A hybrid seasonal prediction model for tuberculosis incidence in China

Tuberculosis (TB) is an often fatal infectious disease caused by the agent mycobacterium tuberculosis. Despite concerted worldwide efforts to control this disease, TB remains a major health issue with a high global health burden, particularly in low and middle-income countries [1, 2]. In 2009, it was estimated that there were approximately 9.4 million newly diagnosed cases, 14 million prevalent cases, and 1.7 million deaths that were attributable to TB in the world [3].

Since tuberculosis can be disseminated widely from active cases through aerosol droplets, it is highly cost-effective to detect a TB epidemic in its early stages in order to optimize disease control and intervention. One important characteristic of TB that assists in predicting epidemics is seasonality. A recent systematic review which reviewed studies from multiple regions around the world, noted a seasonal pattern of tuberculosis across countries. Moreover, the review noted that TB cases tended to reach their peak during the spring and summer seasons [4]. The seasonality of TB epidemics allows more efficient and effective use of existing data and it also provides clues to explore the environmental and social factors which might influence TB epidemics.

There were some retrospective studies using routine surveillance data to describe the patterns of TB occurrence [5, 6], and the TB forecasting models have been developed in various countries to understand and predict the trajectory of a TB epidemic [7‐9]. Up to the present, there has no such studies conducted in China, even though China possesses the world’s second largest tuberculosis epidemic after India.

Given the high priority to tuberculosis control, there have been large numbers of international TB prevalence studies. Nonetheless, measurements of prevalence were usually confined to the adult population and these surveys typically will not include culture-negative pulmonary TB cases [10]. Although there are increasing numbers of countries that possess TB prevalence data from representative, population-based surveys, there has been no nationwide survey of TB incidence in any country.

In order to address these noted gaps in the literature, in this study we aim to develop a model to predict TB epidemics and to analyze its seasonality in China. There are many models which can be used in infectious disease forecasting, such as Markov chain models [8], Grey models, general regression models, autoregressive integrated moving average class models (ARIMA) [11] and artificial neural network [12]. For better forecasting performance, hybrid models which combined two or more single models for communicable disease forecasting have also been explored, and previous findings indicate that hybrid models outperformed single models [13, 14]. We plan to compare our model with a hybrid model in order to compare their performance. The findings of this study will be useful for forecasting TB epidemics and providing reference information for TB control and intervention.

The data set from January 2005 to December 2010 was used to model fitting. For determining main parameters (p, P, d, D, q, Q) of SARIMA, we drew autocorrelation function plot and partial autocorrelation function plot (Figure 2). In the SARIMA time series analysis, the best model generated from the data set was SARIMA (1, 0, 0) (1, 0, 1)₁₂. The model equation is: (1 − 0.272B)(1 − 0.997B¹²)X_t = (1 − 0.888B¹²) × 123088.518. The estimation of model parameters and their testing results were presented in Table 2.

In constructing the SARIMA-GRNN model, the simulation accuracy of the GRNN model was determined by using the smoothing factor δ.After exploring various smoothing factors from 0.1 to 1.0, we found when the smooth factor was 0.1, the hybrid model has lowest MSE, MAE and MAPE. So we selected 0.1 as an appropriate smoothing factor.

We compared SARIMA with SARIMA-GRNN in fitting goodness. The real incidence numbers and estimated incidence numbers of SARIMA model and SARIMA-GRNN model monthly are shown in Figure 3. MSE, MAE and MAPE of the combined model (38969150, 3406.593 and 0.030, respectively) were lower than those of the single SARIMA model (161835310, 8781.971 and 0.076, respectively).

We attempted to predict the number of monthly incident TB cases in 2011 using SARIMA and the hybrid models and compared them with the actual numbers (see Table 3). MSE, MAE and MAPE of the hybrid model were all lower than those of the single mode; and MAPE of the hybrid model was 3.7%.

