Comorbidity risk and distribution characteristics of chronic diseases in the elderly population in China

According to China's seventh population census, the number of elderly people aged > 60 years in China reached 264 million in 2020, accounting for 18.7% of the total population, and the proportion of elderly people suffering from various types of chronic diseases reached 20% [1]. As the Chinese population ages, the proportion of the elderly population suffering from various chronic diseases also gradually increases. Chronic diseases, which have a long duration and, theoretically, cannot be cured and solved, constitute a large part of the medical problems regarding the elderly population. The disease burden of chronic diseases also reached more than 70% of all diseases by 2019 [2]. The Global Health Statistics Report 2017 published by the World Health Organization (WHO) emphasized that chronic diseases cause more than 41 million deaths worldwide, accounting for 71.3% of the total number of deaths [3].

The World Health Organization defines the phenomenon in which individuals suffer from two or more chronic diseases as comorbidities [4]. Comorbidity is a state in which multiple diseases coexist. When an individual already has a chronic disease, the relapse of any other, unaffected chronic disease will lead to the emergence of new comorbidities. Existing studies are mostly based on the risk of a single chronic disease, while the study of comorbidities or chronic disease risk associated with comorbidities has more general significance.

As the aging of China's population accelerates and the resulting health problems become increasingly prominent, studies have gradually paid increasing attention to the incidence of chronic diseases. Research on the incidence of chronic diseases and comorbidities has been divided into two main steps: First, research has mainly focused on the incidence of chronic diseases based on the dynamic data of each hospital and has conducted certain statistical analyses and analyses of the main factors affecting the incidence; second, research has focused on the comorbidity of chronic diseases based on demographic data, analyzed the comorbidity patterns of major chronic diseases, and used methods such as correlation and clustering to identify diseases with similar comorbidity patterns.

At present, most of the research elaborate on the prevalence through statistical analysis and summarize the prevalence characteristics of a certain area for single or multiple chronic diseases. Siyu Li et al. collected monitoring data on four types of chronic diseases, namely, diabetes, stroke, acute coronary heart disease events and malignant tumors, in Taizhou city, Zhejiang Province and obtained the incidence from medical dynamic data [5]. Jiehong Jin et al. analyzed the incidence of chronic diseases such as malignant tumors, stroke, diabetes and coronary heart disease in Dongyang city from 2009 to 2015 using descriptive epidemiological methods [6]. Nan Chen et al. conducted a summary analysis of eight chronic diseases, such as tumors and coronary heart disease, based on annual statistics of noncommunicable diseases in Hedong District, Tianjin, from 2011 to 2015. The authors found that the incidence of these eight chronic diseases increased annually, and the incidence was greater in men than in women [7]. Yan Wang et al. used case reports of five chronic diseases, such as essential hypertension and stroke, in Daqing city from 2004 to 2013 to describe the incidence trends of chronic diseases and calculated the sex- and age-specific incidence of each disease [8]. Huimin Jin et al. selected various physical indicators obtained from the physical examination of a certain school staff member as influencing factors and observed their correlation with chronic diseases such as hypertension and hyperlipidemia. They found that there were significant differences in sex in patients with diseases such as hypertension and hyperlipidemia. Specifically, the correlation is stronger in men that women [9]. Van Oostrom SH et al. analyzed the incidence of chronic diseases in the Netherlands overtime and conducted factor regression analysis [10].

With the accumulation of chronic diseases, the number of elderly patients with comorbid chronic diseases in China is continuing to increase. In recent years, correlation research on comorbidities in the elderly has become a hot topic. Using the CHARLS dataset, Jinjia Lai et al. explored the associations between health-related behaviors and chronic disease comorbidities in middle-aged and elderly people through an association analysis algorithm [11]. Hao Xu et al. used Nanjing's chronic disease surveillance data from 2017 to 2018, adopted a multistage stratified random sampling method to obtain samples, and used a generalized linear mixed model to fit multilevel logistic regression analysis to explore the comorbidity status of hypertension, diabetes and dyslipidemia [12].

