Epidemiology and SARIMA model of deaths in a tertiary comprehensive hospital in Hangzhou from 2015 to 2022

Abstract

Background

By analysing the deaths of inpatients in a tertiary hospital in Hangzhou, this study aimed to understand the epidemiological distribution characteristics and the composition of the causes of death. Additionally, this study aimed to predict the changing trend in the number of deaths, providing valuable insights for hospitals to formulate relevant strategies and measures aimed at reducing mortality rates.

Methods

In this study, data on inpatient mortality at a tertiary hospital in Hangzhou from 2015 to 2022 were obtained via the population information registration system of the Chinese Center for Disease Control and Prevention. The death data of inpatients were described and analysed through a retrospective study. Excel 2016 was utilized for data sorting, and SPSS 22.0 software was employed for data analysis. The statistical inference of single factor differences was conducted via χ2 tests. The SARIMA model was established via the forecast, aTSA, and tseries software packages (version 4.3.0) to forecast future changes in the number of deaths.

Results

A total of 1938 inpatients died at the tertiary hospital in Hangzhou, with the greatest number of deaths occurring in 2022 (262, 13.52%). The sex ratio was 2.22:1, and there were significant differences between sexes in terms of age, marital status, educational level, and place of residence (P < 0.05). The percentage of males in the groups aged of 20 to 29 and 30 to 39 years was significantly greater than that of females (χ² = 46.905, P < 0.001). More females than males died in the widowed group, and divorced and married males experienced a greater number of deaths than divorced and married females did (χ² = 61.130, P < 0.001). The proportions of male students with a junior college and senior high school education were significantly greater than that of female students (χ² = 12.310, P < 0.05). The primary causes of mortality within the hospital setting included circulatory system diseases, injury, poisoning, tumours, and respiratory system diseases. These leading factors accounted for 86.12% of all recorded deaths. Finally, the SARIMA (2, 1, 1) (1, 1, 1)₁₂ model was determined to be the optimal model, with an AIC of 380.23, a BIC of 392.79, and an AICc of 381.81. The MAPE was 14.99%, indicating a satisfactory overall fit of this model. The relative error between the predicted and actual number of deaths in 2022 was 8.02%. Therefore, the SARIMA (2, 1, 1) (1, 1, 1)₁₂ model demonstrates good predictive performance.

Conclusions

Hospitals should enhance the management of sudden cardiac death, acute myocardial infarction, severe craniocerebral injury, lung cancer, and lung infection to reduce the mortality rate. The SARIMA model can be employed for predicting the number of deaths.

Background

With the rapid development of the social economy and changes in the living environment, there has been a corresponding shift in the causes of death among residents [1]. The study of hospital fatalities can be specifically aimed at enhancing the standard of medical technology within hospitals and providing improved care for patients. Our hospital is a comprehensive three-level facility located in Hangzhou city, that has 1,012 open beds and 45 clinical medical technology disciplines. This makes our hospital a significant representative within the field. By using the population information registration system of the Chinese Center for Disease Control and Prevention, data on 1,938 hospitalized patients who died between 2015 and 2022 were meticulously collected. These data were analysed to investigate the epidemiological characteristics of these deaths.

In a comparative analysis of mortality patterns across various hospitals, there appeared to be some variation in the ranking of the leading causes of death. A statistical examination of mortality cases at a tertiary hospital in Sichuan Province revealed that malignant tumours, cardiovascular diseases, and respiratory diseases were the predominant causes of death [2], which was consistent with the results of Li Y et al. [3] However, a study conducted by Du J et al. [4] revealed that circulatory system diseases were the leading cause of death, followed by tumours, injury‒poisoning, and respiratory system diseases, among 3682 deaths in a hospital in Beijing. The results were different from those in Zhuhai, Guangdong [5] and Xi ‘an, Shanxi [6]. Therefore, investigating the primary causes of mortality in the hospital’s vicinity and enhancing the level of medical technology on the basis of specific circumstances are essential. This will ultimately lead to a reduction in disease-related fatality rates.

