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Prediction of acute onset of chronic cor pulmonale: comparative analysis of Holt-Winters exponential smoothing and ARIMA model

BMC Medical Research Methodology volume 24, Article number: 204 (2024) Cite this article

Abstract

Background

The aim of this study is to analyze the trend of acute onset of chronic cor pulmonale at Chenggong Hospital of Kunming Yan’an Hospital between January 2018 and December 2022.Additionally, the study will compare the application of the ARIMA model and Holt-Winters model in predicting the number of chronic cor pulmonale cases.

Methods

The data on chronic cor pulmonale cases from 2018 to 2022 were collected from the electronic medical records system of Chenggong Hospital of Kunming Yan’an Hospital. The ARIMA and Holt-Winters models were constructed using monthly case numbers from January 2018 to December 2022 as training data. The performance of the model was tested using the monthly number of cases from January 2023 to December 2023 as the test set.

Results

The number of acute onset of chronic cor pulmonale in Chenggong Hospital of Kunming Yan’an Hospital exhibited a downward trend overall from 2018 to 2022. There were more cases in winter and spring, with peaks observed in November to December and January of the following year. The optimal ARIMA model was determined to be ARIMA (0,1,1) (0,1,1)12, while for the Holt-Winters model, the optimal choice was the Holt-Winters multiplicative model. It was found that the Holt-Winters multiplicative model yielded the lowest error.

Conclusion

The Holt-Winters multiplicative model predicts better accuracy. The diagnosis of acute onset of chronic cor pulmonale is related to many risk factors, therefore, when using temporal models to fit and predict the data, we must consider such factors’ influence and try to incorporate them into the models.

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Background

Chronic cor pulmonale refers to the abnormal structure and function of the lungs that arise due to chronic diseases affecting the lungs or thorax. This condition is characterized by an increase in pulmonary arterial pressure and resistance in the pulmonary circulation, leading to right ventricular hypertrophy and dilation. In more severe cases, it can eventually lead to right heart failure [1]. The prevalence of chronic cor pulmonale is approximately 13%. This prevalence tends to increase with age and is often associated with repeated acute exacerbations and a poor prognosis [2]. Consequently, chronic cor pulmonale has emerged as a significant contributor to cardiac mortality [3], leading to a considerable long-term disease burden in affected patients.

Chronic cor pulmonale is classified into two phases based on clinical manifestations: the remission phase and the acute exacerbation phase [4]. Chronic cor pulmonale is particularly susceptible to the worsening of acute symptoms and higher mortality rates during sudden weather changes in winter and spring [5, 6]. The acute attack stage is primarily observed in cases of acute pulmonary embolism, where patients experience severe hypoxia and are highly susceptible to infection. This stage is characterized by a high fatality rate. The acute attack stage is primarily observed in cases of acute pulmonary embolism. During this stage, patients experience severe hypoxia and are highly susceptible to infection, resulting in a high fatality rate [7, 8]. According to Liu Pan’s data, China is a densely populated country that experiences a high prevalence of heart and lung diseases, resulting in a mortality rate of 15% [9], indicating that it is a prevalent condition [10]. According to the model’s prediction, it is recommended to enhance chronic disease management and family nursing guidance for patients with chronic pulmonary heart disease before the peak of acute exacerbation. This approach aims to minimize the disease burden and alleviate the strain on medical resources.

The Autoregressive integrated moving average (ARIMA) model and the Holt-Winters model are two popular methods in time series forecasting. They are suitable for different types of time series models that can capture long-term trends, seasonal patterns, and periodic or rhythmic patterns. These models are used for modeling and forecasting future outbreaks [11]. The Holt-Winter model is used to analyze trends and seasonality in the data, whereas the ARIMA model is specifically designed to capture autocorrelation in the data [12].

This study aims to establish the ARIMA model and the Holt-Winters model using the monthly number of cases recorded from January 2018 to December 2022. The objective is to predict the monthly number of cases from January to December 2023 and evaluate the performance of the models. We propose a temporal model that can serve as a reference for studying the epidemic trend of cute onset of chronic cor pulmonale. This model can also assist the hospital in implementing rational measures for disease prevention.