An important aspect of comorbidity research is to focus on one or more chronic diseases and explore the comorbidity status and comorbidity patterns of these chronic diseases and other diseases. Based on data from tertiary hospitals in Henan Province, Qianqian Hu et al. explored the correlation between comorbidities and ischemic stroke incidence and used a cluster analysis method to explore their comorbidity patterns [13]. Derong Peng et al. used association rule analysis to analyze the associations between comorbidities and various diseases in hypertension patients in Shanghai communities, and they found that comorbidities were strongly associated with different numbers of comorbidities [14]. Ye Pan et al. used four methods, namely, association rule analysis, cluster analysis, principal component analysis and potential category analysis, to explore the comorbidity patterns of elderly people in China and revealed a consistent comorbidity pattern through comparative analysis [15]. Chunzi Cui et al. used systematic cluster analysis and the Apriori algorithm to determine the mode of chronic disease comorbidity [16]. Yanna Li et al. explored the trend of comorbidities by the chi-square test, and the significant associations between chronic diseases were analyzed by network analysis [17].

In foreign studies, Oflaz Zarina et al. combined hidden Markov theory with copula functions and constructed a model to describe the interaction process of two or more comorbidities; this model was verified to be effective on the basis of no clinical medical data [18]. Caldeira, T.C.M. et al. studied the comorbidities of obesity and hypertension or diabetes during the 16-year period from 2006 to 2021 and reported that the incidence of these conditions increased significantly in male and elderly individuals over time [19]. Sun MX et al. studied the prevalence of multiple diseases in the Chinese population, analyzed the effects of different comorbidity modes and their corresponding all-cause mortality risks, and found that the comorbidity combinations associated with the highest incidence were hypertension–chronic kidney disease and hypertension–diabetes–chronic kidney disease, among which the comorbidity combination with diabetes–chronic kidney disease would was associated with the highest mortality risk [20]. Sun, P. et al. established a simulation model of the whole life cycle to characterize disease metastasis within the cycle, built a simulation framework of the whole life cohort on the basis of the probability model of chronic disease transition, and verified the effectiveness of the framework using the original short- and medium-term data [21]. Uddin S et al. used a total of 24 years of administrative medical data from 1995 to 2018 to explore common chronic diseases and their major comorbidities and used network analysis methods to rank comorbidity conditions leading to the onset of different diseases. They found that patients with cardiovascular disease and diabetes had a greater probability of developing the remaining comorbidities that also increased significantly with time and age [22].

The existing studies have the following limitations. First, studies on the incidence of chronic diseases in elderly individuals have been based mainly on pathological data. The existing studies in which the incidence of diseases was obtained through dynamic medical data have few data sources, high access thresholds, small sample sizes and poor universality; moreover, traditional statistical methods are mainly used in these kinds of studies. Second, studies on the calculation and analysis of disease incidence on the basis of disease comorbidities are rare. Most of these studies separate the modes of disease comorbidities through association and clustering but lack calculations of incidence on the basis of disease comorbidities. In some studies, the concepts of disease incidence and incidence are vague, and most studies have focused more on the association between disease prevalence and incidence. Finally, even fewer studies have focused on most chronic diseases at the same time; most studies are based on two or three specific diseases and their comorbidities. The main contributions of this article include the following aspects:

We constructed a chronic disease incidence calculation model based on single cross-sectional data using the hypothetical cohort, complex network was constructed to identify the diseases with the highest frequency among all comorbid conditions and reduce the computational dimension. Then, we used a multistate transition model to calculate the incidence of each chronic disease in the process of identifying a new comorbidity if it became debilitating. We applied the above model on the basis of Chinese Longitudinal Healthy Longevity Survey (CHLHS) data and obtained information on the mutual promotion of major chronic diseases under comorbid conditions. We mainly analyzed the incidence of chronic diseases from two aspects. For each specific target chronic disease, from one perspective, we can see which diseases most significantly affect it. We rank the risk of each chronic disease under other different combinations of chronic diseases; from another perspective, we can analyze how much impact a chronic disease will have on other chronic diseases during the formation of comorbidities. In this perspective, the target disease can be seen as the basic disease in comorbidity. We give the marginal impact and ranking of each chronic disease on other chronic diseases.