Currently, the autoregressive integrated moving average (ARIMA) model is extensively utilized in disease prediction, health expenditure prediction, weather forecasting, and other fields. Building upon the traditional ARIMA model, a new SARIMA model was constructed by incorporating seasonal factors [7,8,9]. The SARIMA model is capable of capturing the periodicity, trend, and randomness of data, and it has been shown to have higher prediction accuracy than the ARIMA model. James A [10] utilized the SARIMA model to predict the death toll of the novel coronavirus in Brazil. On the other hand, Qi Feng [11] et al. utilized the number of cancer deaths attributed to smoking in Qingdao to develop a SARIMA model for predicting the trend of smoking-related cancer fatalities. Furthermore, Guo J [12] et al. applied the SARIMA model to analyse meteorological data from the Hailun Agricultural Ecology Experimental Station. However, there is a scarcity of published research on the application of SARIMA models in predicting hospital death.

Therefore, an epidemiological analysis was conducted by selecting all inpatient deaths that occurred in the hospital from 2015 to 2022. The main causes of death and specific disease composition were identified, and the SARIMA model was adopted to predict the number of new deaths. This approach allowed for a better understanding of the development trend of hospital deaths, providing insights for targeted medical service quality improvement aimed at reducing disease mortality rates.

Methods

Data collection

The mortality data were obtained from the population information registration system of the Chinese Center for Disease Control and Prevention [13, 14]. A total of 1,938 inpatient death records were collected from a tertiary general hospital in Hangzhou, covering the period from January 1, 2015, to December 31, 2022. These data were used to establish a comprehensive statistical analysis database. The main contents included in the study were sex, age, educational level, marital status, residential address, date of death and underlying cause of death. This study was approved by the Hospital Ethics Committee. The mechanisms of death were coded using the International Classification of Diseases, 10th Edition (ICD-10) [15].

Quality control

The data were obtained from the cause of death registration and reporting system of the Chinese Center for Disease Control and Prevention. The public health department of the hospital was responsible for reporting the daily Death Report Card to ensure the completeness and accuracy of the information. The review of problematic cases was conducted by a medical records team, which consists of two medical records professionals and one clinician. The hospital performs monthly quality checks on death reports. Additionally, the Hangzhou Center for Disease Control and Prevention conducted regular checks on the number of deaths in collaboration with the hospital’s statistics department. They also verified the underlying cause of death by cross-checking with the medical record room. The annual rate of missing death data in hospitals is less than 2%, the rate of correct underlying cause of death codes is more than 96%, and the rate of complete identity information is more than 99%, which ensures the reliability of death data. The underreporting rate of hospital deaths is less than 2% per year, and it is concentrated in a few individuals. This under-reporting occurs randomly within the whole population and does not have any effect on the results of this study.

The study involved an analysis stratified by sex (Tables 1 and 2) to reduce the influence of confounding factors. In addition, the COVID‒19 pandemic may have had an impact on the number of deaths in hospitals. The literature has reported that COVID‒19 infection is linked to increased mortality in hospitalized patients with acute myocardial infarction [16]. Furthermore, studies have shown that lockdowns caused by COVID‒19 are associated with a significant decrease in the number of hospitalized patients with myocardial infarction, but do not affect mortality [17]. In contrast, DZ Wang et al. reported a decrease in in-hospital mortality related to injury, poisoning, tumours, and respiratory diseases during the COVID‒19 pandemic [18]. In response, an analysis was conducted to determine whether the COVID‒19 pandemic had any effect on the number of hospital deaths and is described in the discussion section.