Methods

Data on chronic cor pulmonale

Cases of acute onset of chronic cor pulmonale were collected from 2018 to 2022 at Chenggong District People’s Hospital. All diagnoses were by the ‘2021 Edition Guidelines for the Diagnosis and Treatment of Chronic Cor pulmonate’. The monthly calculation of acute cases of chronic cor pulmonale was used to establish the ARIMA model and the Holt-Winters exponential smoothing model, using the number of cases between January 2018 and December 2022. The testing and prediction effect evaluation of the models were conducted using the number of acute onset cases of chronic pulmonary heart disease from January to December 2023.

The ARIMA model is expressed as ARIMA (p, d, q) (P, D, Q) S, where the parameters p, P, q, and Q represent the order of autoregressive and moving average, d and D represent the number of differences, and s represents the cycle length [13]. Steps to establish ARIMA seasonal model:

  1. (1)

    Time series stationarity: Make the original series satisfy the smoothness requirements of ARIMA modeling by differencing and/or seasonal differencing.

  2. (2)

    Model identification: Plot the autocorrelation function (ACF) and partial autocorrelation function (PACF) according to the smooth time series, initially determine the model parameters d, D, s, and then determine the optimal order value by combining with the principle of minimization of BIC information criterion.

  3. (3)

    Model diagnosis: Based on the parameters selected in (2), model construction, model accuracy test, determine whether the statistical indicators of the selected parameters of the model are consistent with the model residuals, and further diagnostic analysis of the model residuals to determine whether the model residuals are white noise sequences.

  4. (4)

    Forecast evaluation: The selected optimal model is used to predict the future value and sequence trend, and the predicted value is compared with the actual value to evaluate the model prediction effect.

The Holt-Winters model is very similar to the ARIMA model in that the smoothing parameters are level and trending and are not constrained by the values of each other. The Holt model is more versatile than the Brown model but takes longer to compute large series. Steps to build the Holt-Winters model:

  1. (1)

    Level: the change in level of the original time series over the course of its rise and fall.

  2. (2)

    Trend: Observe the change of the original series at a given level through differencing and/or seasonal differencing.

  3. (3)

    Seasonality: Observe whether the peaks of the smoothed time series plot fluctuate above and below the “0” boundary value, and carry out the serial t-test, P>0. 05 indicates that there is seasonality in the process of the rise and fall of the time series.

  4. (4)

    Noise: The Ljung-Box Q-test is performed on the model residuals, and the difference of P>0. 05 is not statistically significant, so the residual series can be regarded as a white noise series.

Statistical analysis

Time series analyses and graphs are performed using IBM SPSS Statistics 23.0 and the results with P<0. 05 would be considered as significant. The evaluation of the models is done using the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).

Results

General characteristics

A total of 1704 patients with acute onset of chronic cor pulmonale, including 1242 males and 462 females, were admitted for acute onset of chronic cor pulmonale Overall, there were 14 patients with acute onset of chronic cor pulmonale per month. The median number of patients with acute onset of chronic cor pulmonale was higher among males than which among females (20.0 vs.8.0). Up to 63 patients in hospital were diagnosed with acute onset of chronic cor pulmonale per month. The mean age of the patients was 77 years, and most of the cases occurred in the elderly, as shown in Table 1.

Table 1 Frequency of acute onset of chronic cor pulmonale, 2018–2022
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Model sequence smoothing

The data from 2018 to 2022 totaling 60 months are applied to predict the number of acute cases of lung-borne heart disease by ARIMA model. We do the time series graph of lung-borne heart disease in 2018–2022 (Fig. 1). The sequence is determined to be an unsteady sequence after T-test with P < 0. 05, so it is different to smooth its seasonal trend and random fluctuation trend. After passing the 1st-order differencing and the 1st-order seasonal differencing (Fig. 2). The time series graph fluctuates above and below 0 after differencing, meanwhile the sequence T-test with P > 0. 05, it can be considered that the original data tends to be smoothed.