The remainder of this article is organized as follows: the next section provides a literature review, and the second section provides an explanation of the model and specific methods used in the article. The third section provides an analysis of the empirical results, the fourth section provides a discussion of related issues, and the conclusion concludes the article.

We constructed a set of chronic disease comorbidity risk assessment models based on cross-sectional data. This model first performs data scaling on the original survey sample to obtain a hypothetical cohort in which the incidence of chronic diseases changes with age; then, the complex network method is used to screen the main chronic diseases based on the above normalized data, that is, to reduce the dimensionality of the number of chronic diseases; and finally, the conditional incidence of each chronic disease in the development of various comorbidities is calculated. The model framework is shown in Fig. 1.

The dataset includes as many older individuals as possible and includes each individual's current chronic disease situation. The CLHLS dataset is a tracking dataset that includes information from elderly people. In addition to death samples, this dataset conducts surveys on the same samples in each survey round, while some new samples are added. The survey covered 23 provinces across the country; 65 and above respondents were included, and abundant samples were collected for people 80 years or older. We obtained complete response data for 16 major chronic diseases from the CLHLS dataset from 2017–2018; a total of 12,139 complete samples were obtained, including 5412 elderly men and 6727 elderly women. A total of 41 age groups ranging from 65 to 105 + years were considered; patients that were 65 ~ 104 years old were divided into groups by year, and people older than 105 years were included in the 105 years old group. The chronic diseases included hypertension, diabetes, heart disease, stroke, chronic lung disease (including bronchitis, emphysema, pneumonia, and asthma), cancer, chronic stomach disease, Parkinson's disease, arthritis, dementia, epilepsy, cholelith disease, dyslipidemia, rheumatism, chronic nephritis, and chronic hepatitis. Table 1 shows the baseline characteristics of the data we used.

To calculate the probability of chronic disease transition from cross-sectional data, this article used the method of a hypothetical cohort, in order to convert samples of different cohorts into samples of the same cohort, so as to calculate the state transition probability with age, and smooth the data.

First, the age-specific distribution of single survey data does not conform to the age distribution of birth cohorts to a large extent. The construction of hypothetical cohorts can help us convert the data on diseases of different aged cohorts that were born in the same year into a cohort that changes with age. Second, although some survey data can be traced, survey errors in a small range will lead to certain data errors. Using the imaginary queue method to correct the data can reduce the error.

Our basic method of constructing a hypothetical cohort was as follows: we obtained the age-specific mortality rate \({s}_{i}\left(t\right)\) in the survey year to construct a life table and a hypothetical cohort based on it. The survival of the elderly population \({p}_{i}\left(t\right), i= 65,\cdots ,105;t=2018\) at all ages is known. Taking the 65-year-old population in 2018 as the base number, the number of survivors in each age group older than 65 years is scaled according to the age-specific mortality rate in the life table.

The 65-year-old surviving population of the hypothetical cohort is set to \({P}_{65}={p}_{65}\left(2018\right)\), then traced \({p}_{66}\left(2018\right)\) back to 2017:

The scaling rate can be written as \({w}_{66}={p}_{65}\left(2018\right)/{p}_{65}\left(2017\right)\).

Similarly, we can extrapolate the population aged 67 to 105 in 2018 by tracing it back to the corresponding previous years. After obtaining the scaling rate, we scaled the cohort population in each disease state by rates to obtain data for each cohort that matched the scaled total population.