SARIMA model

The ARIMA model is widely utilized in time series analyses for decomposing time series data into general trends, cyclical patterns, and random fluctuations [19]. The monthly time-series observations were utilized to enhance the predictive ability of the model. The SARIMA (p, d, q) (P, D, Q) s model was developed based on the ARIMA model. In the case of a nonseasonal ARIMA, the parameters include the autoregressive order (p), differencing order (d), and moving average order (q). For the SARIMA (P, D, and Q) model, the parameters include the seasonal autoregressive order (P), seasonal differencing order (D), and seasonal moving average order(Q), and s is the seasonal period length (s = 12 for 12 months). SARIMA modelling involves four key steps: stationary model fitting, parameter estimation, model diagnosis, and prediction. First, the stationarity of the SARIMA model was tested via the Dickey‒Fuller test. Nonstationary time series can be differenced and seasonally differenced until they achieve stability. When the SARIMA model was constructed, the orders of (p, d, q) (P, D, Q) were determined on the basis of autocorrelation function (ACF) and partial autocorrelation function (PACF) plots. The cut‒off point for the ACF plot and the slow decay in the PACF plot were used to identify the correct parameters. Additionally, the model parameters were estimated via a least-squares approach. Whether the residual sequence was white noise was determined according to the Ljung–Box Q test, and the test level was α = 0.05. When P > 0.05, the residual sequence was classified as a white noise sequence. Third, diagnostic test parameters such as the mean absolute percentage error (MAPE), root mean square error (RMSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC) were employed to assess the goodness-of-fit of the constructed model and determine the optimal model [20, 21]. Finally, the SARIMA (p, d, q) (P, D, Q) s model was used for prediction, and this model was applied to predict deaths from January to December 2023. To assess the predictive ability of the model, we utilized data from 2015 to 2021 for the training set and data from 2022 for the validation set.

Statistical analysis

In this study, Excel 2016 was used to organize the death data. To address missing variables in the sample, information such as patient name, medical record number, ID number, or death date was retrieved from the hospital’s medical record management system and filled in to ensure data integrity. SPSS 22.0 and R4.3.0 software (forecast, aTSA, tseries) were used to analyse the data and establish the model. The count data were analysed via frequencies and percentages, and the single factor difference was statistically inferred via χ2 tests. A two-sided P < 0.05 indicated statistical significance.

Results

Epidemiological characteristics of deaths

In this study, 1336 patients were males (68.94%), and 602 were females (31.06%), with a sex ratio of 2.22:1. The epidemiological analysis revealed no significant difference between males and females across different years (χ² = 4.695, P = 0.697). There were variations in the age distributions of the different sexes. The percentage of males in the groups aged 20 to 29 and 30 to 39 years was significantly greater than that of females (χ² = 46.905, P < 0.001). In the widowed group, more females died than males did. However, in the married group, divorced and married males experienced a greater number of deaths than divorced and married females did (χ² = 61.130, P < 0.001). In terms of educational attainment, the proportion of males with junior college and senior high school educations was significantly greater than that of females (χ² = 12.310, P<0.05). There was no difference in the sex distribution among the different ethnic groups (χ² = 0.417, P>0.05). The number of deaths among males was significantly greater than that among females in out-of-province areas (χ² = 26.957, P < 0.001). There was no difference in the sex distribution across the different seasons (χ² = 0.953, P > 0.05) (Table 1).

Table 1 Epidemiological characteristics of deaths between 2015 and 2022 (n/%)