Fig. 1
figure 1

Original time series

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Fig. 2
figure 2

Smoothing processed time series

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Fig. 3
figure 3

Model checking

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The analysis of ARIMA model

Model identification and selection

After differential transformation, the model is temporarily set as ARIMA (p, 1, q) (P, 1, Q) 12, and the ACF plot and PACF plot of the differential smooth time series are plotted (Fig. 3). Since p (P) and q (Q) are generally not more than 2 [14, 15], the piecing method is used to take the values of 0, 1, and 2 for testing and comparing the models according to the overall significance of the model, goodness-of-fit and other indexes, the model ARIMA (0,1,1) (0,1,1)12 and ARIMA (0,1,1) (1,1,1)12 indicators are better. Two models residual Ljung-Box Q test P > 0.05, indicating that the residuals are white noise. In the comparison of the two models, the smaller BIC is superior, determining the final model as (0, 1, 1) (0, 1, 1)12, as shown in Table 2.

Table 2 ARIMA Model goodness, test, and model fitting results
Full size table

The analysis of the Holt-Winters model

The given text already adheres to the given principles and lacks context. Therefore, the improved text is: The Holt-Winters model has been applied to estimate the monthly occurrences of pulmonary heart disease cases between 2018 and 2022. The analyzed results of the Ljung-Box Q test showed no notable differences in the model residuals (P>0. 05), suggesting white noise sequences. The smoothing parameters of the model were auto-calibrated, and the one with lower levels of RMSE, MAE, and MAPE was selected as ideal. The Ljung-Box Q test outcomes for the Holt-Winters additive model suggest that the residual sequence was not white noise. The Holt-Winters multiplicative model was the most suitable model, as shown in Table 3.

Table 3 Holt-Winters Model goodness, test, and model fitting results
Full size table

Comparison of model forecasting results

Employing the constructed ARIMA (0,1,1)(0,1,1)12 and Holt-Winters multiplicative models, this study forecasts the number of acute morbidity stemming from pulmonary origin heart disease for January- December 2023. Moreover, a comparison with electronic medical record system data on patients with acute morbidity originating from pulmonary heart disease is conducted. The ARIMA (0,1,1) (0,1,1)12 model demonstrated a relative error ranging from 6.90 to 94.44% when compared to the actual relative errors of reported numbers. The calculated RMSE, MAE, and MAPE for this model were 4.941, 3.564, and 14.167% respectively. Similarly, the Holt-Winters multiplicative model displayed relative errors ranging from 0 to 72.22% when compared to actual reports, with an RMSE of 0.425, MAE of 0.344, and MAPE of 1.347%. The combined data indicate that the Holt-Winters multiplicative model is more accurate in predicting compared to the ARIMA (0,1,1) (0,1,1)12 model. It was clear that the Holt-Winters multiplicative model produced the smallest error, as shown in Table 4; Fig. 4.

Table 4 Comparison of prediction results of 2 models
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Fig. 4
figure 4

Model prediction comparison

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Discussion

As can be seen in Fig. 1, the number of cases from November-December 2019 to January 2020 was significantly lower than the previous two years. COVID-19 outbreak in early 2020. Riskiness of access may have been a possible reason for the decline in the number of hospital cases during this period [16]. As can be seen from Fig. 1, the peaks in the number of acute cases of pulmonary heart disease occur in November-December and January of the following year, with the following possible reasons for the peaks.

  1. (1)

    Respiratory tract infections: falling temperatures in the autumn and winter seasons easily cause acute respiratory tract infections to be triggered, with acute exacerbation of the condition, causing patients to be admitted to hospitals for treatment, and even serious cardiac and pulmonary failure, leading to death, with a morbidity and mortality rate of 10 to 15% [17].

  2. (2)

    Atmospheric pollution: Atmospheric pollution is more serious in autumn and winter, and airborne particles and harmful gases have a stimulating effect on the respiratory system, leading to acute episodes of chronic lung diseases and an increased burden on the heart [18, 19].