The comorbidity of all chronic diseases increases exponentially as the number of chronic diseases increases. When the number of dimensions involved in all comorbidities is too high and the data dimension cannot meet the requirements of the analysis, it is necessary to select the most significant diseases among all comorbidities. The closeness of the comorbid relationship between diseases can be measured to some extent by frequency.

A complex network is a precise way to describe the complex relationships between entities in the physical world. Through network characteristics, we can accurately learn the relationships, community structure, hierarchy, and many other features of the actual network. In this study, we traverse each individual sample according to disease status and construct a complex network in which the nodes are involved.

Once we calculate the number of comorbid events between two kinds of chronic diseases, we give z values to measure the relative position in the overall sample data. The z score can be expressed as:

In the complex network, x is represented by the weighted degree of each node. The possibility of emergency and frequency of comorbidity are considered comprehensively to determine which diseases have stronger and closer comorbidity connections. With a specific degree of dimensionality reduction as the goal, the z score can be used to select more connected multidimensional comorbid diseases.

When we consider m-dimensional chronic diseases associated with comorbidities, for each chronic disease, except for the conditions that have suffered from the target disease, \({d}_{i}=1\) all have \(n={2}^{m}/2-1\) kinds of comorbidities, for which the incidence of the target disease is nonzero. Determining how to find several nonzero conditions far from the incidence in healthy patients requires further work that is based on the calculation of comorbidities, which is also how to analyze the incidence in patients with comorbidities.

The incidence of each chronic disease in patients with comorbidities changes differently with age and sex, and we cannot accurately express with which comorbidities the incidence of the target disease is highest. By determining the difference between the incidence of basic disease and the incidence of disease in healthy individuals, the superimposed effect of basic disease on the target disease can be determined. Therefore, to explore the difference in the incidence of the target disease in each disease state and the incidence of the target disease in the healthy state, we subtracted the incidence in the healthy state from the incidence rate in each comorbid state to obtain the difference sequence of incidence rates. The difference sequence values change with age, and there are n sequences corresponding to n comorbid states.

We observe whether the difference series has trends, cycles, etc., as the age of the cohort changes. When most of the difference series are stable time series at each age, we can generally use a constant, that is, the average of the differences, to estimate the total impact of basic diseases in comorbidities on the incidence of the target disease.

Through normalization of the hypothetical cohort data, we obtained the change in the number of samples with age, as shown in Fig. 3.

After traversing the disease state of each sample, if there are pairs of disease comorbidities, a comorbidity link edge is generated, and the disease comorbidity network is obtained as shown in Fig. 4 below. Through a complex network of dimensionality reduction, when the mean value of comorbidity of weighted degree was taken as the significance threshold (Table 3), we selected 7 chronic diseases, namely, hypertension, diabetes, heart disease, stroke, chronic lung disease, arthritis and dyslipidemia, that showed more significant comorbidity states when taking elderly men as the main research objects. Six kinds of chronic diseases were selected as the analysis objects for elderly women, namely, hypertension, diabetes, heart disease, stroke, arthritis and dyslipidemia. The comorbidity of chronic lung disease with other chronic diseases was more significant in elderly men than in elderly women.

Considering the 7 chronic diseases of elderly men, any pair of diseases can be constructed to calculate the incidence by sex and age, and the incidence of these 7-dimensional diseases under the condition of comorbidity can be weighted to obtain the following: There are two states, \({d}_{i}=0\) and \({d}_{i}=1\), for each chronic disease, corresponding to the 7-dimensional comorbidity \(({d}_{1},{d}_{2},{d}_{3},{d}_{4},{d}_{5},{d}_{6},{d}_{7})\); in total, there are \({2}^{7}=128\) kinds of conditions, where the complete healthy state can be expressed as \(\left({d}_{1},{d}_{2},{d}_{3},{d}_{4},{d}_{5},{d}_{6},{d}_{7}\right)=(\mathrm{0,0},\mathrm{0,0},\mathrm{0,0},0)\). The six chronic diseases considered by older women involved a total of 64 disease conditions.