Distribution characteristic of diseases leading to mortality from 2015 to 2022

According to the ICD‒10 category statistics, the primary causes of death in the hospital were circulatory system diseases, injury, poisoning, tumours, and respiratory system diseases. These leading causes accounted for 86.12% of all deaths. The total number of deaths from circulatory diseases was 633 (452 males, 181 females), including sudden cardiac death (30.02%), acute myocardial infarction (29.54%), cerebral haemorrhage (9.32%), cerebral infarction (6.64%) and acute coronary syndrome (6.00%). Among these deaths, sudden cardiac death was the most prevalent cause of mortality in males, whereas acute myocardial infarction was the leading cause of death in females. The number of injury‒poisoning deaths totalled 547, with 397 occurring in males and 150 in females. The primary causes observed were severe craniocerebral injury (48.45%), multiple injuries (13.53%), thoracic injuries (8.04%), drowning (7.13%), and asphyxia (6.95%). The distributions of major diseases were consistent between males and females. There were 286 deaths from malignant tumours (177 males, 109 females), which included lung cancer (22.03%), liver cancer (20.63%), lymphoma (7.69%), pancreatic cancer (6.64%) and colorectal cancer (5.59%). Liver cancer was the leading cause of death in males, whereas lung cancer was the leading cause of death in females. In total, there were 203 deaths from respiratory diseases, with 135 occurring in males and 68 occurring in females. The main causes of these deaths were pulmonary infection (39.90%), chronic obstructive pulmonary disease (9.85%), hypostatic pneumonia (8.37%), bacterial pneumonia (7.88%), and lobar pneumonia (5.91%). Among these causes, pulmonary infections was the main cause of respiratory system‒related death in both males and females (Table 2).

Table 2 Distribution and sex composition of patients who died from circulatory system disease, injury‒poisoning, tumours and respiratory system disease (n/%)

SARIMA model

Monthly death cases were utilized to establish a SARIMA model covering the period from January 2015 to December 2021. The data were organized, and a sequence chart was created. The average annual number of deaths was 242. Figure 1 shows the monthly deaths from January 2015 to December 2021, revealing no significant trend of change. The number of deaths during this period was analysed via deterministic factors, and the original data were confirmed to be a nonstationary sequence via the Dickey‒Fuller test (P > 0.05). Moreover, the data exhibited seasonal trends. The Ljung–Box Q test demonstrated that the sequence was not a purely random sequence but rather a nonwhite noise sequence (P < 0.05) (Fig. 2). Therefore, a SARIMA model could be established.

To achieve stationarity in the series, first-order differencing adjustments were applied both seasonally and nonseasonally (Fig. 3). Figure 4 shows that the ACF and PACF of the new data tended to be stationary after the first-order seasonal difference adjustment was applied. This indicates that the values of d and D in the SARIMA (p, 1, q) × (P, 1, Q)₁₂ model were 1 and 1, respectively. For the fitting of the respective models, a combined spectrum of parameters was compared for the SARIMA (p, 1, q) × (P, 1, Q)₁₂ model, and an optimal model was selected according to the criteria of the minimum AIC, BIC and MAPE. The final model for deaths was the SARIMA (2, 1, 1) (1, 1, 1)₁₂ model, which showed the best goodness of fit, with an AIC of 380.23, a BIC of 392.79, an AICc of 381.81, a MAPE of 14.99%, and an RMSE of 3.83. The residuals in the fitted SARIMA models were found to be pure random sequences, as confirmed by the Ljung–Box Q test (P = 0.956).

The SARIMA (2, 1, 1) (1, 1, 1)₁₂ model was employed to analyse the number of deaths in the hospital from January 2015 to December 2021. The results indicated that the SARIMA (2, 1, 1) (1, 1, 1)₁₂ model effectively predicted the number of deaths within a short time (Fig. 5). The model was used to predict the number of deaths in 2022, and the actual value was employed to assess the model’s accuracy. Table 3 indicates that the 95% confidence interval for nearly all the predicted values encompassed the actual values, with a relative error of 8.02%, demonstrating a strong fit for the model. Finally, the SARIMA (2, 1, 1) (1, 1, 1)₁₂ model was used to predict the number of deaths among hospital patients from January to December 2023. The model predicted a total of 241 deaths during this period.

