, method 3) projects a higher number of male T2D cases in Germany.

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Table 1. T2D case projection results (in million).

https://doi.org/10.1371/journal.pone.0264739.t001

S1 and S2 Figs in S2 File refer to the age-specific prevalence among males in Germany from 2010 to 2040 projected using the different methods. We find apparent discrepancies in the age-specific prevalence for the methods. Compared to the constant prevalence assumed by method 1), the prevalence computed with methods 2) and 3) is expected to increase considerably, particularly for people older than 60 years. Additionally, the peak prevalence is presumed to shift towards older age groups. We provide further details in the supporting information.

Discussion

The aim of this article is to assess and advance the usage and performance of different projection methods in chronic disease modelling. While there is a lack thereof in previous publications, we compared the underlying assumptions, mathematical details, strengths, and limitations of three distinct projection methods and demonstrated their usage. Precisely, in this article, we discussed three methods to project age- and sex-specific case numbers of a chronic condition from age- and sex-specific prevalence, incidence, and mortality data. Further, we illustrated each method in a practical application in the context of T2D among males in Germany for the time period from 2010 to 2040. We found considerable differences between the results of the three methods.

Generally, all three methods can be easily adapted to other chronic diseases or countries. Additionally, for Germany, data about the future population number is available until 2060, i.e., the projection of T2D case numbers can be extended easily to the far-off future. Nonetheless, a projection is subject to some unforeseen changes in the economic, political, or disease-specific environment amongst others. Generally, the reliability of projections decreases over time. Therefore, instead of delving further into the future and thereby decreasing certainty, we restricted the projection until 2040.

In many previous projections on chronic diseases, age- and sex-specific prevalence from a base year is transferred to population projections as in method 1) [6, 9–11]. Population projections required for this purpose, generated using the so-called cohort component method [6, 29], are widely used and publicly available in Germany. For the calculation, the birth cohorts are hypothetically extrapolated from a base year under assumptions on the future development of fertility, mortality, and net migration. But just as the future population depends on several components, the development of a disease is also influenced by various disease-specific aspects [6]. However, the latter are ignored in method 1). Without a doubt, method 1) is the least reliable of the three discussed approaches. Assuming a constant prevalence and not reflecting on changes in disease-specific factors substantially limit the reliability of this method’s results. Unfortunately, in some contexts, data on the latter may be rarely available. If that is the case, method 1) could at least provide a short-term indication of future case numbers. Furthermore, short-term projections could reflect a second context in which method 1) may be applicable. A projection is always subject to some unforeseen changes in the economic, political, or disease-specific environment amongst others. Consequently, when keeping the overall time-horizon to a minimum, changes in relevant factors such as the mortality rate ratio or the incidence rate may be minimal and therefore less impactful, too. Nonetheless, method 1) should be used with caution and whenever possible, method 2) or 3) should be the preferred options. Methods 2) and 3) include disease-specific information on mortality, prevalence, and incidence rates as input factors in addition to the demographic components mentioned above. Thus, as opposed to method 1), the PDEs used in method 2) and 3) account for temporal trends in the prevailing epidemiological situation. To do so, aggregated data are sufficient. Method 2) incorporates the MRR and IR, as opposed to solely using the prevalence as is done by method 1). Though, method 2) is, as method 1), still based on projections of the population and the general mortality in Germany. The future estimates of the German FSO do not consider potential epidemiological influences and simply extrapolate future values based on long-term trends of the past [20]. Contrarily, using method 3), we can take short-term fluctuations in the mortality into account. The results of method 3) are independent from projections of the German FSO beyond the year used to estimate m₀ and m₁. Instead, this method purely relies on input values on the age- and sex-specific prevalence, the MRR and the general mortality for a base year. The latter are used to estimate the mortality of the non-diseased and the mortality of diseased people. Furthermore, instead of calculating the prevalence in each year for each age group, method 3) directly returns future changes in absolute case and population numbers.

Besides, some health actions or interventions may not directly alter the prevalence of a disease but still have far-reaching consequences with regards to a particular disease situation [28, 30, 31]. Consequently, other health indicators such as life expectancy, years of life lost, or years of productivity lost may provide a more appropriate insight to anticipate the potential impact of such interventions. Nonetheless, in most cases, a disease’s prevalence is a necessary input factor for the computation of other health indicators. Accordingly, using the illness–death model and the corresponding PDE in a first step to estimate a future prevalence allows to derive other health characteristics of a population associated with T2D in Germany in 2020 and 2040 from an individual and population perspective in a second step [28, 31]. In fact, this reflects another drawback of method 1). In contrast to method 2) and 3), the approach assumes a stable prevalence, and consequently, this does not allow to easily infer the future development of other epidemiological indicators.

Lastly, different future scenarios that anticipate potential impacts of alternative scenarios of prevention and intervention or disease-dynamics can be computed and compared using method 2) or 3). The comparison of methods 2) and 3) with method 1) reveals the great impact of trends in incidence and mortality on future disease burden. Our findings confirm the suggestion that ignoring temporal trends in incidence and mortality provokes an underestimation of the actual number of cases [4]. Consequently, a future course can be better, if not optimal, approximated using method 2) and 3).

As a further remark, we are convinced that our work provides a good basis for future research. Our study discusses the large importance of choosing a suitable projection method which is supported by a practical application to the context of T2D in Germany. Since our approach to use a PDE that describes the IDM is not the only one that has been proposed and published [31, 32], it would be interesting to extend the comparison and focus on different approaches that are based on the IDM. Since this would have been beyond the scope of this article, this investigation could prove desirable for future work.

Conclusion

Forecasts of the growing non-communicable disease burden will be key to guide future healthcare policies. With this work, we compare three projection methods and demonstrated how to apply each of them to quantify future T2D case numbers in Germany until 2040. The three methods uniformly confirm that there is a substantial increase in the number of males diagnosed with T2D ranging from 0.8 million (+29%) to 3.3 million (+116%) additional cases in Germany in 2040. Assessing the strengths and limitations of three different methods may help researchers to better apply statistical methods for projecting future case numbers of chronic diseases. We suggest that future projections should move away from blunt prevalence extrapolation and instead, employ methods that are based on theory from the IDM.

Supporting information