  3. (3)

    Temperature changes: temperature fluctuates greatly in autumn and winter, and the onslaught of cold air causes vasoconstriction, increases pulmonary artery pressure, and adversely affects cardiopulmonary function.

  4. (4)

    Indoor air quality: People spend more time indoors during the autumn and winter months, and indoor air is often of poorer quality than outdoor air, especially in confined spaces where smoke, dust, and other harmful substances can irritate the respiratory system, which in turn hurts the heart and lungs [20, 21].

In addition, in seasons such as winter and spring, the relatively long hospitalization period of patients not only increases the disease burden of patients but also increases the burden of hospital beds and the workload of medical staff [22]. Therefore, to diagnose seasonal diseases effectively and promptly, the relevant authorities should improve the accuracy of medical examinations in addition to increasing the number of medical staff to reduce the rate of under diagnosis and the morbidity rate at the level of primary prevention. During the season of high disease incidence, patients with pulmonary heart disease need to be protected to reduce the burden of disease caused by seasonal changes and to maximize recovery [23]. This suggests the need for greater awareness of the need to prevent high-risk diseases, which would reduce morbidity at the level of primary prevention. During seasons of high disease incidence, patients with pulmonary heart disease need to be protected to reduce the burden of disease associated with seasonal changes and to maximize recovery [24, 25].

The ARIMA model has a flexible application is not constrained by the type of data and has a strong applicability [26]. The Holt-Winters model has a high prediction accuracy for diseases with trend changes and seasonally fluctuating incidence patterns by weakening the effect of short-term stochastic fluctuations on the series through a trimming technique [27, 28]. In this study, we found that the Holt-Winters multiplicative model had MAPE, RMSE, and MAE statistics that were smaller than those of the ARIMA (0,1,1) (0,1,1 ) 12 model and that the accuracy of the prediction of the number of illnesses from January to December 2023 was better than that of the ARIMA model. This may be due to the properties of the model. In terms of models only, the ARIMA model is more suitable for predicting data with a steady trend of change than the Holt-Winters model, which is more suitable for data with a single trend of change. As shown in Fig. 1, although the onset of acute onset of chronic pulmonary heart disease is distinctly seasonal, the variation is not stable and therefore some information is lost in the ARIMA modeling process. Furthermore, as can be seen in Fig. 1, the raw data increases significantly in a given season and different weights are given to the model. Therefore, the Holt-Winter additive model is more appropriate for predicting the acute incidence of chronic pulmonary heart disease in this study.

In this study, the Holt-Winters multiplicative model was better than the ARIMA model in predicting the acute onset of pulmonary heart disease. As can be seen from Table 4, there is a significant difference between the predicted and actual number of cases per month in January 2023, which may be related to the large increase in the number of new coronavirus infections in December 2022 at the beginning of the new coronavirus “Category B, Tube B”. This study only used 5 years of data as a test set, the sample size may be slightly insufficient and more samples are needed to create a training set. In addition, this is a hospital-based study, and there may be admission rate bias and detection signal bias, leading to a bias between real and recorded data, which also affects the prediction accuracy of the model. Therefore, more methods are needed to prove that the Holt-Winters multiplicative model is superior to ARIMA, such as combining it with other prediction models and constructing a combined model containing multiple factors [29].

The Holt-Winters model is constructed solely on historical data, without considering external factors, thereby limiting its applicability in practice. It does have some value as a reference for predicting acute onset of heart disease with pulmonary origin, however, various external changes should be taken into account to enhance prediction accuracy. There is no cure for pulmonary heart disease, and age, seasonal temperature, and viral infections are risk factors for morbidity. The study aims to assist in rationalizing healthcare resource and staff allocation while providing insights for combatting the disease through data analysis.

Conclusions

In general, although the Holt-Winters multiplicative model predicts better accuracy for Chronic cor pulmonale, the accuracy of time series models in predicting Chronic cor pulmonale was still inadequate. More detailed information on cases should be collected and an improved time series model is necessary to predict the number of new cases with Chronic cor pulmonale in the future. Assisting in rationalizing healthcare resource and staff allocation while providing insights for combatting the disease through data analysis.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Ge JB, Xu YJ, Wang C. Internal Medicine. People’s Health Publishing House: Beijing; 2018. p. 98.