Fig. 1

Sequence chart of hospital deaths from January 2015 to September 2021

Fig. 2

Deterministic analysis chart of hospital deaths from January 2015 to September 2021

Fig. 3

ACF and PACF charts of the number of hospital deaths from January 2015 to September 2021

Fig. 4

Significance test diagram of the model fit

Fig. 5

Fitting and prediction of the SARIMA (2, 1, 1) (1, 1, 1)₁₂ model

Table 3 Comparison between actual values and predicted values of the number of deaths from the SARIMA model in 2022

Discussion

The number of inpatient deaths in the hospital from 2015 to 2022 showed minimal overall change, with the figure remaining steady at approximately 242 cases. The trend of inpatient deaths in a top-three hospital in Urumqi [22] was similar to the change trend but differed from the trend observed in a top-three hospital in Shenzhen. In the latter case, there was a consistent downward trend in the number of inpatient deaths from 2014 to 2019 [23]. This study revealed that the establishment of a critical care centre in third-level hospitals in Shenzhen improved the ability to diagnose, treat and rescue critical care diseases. This has led to a gradual reduction in the number of inpatient deaths. Reducing mortality and improving the health of hospitalized patients are common objectives of hospitals. Notably, the most severe COVID-19 outbreaks occurred in 2020, posing significant challenges for health care facilities worldwide. Compared with that in previous years, the number of deaths from cardiovascular and cerebrovascular diseases has increased. However, there has been a decline in injury‒poisoning deaths. The number of tumour deaths has not fluctuated significantly. Respiratory deaths have been increasing. COVID‒19 required the use of some medical resources, seriously affecting the hospitalization of patients with critical diseases such as acute myocardial infarction. As a result, the level of treatment decreased after the pandemic compared with that before pandemic [24]. The decrease in the rate of mortality due to motor vehicle traffic accidents and accidental falls may be attributed to a decrease in exposure to related risk factors due to vehicle restrictions, and production shutdowns during the pandemic period [18]. The spread of COVID‒19 during an outbreak increased the risk of respiratory illness and death [25].

Male patients had a higher mortality rate than did the female patients in the hospital (2.22:1), which aligns with the findings of Salaj D and Campbell JE et al. [26, 27]. Males are more likely than females to have unhealthy lifestyles, such as smoking, drinking, staying up late, engaging in occupations in high‒risk industries and engaging in high-intensity physical activity. It is important to pay more attention to men’s health problems to reduce male mortality. There were differences in age, marital status, education level, residence and other aspects of death between the sexes (P < 0.05), which aligns with the findings of Wang Z’s study [22]. The distribution of deaths spanned all age groups. Among these deaths, 6.66% occurred in patients aged 0 to 19 years, primarily because of congenital heart disease and accidental injury. The group aged 20 to 59 years accounted for 42.10% of the deaths, with causes including sudden death, acute myocardial infarction, and traffic accidents. Those aged 60 years or older accounted for the largest proportion at 51.24%, with causes such as sudden cardiac death, cerebral infarction, cancer, and pulmonary infection. Therefore, hospitals should focus on strengthening the ability to rescue patients with acute and critical illnesses and establish and improve prevention and treatment systems for senile diseases.

On the basis of the results of the statistical analysis according to the ICD‒10 classification, the primary causes of death in the hospital were circulatory system diseases, injury, poisoning, tumours, and respiratory diseases. These findings are consistent with those of previous domestic studies and reflect the current trend of disease development in China [28, 29]. Cardiovascular disease is the leading cause of death worldwide [30]. This study revealed that the main causes of death from circulatory diseases were sudden cardiac death, acute myocardial infarction and cerebral haemorrhage. Huang S et al. [31] reported that the annual incidence of sudden cardiac death in China is approximately 41.84 deaths per 100,000 people, making China the country with the highest incidence of sudden cardiac death worldwide. In addition, injury‒poisoning contributes significantly to the disease burden on society. Mulima G et al. [32] reported that over five million individuals succumb to injuries annually, constituting 9% of all fatalities worldwide. The study revealed that traffic accidents accounted for approximately 40% of incidents, falls from heights accounted for approximately 30%, and drownings accounted for approximately 10%. This trend is closely associated with the significant increase in the number of motor vehicles, rapid growth in the construction industry, illegal driving practices, and a lack of public awareness regarding traffic safety. The global burden of malignant tumours is substantial and continues to increase. In our hospital, lung cancer accounted for a significant proportion (22.03%) of deaths from malignant tumours, which aligns with the findings of Zhang JY [33] and Ha L et al. [34]. The occurrence of liver cancer, pancreatic cancer, colorectal cancer, and other digestive system tumours may be associated with an unbalanced diet, excessive drinking, overeating, and a lack of exercise. Deaths from respiratory diseases included deaths due to pulmonary infections, chronic obstructive pulmonary disease, and hypostatic pneumonia. These findings are consistent with the research of Halpin DMG et al. [35,36,37]. Studies have shown that as urban air pollution intensifies and population density increases, there is a greater likelihood of the spread of viruses and bacteria, leading to an increased incidence of respiratory diseases [38].

