Study On The Early Warning Indicators System And Three Types Of Forecasting Models For Infectious Diseases

Emergent public health events, of which mainly are grave infectious diseases epidemic, don't only influence the safety of life and property greatly, but also cause panic and turbulence, almost affect every aspect of social life, and even block the economic development. It is important for infectious diseases control to establish and develop the technology of forecasting and early warning. It has been proved that conducting forecasting and early warning in infectious diseases control practice is of great health economic benefits.Accurate forecasting is the premise for establishing short or long term strategies for infectious disease prevention and control. Forecasting can be used for the infectious diseases epidemic trends analysis, establishing foundation for early warning and providing theory basis for combating strategies and measures. Establishing appropriate prediction models and improving the forecasting accuracy can be applied by management departments to learn about the current condition and make plan for the future.In China, late as the start was, the forecasting methods for infectious diseases had demonstrated a rapid development in the late 1990s. Most of the forecasting methods are traditional linear prediction models with great error, and it is inappropriate for application in practice. Thus, it is urgent for studying new models for infectious diseases forecasting. The forecasting research works for the analysis of diseases epidemic trends in the future and mainly focus on various mathematical models. Besides learning about the trends of diseases in the future, early warning required to identify the early abnormal events timely, send out alarm signals and start out an emergency response action. For early warning system establishment, a sensitive and effective early warning indicators system is the premise and foundation. According to indicators system, data can be collected, analyzed and investigated on purpose, which can ensure the production of effective alarm signals and reduction of the resource waste.Searching for sensitive and effective early warning indicators includes two aspects. One is collecting data from current communicable disease reporting network, and the other aspect refers to exploit and search for new data source. These new data source will have better values in early detection of diseases epidemic and outbreak.At first, this study established an early warning indictors system, determined the data source which can be used for early warning and provided theory basis for the development of the alarming and surveillance network. And then, this study focused on the establishment of forecasting models, with the legal infectious diseases reporting data which were very common and available in early warning indicators system. Three types of forecasting models were constructed, compared and evaluated.Part I The early warning indicators system for infectious diseases[Objectives] Establishing early warning indicators system for emergent public health events, especially for infectious disease outbreak in China and putting forward effective measures and suggestions that can ensure the system's implementation.[Methods]1 Using literature review, existing data analysis, field investigation, semi-structured interview and focus group interview to learn about the current condition of early detection for infectious disease outbreak in China;2 Using literature review, existing data analysis, group discussion and expert consulting meeting to build the rudiment of the indicator system;3 Applying expert consulting meeting and Delphi methods to construct the indicator system;4 Using group discussion and some experts'consultations to revise the indicator system and to analyze its establishment and application. [Results]1 Framework of indicator system: according to the early warning theory in other fields and the natural history of infectious disease outbreak, the framework was set up which included 3 categories: pre-outbreak indicators, early-symptom-period indicators and specific-syndrome-period indicators:2 The rudiment of indicator system: it consisted of three categories and 89 indicators that were filtered from 109 indicators according to the indicator building principle and suggestions from experts in the related fields.3 The composing of consultants: consultants came from the areas of epidemiology, infectious disease prevention and control, health management and health education, etc. Researchers, CDC staff members and decision-makers were all included. 92 percent of all consultants had over ten-year working experience and 89 percent were in senior position.4 The results of Delphi consulting: positive coefficients of two rounds of consultations were 78% and 100% respectively, and 70% consultants put forward written suggestions for improving indicator system, which meant consultants were very concerned about this project; the acquaintance grades to indicators were above 0.7 and authority coefficients beyond 0.8, which proved the consultation result was credible; after two consultations, harmonious coefficient was 0.782 and was of statistics significance, which proved the opinions from experts were harmonious; the final indicator system included 3 categories and 25 indicators.5 The availability of indicators: the capability of obtaining the data for those indicators was different for different-level CDC.[Conclusions]1 The established indicator system included 3 categories and 25 indicators, which covers the most scope of early warning for outbreak and can be used as basic indicators for early warning.2 The construction of indicator system combined the related opinions of early warning indicators in other fields (early warning indicators should include warning source, warning sign and warning situation indicator) with the timeline of epidemic development.3 The weighted coefficients of the emergence of early warning case, the number of reported cases, the epidemic in other areas, immunization coverage rate and the occurrence of disasters or calamities were ranked in the first 5 place. These indicators with relatively higher weighted coefficients were the ones that were usually paid more attention and applied in practice, so the result was in accordance with the practice.4 The established indicator system is a basic prototype system of indicators for early warning, for a specific disease, the application of indicators may be revised, customized according to the features of different diseases and local circumstance at that time.