From the model curve (Figure 3), we found that yearly TB incidence number in China showed a slightly decreasing trend. There was also a seasonal pattern in the number of new TB cases. The monthly incidence of TB was lower in January and February and higher from March to June.

We developed a SARIMA model and a SARIMA-GRNN hybrid model to predict monthly incidence of TB in China. Although both models could simulate the TB time series data well, the hybrid model, which takes both linear and nonlinear components into account, outperformed the SARIMA model. We believed that models combining ARIMA and artificial neural network contain more data characteristics than non-hybrid models and may thereby be better for forecasting.

Based upon the results of this study, we believe that there will be no obvious improvement in the high burden of TB in China in the near future. The results indicated that in the near future, the reported annual TB incidence numbers in China will decrease only slightly. Even though this study’s analysis was based only on reported cases of TB since time series data of real incidence of TB in China cannot be readily obtained, the web-based and case-based mandatory TB reporting system has been fully operational since 2005 and covers almost 100% of detected TB cases in China [16]. Hence, the reported incidence number should closely mirror the real incidence of TB. Moreover, the trends and epidemics from reported incidence numbers are very similar to those actual incidence and epidemic situation of TB. These findings reveal that the China’s progress in TB control has been very incremental and intensified interventions are urgently needed.

In this study we concluded that there is a seasonal variation in TB incidence that showed periodicity in China. The monthly incidence number demonstrated a trough in January and February and was higher from March to June. This seasonal trend of TB incidence in China differed from that of many other nearby regions. For instance, in Hong Kong, the peak season of TB incidence is summer only [17]. In northern India the peak time season of TB incidence occurred between April to June and in October and December; although the TB incidence was lower in other months, there was no obvious seasonal trends [18]. One plausible explanation of these seasonal trends in China may be that the annual Spring Festival, the most important traditional festival of the year, usually falls in mid-February. During the entire month of February, there are huge population movements throughout China by various transportation modes. In view the TB incubation period, we suggest that the peak time of TB incidence may be partly attributed to the large population flows and the poor ventilation of public transportation during the Spring Festival period. The Spring Festival period may be the peak time of TB transmission. Hence, measures to prevent TB transmission within public transportation during the Spring Festival may play an important role in decreasing incidence number particularly from March to June. Other possible mechanisms for the seasonal variations in TB incidence in China need to be further studied.

There are a number of limitations in present study as follow. Firstly, climate–related data and data related to population movements were not included in the model fitting because of limitations in data availability. Secondly, China is a vast country and with a wide variation in climate, so seasonality of TB in the various geographic regions may differ. Due to lack of available data, seasonality at smaller area levels was not been analyzed. Lastly, the models were derived using data only from 2005 through 2010 and tested against only one year of data. Hence, these findings should be interpreted with caution and may be re-examined with additional time series data.

Limitations inherent in non-hybrid forecasting models can be compensated by developing applying hybrid model that combines two or more models. The resulting hybrid model may thereby be more effective than a single model in producing reliable forecasts of TB. Since the models suggest that the TB epidemic in China will not decrease markedly in the coming years, there is a need to implement greater TB control measures in China. The seasonality of the TB incidence suggested by the models also indicate the need for interventions focused on reducing infectious disease transmission on public transportation during the Spring Festival period.

Shiyi Cao: Doctoral candidate in Tongji Medical College, Huazhong University of Science and Technology

Feng Wang: Research Assistant Professor in School of Public Health and Primary Care, the Chinese University of Hong Kong

Wilson Tam: Research Assistant Professor in School of Public Health and Primary Care, the Chinese University of Hong Kong

Lap Ah Tse, Assistant Professor in School of Public Health and Primary Care, the Chinese University of Hong Kong

Jean Hee Kim, Assistant Professor in School of Public Health and Primary Care, the Chinese University of Hong Kong

Junan Liu: Associate professor in Tongji Medical College, Huazhong University of Science and Technology

Zuxun Lu: director and professor in Tongji Medical College, Huazhong University of Science and Technology