The SARIMA model not only considers seasonal periodicity but also captures nonseasonal components on the basis of sequential changes within the seasonal cycle. This feature enhances the practicality and accuracy of the model, making it suitable for academic research and analysis [39, 40]. Yang WJ et al. [41] used the SARIMA (2, 2, 2) (0, 1, 1)₁₂ model to predict the number of inpatients in the top three hospitals in Zhejiang Province, and the prediction effect was good. Liu JC et al. [42] modelled and predicted the number of inpatients with acute mountain sickness (AMS) via the ARIMA seasonal product model and ultimately determined that the ARIMA (1, 1, 1) (1, 0, 1)₁₂ model was the optimal model. In this study, a preliminary model was established on the basis of the ACF and PACF, considering both seasonal and nonseasonal factors. After many attempts, the ARIMA (2, 1, 1) (1, 1, 1)₁₂ model was identified as the optimal model. The relative error between the predicted value and the actual value in 2022 was 9.54%, indicating the strong forecasting ability of the model. Compared with previous years, the SARIMA (2, 1, 1) (1, 1, 1)₁₂ model predicted 241 deaths in 2023 with little fluctuation. The analysis of this time series model not only helps analyse the impact of changes in the number of deaths in hospitals but also provides a reference for how to reduce the case fatality rate in hospitals after the end of the pandemic.

According to the aforementioned findings, the following recommendations for hospital management are proposed. First, given the significance of response time in cases of cardiovascular and cerebrovascular diseases, it is crucial to conduct regular first-aid drills and enhance first-aid proficiency. Second, there is a need to increase the capacity for multidisciplinary collaboration in treatment and establish a streamlined process for trauma care. Additionally, efforts should be made to increase cancer screening, early detection, and treatment for high‒risk populations to reduce disease mortality rates. It is important to acknowledge certain limitations of this study. First, the in-hospital death data were incomplete because some patients and their family members discontinued treatment, leading to information bias. Second, our study only analysed hospital death data from 2015 to 2022, which may reduce the accuracy of the SARIMA model’s predictions as the time horizon extended. Finally, the data was obtained from a tertiary general hospital in Hangzhou, which can reflect only the death situation within the hospital’s jurisdiction. Analysing the death case data solely from the perspective of one hospital is insufficient to fully represent the overall mortality situation in the entire Hangzhou area. Therefore, the representativeness of this study is limited. In the future, more comprehensive death data will be collected to increase the specificity and depth of the study. Furthermore, future research will explore the use of the SARIMA model in developing a predictive model for the incidence of specific diseases. Comparing the SARIMA model with other models, such as the seasonal autoregressive fractionally integrated moving average (SARFIMA) model, the SARIMA‒ETS‒SVR hybrid model, and the Holt‒Winters model, can help in selecting a model with higher predictive efficiency [21, 43, 44].

Conclusions

An analysis of the causes of death in the hospital over an 8‒year period revealed that sudden cardiac death, acute myocardial infarction, severe craniocerebral injury, lung cancer, and pulmonary infection were the primary causes of fatalities observed in the hospital. The SARIMA (2, 1, 1) (1, 1, 1)₁₂ model is suitable for predicting the number of hospital deaths and can serve as a basis for the rational allocation of medical resources in hospitals.