[Suggestions]In order to ensure the system effective implementation, recommendations were put forward as follows:1 Improving and perfecting the current disease surveillance systems;2 Establishing and developing syndromic surveillance gradually;3 Increasing investments on construction of grassroots health care institutions;4 Establishing information exchange platform with other related units;5 Strengthening the construction of related policies, laws and regulations;6 Building and developing real-time data collection, transmission and storage system;7 Improving the technical level of data (from different sources) synthesis and analysis; 8 Enhancing collaboration with experts from different fields such as information technology, mathematics, computer science and so on;9 Increasing cooperation with other countries in the related fields and learning experiences and lessons from other countries'practice;10 Establishing and implementing early warning indicators system should be carried out step by step.Part II Three types of mathematical models for infectious diseases forecasting [Objectives] The monthly incidence data of infectious diseases showed linear and nonlinear characteristics, but previous forecasting models were mostly based on traditional linear models. In this study, linear ARIMA model, nonlinear RBF neural network and combined model which included linear and nonlinear models were constructed for infectious diseases forecasting. The three types of mathematical models were constructed, compared and evaluated in order to search for new models for infectious diseases forecasting.[Materials and contents] With the legal notifiable communicable disease data from 1997- 2005 in Yichang city, ARIMA model, RBF neural network and ARIMA-GRNN combined model were constructed to predict the reporting incidence rate of A and B communicable diseases, pulmonary tuberculosis and bacillary dysentery in the first six months of 2006 in Yichang city. The models were evaluated with the comparison of the fitting and prediction effects.[Methods] Statistical descriptions were conducted with EXCEL software; ARIMA model was constructed with SPSS 12.0 and SAS 8.1 package; the construction of RBF and GRNN neural network was completed with the neural network toolbox in Matlab 7.1.[Results]:(1) The forecasting of monthly reporting incidence rate of A and B communicable diseases Based on the legal notifiable A and B communicable diseases incidence data from 1997-2005 in Yichang city, models were constructed to predict the incidence data in the first six months of 2006. The actual incidence rates were applied as reference values to evaluate the accuracy of the models. The ARIMA model expression was: (1 ? B ) xt = 1 + 0.243 Bε4 t+ 0.281B6, the fitting error: MSE=20.004, MAE=3.113, MAPE=0.172;the prediction error: MSE=19.637, MAE=3.553, MAPE=0.166. The prediction error of RBF neural network: MSE=13.389, MAE=3.177, MAPE=0.127;the simulation error of combined model: MSE=2.304, MAE=0.943, MAPE=0.053;and the prediction error: MSE=3.402, MAE=1.595, MAPE=0.068. It is found that the simulation error of the combined model was less than the ARIMA model. Among the three models, the forecasting accuracy of the combined model was the best, and then was the RBF neural network and ARIMA model.(2) The forecasting of monthly reporting incidence rate of pulmonary tuberculosis Based on the monthly reporting incidence rates of pulmonary tuberculosis from 1997 Jan. to 2005 Dec. in Yichang city, the incidence rates between Jan. and Jun. in 2006 were forecasted. The optimal model of ARIMA model was ARIMA(1,1,1),and the expression was The simulation error of the model were represented as follows: MSE=4.316, MAE=1.547, MAPE=0.227;the prediction error: MSE=9.748,MAE=2.661,MAPE=0.199. The prediction error of RBF neural network: MSE=2.867, MAE=1.140, MAPE=0.091; the simulation error of the combined model: MSE=0.535, MAE=0.472, MAPE=0.074; and the prediction error: MSE=3.580,MAE=1.563,MAPE=0.124. The simulation error of combined model was less than the traditional ARIMA model. The accuracy of forecasting models represented as: RBF neural network >combined model >ARIMA model.(3) The forecasting of monthly reporting incidence rate of bacillary dysentery Based on the monthly reporting incidence rates of bacillary dysentery from 2000 Jan. to 2005 Dec. in Yichang city, the incidence rates for the first six months in 2006 were forecasted. After simulation and selection, SARIMA (0, 1, 1) (1, 1, 0)12 was determined and its expression was (1 + 0.389 B1 2 )(1 ? B )(1 ? B1 2) X t = (1 ? 0.822 B )εt. The simulation error of the model could be described as: MSE=0.263, MAE=0.406, MAPE=0.185;for prediction error, MSE was 0.088, MAE was 0.286 and MAPE was 0.182. For the prediction error of RBF neural network, the MSE was 0.084, MAE was 0.222 and MAPE was 0.136. For SARIMA-GRNN hybrid model, the simulation error represented as: MSE=0.051, MAE=0.177, MAPE=0.079, for prediction error of this model, MSE was 0.026, MAE was 0.139 and MAPE was 0.083. Obviously, the simulation error of SARIMA model was greater than the hybrid model. The accuracy of the hybrid model was better than the RBF model and SARIMA model.[Conclusions]:(1) Trend extrapolation, which was based on the historical incidence rates, could be used for the forecasting of communicable diseases; (2) The prediction accuracy of RBF neural network, which was a nonlinear model, was better than the ARIMA model; (3) The ARIMA-GRNN combined model, which integrated linear and nonlinear models, represented better simulation and prediction effects than traditional ARIMA model; (4) For neural network, it is unnecessary to build complex mathematical models, learn about the structure of models and the relationship between input and output variables, so it was more easy to be applied in practice; (5) Trend extrapolation based on time series data can only be applied for short-term forecasting.