  2. Guo J. New progress in clinical syndrome and treatment of cor pulmonale. Clinical Research of Traditional Chinese Medicine. 2020;12(31):146–8.

    Google Scholar 

  3. Li BJ. Research progress on the pathogenesis of cor pulmonale. Chinese Community Physician. 2019;35(22):13.

    CAS  Google Scholar 

  4. Lin GW, Wang JY, Ge JB. Practical Internal Medicine 15th Edition. Beijing: People’s Health Publishing House.

  5. Chinese Medical Association, Chinese Medical Association Magazine, Chinese Medical Association General Practice Branch, etc. Guidelines for primary diagnosis and treatment of chronic pulmonary heart disease (2018). Chinese Journal of General Practitioners. 2018;17(12):959–65.

    Google Scholar 

  6. Pulmonary Diseases Professional Committee of China Association of Chinese Medicine. Guidelines for TCM diagnosis and treatment of chronic cor pulmonale (2014 edition). Journal of Traditional Chinese Medicine. 2014;55(6):526–31.

    Google Scholar 

  7. Cui ZY, Liu CH, Wang HY, et al. Expression and significance of plasma periostin, endothelin-1, and N-terminal pro-brain natriuretic peptide in patients with acute exacerbation of chronic pulmonary heart disease. Chinese Journal of Evidence-Based Cardiovascular Medicine. 2019;11(01):51–4.

    Google Scholar 

  8. Konstantinides SV, Meyer G, Becattini C, et al. 2019 ESC guidelines for the diagnosis and management of acute pulmonary embolism developed in collaboration with the European Respiratory Society (ERS). Eur Heart J. 2020;41(4):543–603.

    Article  PubMed  Google Scholar 

  9. Liu P. Clinical manifestations of phlegm-heat blocking lung syndrome in acute exacerbation of chronic cor pulmonale and its correlation with physical and chemical indicators. Chengdu University of Traditional Chinese Medicine; 2020.

  10. Gwenaelle Lheritier ,Annick Legras ,Agnes Caille et al. Prevalence and prognostic value of acute chronic cor pulmonale and patent foramen ovale in ventilated patients with early acute respiratory distress syndrome: a multicenter study. Intensive CareMedicine2013.

  11. Xu W, Shao Z, Lou H, et al. Prediction of congenital heart disease for newborns: comparative analysis of Holt-Winters exponential smoothing and autoregressive integrated moving average models. BMC Med Res Methodol. 2022;22(1):257.

    Article  PubMed  PubMed Central  Google Scholar 

  12. Wang S, Wei F, Li H et al. Comparison of SARIMA model and Holt-Winters model in predicting the incidence of Sjögren’s syndrome Int J Rheum Dis. 2022 undefined;25(11):1263–69.

  13. Ren S, Cui HB. Application of SARIMA time series analysis in tax forecast: take Guizhou Province as an example. J Hubei Univ. 2021;43(1):80–5.

    Google Scholar 

  14. Li F, Chen YZ, Xu SL, et al. Application of ARIMA product seasonal model in predicting hand, foot and mouth disease epidemic in Yancheng City. Disease Surveillance. 2016;31(10):864–9.

    Google Scholar 

  15. Zhang W, Zhang YQ, Yang X. ARIMA seasonal product model for time series data and its application. Third Military Med J. 2002;8:955–7.

    Google Scholar 

  16. Xie B, Chen XR, Ling CL, et al. Characteristics and constraints of the medical behavior of patients with new coronary pneumonia in the early stage of the epidemic–taking Wuhan as an example. Urban Development Research. 2021;28(03):18–26.

    Google Scholar 

  17. Hu SS, Gao RL, Liu LS, et al. Summary of the China Cardiovascular Disease Report 2018. Chin J Circulation. 2019;34(3):209–20.

    Google Scholar 

  18. Global initiative for chronic obstructive lung disease. Global strategy for the diagnosis, management, and prevention of chronic obstructive pulmonary disease (2021 REPORT). https://goldcopd.org/goldreports/

  19. Chronic Obstructive Pulmonary Disease Group of the Respiratory Disease Branch of the Chinese Medical Association, Chronic Obstructive Pulmonary Disease Working Committee of the Respiratory Physicians Branch of the Chinese Medical Association. Guidelines for the diagnosis and treatment of chronic obstructive pulmonary disease (2021 Revision). Chinese Journal of Tuberculosis and Respiratory Disease. 2021;44(3):170–205.

    Google Scholar 

  20. Chua F, et al. Seasonal variation in admissions for heart failure and chronic obstructive pulmonary disease: the effect of temperature and atmospheric pollution. Intern Med J. 2006;36(4):231–7.

    Google Scholar 

  21. Gong H, et al. Short-term effects of ambient air pollution on chronic obstructive pulmonary disease admissions in Beijing, China. Environ Health Perspect. 2014;122(10):1114–9.

    Google Scholar 

  22. Xin Z, Xiu LD, Hui S. From the distribution of patients’ diseases in the family sickbed department to see the allocation of medical staff. Qilu J Nurs. 2011;17(30):79–80.

    Google Scholar 

  23. McCormick N, Rai SK, Lu N, Yokose C, Curhan GC, Choi HK. Estimation of primary prevention of gout in men through modification of obesity and other key lifestyle factors. JAMA Netw Open. 2020;3:e2027421.

    Article  PubMed  PubMed Central  Google Scholar 

  24. Feng W, Xiong G. Clinical classification and treatment experience of wrist gouty arthritis. Chin J Reparative Reconstr Surg. 2021;35(11):1411–6.

    Google Scholar 

  25. Wyber R, Bowen AC, Ralph AP, Peiris D. Primary prevention of acute rheumatic fever. Aust J Gen Pract. 2021;50(5):265–9.

    Article  PubMed  Google Scholar 

  26. Wang P, Peng Y, Yang S. Application of ARIMA model and Holtwinters exponential smoothing model in predicting influenza-like cases in Wuhan. Modern Prev Med. 2018;45(3):5.

    Google Scholar 

  27. Wang Y. Time Series Analysis-based on R. Beijing: Renmin University of China Publishing; 2015. pp. 117–24.

    Google Scholar 

  28. Zhu YY, ZHAO Q, FENG W et al. Application of exponential smoothing method to predict the incidence trend of viral hepatitis A in Shanghai. China Health Statistics. 2013;30 (1): 31–3,6.

  29. Xun LN, Cui Z, Sun JX, et al. Comparison of the predictive effects of ARIMA model and Holt-Winters exponential smoothing in suicide deaths. Practical Preventive Medicine. 2021;28(06):661–5.

    Google Scholar 

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Authors and Affiliations

  1. Chenggong Hospital of Kunming Yan’an Hospital, Kunming, China

    Nan Wang, Weiyi Zhuang & Pinxi Wan

  2. Kunming Guandu District Center for Disease Control, Kunming, China

    Zhen Ran & Jian Fu

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  1. Nan Wang
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Contributions

Nan Wang, Weiyi Zhuang, Zhen Ran, Pinxi Wan and Jian Fu proposed the study concept and design; Nan Wang , Pinxi Wan and Zhen Ran drafted the manuscript; Nan Wang and Zhen Ran performed statistical analysis; Weiyi Zhuang conducted study supervision; and all authors critically revised the manuscript for important intellectual content.

Corresponding author

Correspondence to Nan Wang.

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Since the simulated datasets did not involve any human data, ethics approval was not applicable and the real data was publicly available, thus ethics approval was not required.

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Wang, N., Zhuang, W., Ran, Z. et al. Prediction of acute onset of chronic cor pulmonale: comparative analysis of Holt-Winters exponential smoothing and ARIMA model. BMC Med Res Methodol 24, 204 (2024). https://doi.org/10.1186/s12874-024-02325-z

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BMC Medical Research Methodology

ISSN: 1471-2288

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