Li et al. Infect Dis Poverty (2020) 9:151 https://doi.org/10.1186/s40249-020-00771-7 RESEARCH ARTICLE Open Access Comparing the performance of time series models with or without meteorological factors in predicting incident pulmonary tuberculosis in eastern China Zhong‑Qi Li1†, Hong‑Qiu Pan2†, Qiao Liu1†, Huan Song1 and Jian‑Ming Wang1* Abstract Background: Many studies have compared the performance of time series models in predicting pulmonary tuber‑ culosis (PTB), but few have considered the role of meteorological factors in their prediction models. This study aims to explore whether incorporating meteorological factors can improve the performance of time series models in predict‑ ing PTB. Methods: We collected the monthly reported number of PTB cases and records of six meteorological factors in three cities of China from 2005 to 2018. Based on this data, we constructed three time series models, including an autore‑ gressive integrated moving average (ARIMA) model, the ARIMA with exogenous variables (ARIMAX) model, and a recurrent neural network (RNN) model. The ARIMAX and RNN models incorporated meteorological factors, while the ARIMA model did not. The mean absolute percentage error (MAPE) and root mean square error (RMSE) were used to evaluate the performance of the models in predicting PTB cases in 2018. Results: Both the cross‑correlation analysis and Spearman rank correlation test showed that PTB cases reported in the study areas were related to meteorological factors. The predictive performance of both the ARIMA and RNN models was improved after incorporating meteorological factors. The MAPEs of the ARIMA, ARIMAX, and RNN models were 12.54%, 11.96%, and 12.36% in Xuzhou, 15.57%, 11.16%, and 14.09% in Nantong, and 9.70%, 9.66%, and 12.50% in Wuxi, respectively. The RMSEs of the three models were 36.194, 33.956, and 34.785 in Xuzhou, 34.073, 25.884, and 31.828 in Nantong, and 19.545, 19.026, and 26.019 in Wuxi, respectively. Conclusions: Our study revealed a possible link between PTB and meteorological factors. Taking meteorological factors into consideration increased the accuracy of time series models in predicting PTB, and the ARIMAX model was superior to the ARIMA and RNN models in study settings. Keywords: Pulmonary tuberculosis, Meteorological factor, Time series, Predicting Background Tuberculosis (TB) is a chronic communicable disease *Correspondence: [email protected] that severely threatens human health, ranking among †Zhong‑Qi Li, Hong‑Qiu Pan and Qiao Liu contributed equally to this work the top ten causes of death worldwide. Te World Health 1 Department of Epidemiology, Center for Global Health, School of Public Organization (WHO) estimated that approximately Health, Nanjing Medical University, 101 Longmian Ave., Nanjing 211166, 10 million people fell ill with TB around the world in China Full list of author information is available at the end of the article 2019. Furthermore, there were an estimated 1.2 million © The Author(s) 2020. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creat iveco mmons .org/publi cdoma in/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Li et al. Infect Dis Poverty (2020) 9:151 Page 2 of 11 TB deaths among HIV-negative people and 208 000 TB included Xuzhou, Nantong, and Wuxi as the study sites. deaths among HIV-positive people [1]. To curb the TB Te geographical locations of the three cities in Jiangsu epidemic, the WHO set a goal of reducing the morbid- Province are shown in Fig. 1. Te ranking of the gross ity and mortality of TB by 90% and 95%, respectively, domestic product (GDP) per capita within the province between 2015 and 2035. Accurately predicting the trend in 2019 was 9 for Xuzhou, 7 for Nantong, and 1 for Wuxi, of this epidemic can help foresee the possible peaks and and the population density in 2019 was 750.16 people/m2 provide a reference for the prevention and control of TB for Xuzhou, 914.64 people/m2 for Nantong and 1424.43 [2]. people/m2 for Wuxi. A time series is formed by recording the development process of a random event over time. Time series analy- Data collection sis plays a vital role in predicting trends by identifying All newly diagnosed PTB cases in China are registered in the way in which health-related events change with time. an online surveillance system (https ://10.249.6.18:8880/) Te autoregressive integrated moving average (ARIMA) operated by the Center for Disease Control and Preven- model is the most classic time series analysis model tion. Te registry system is a particular virtual private and has been widely applied to predict various infec- network. For confdentiality, only authorized organi- tious diseases, such as hepatitis B [3], hemorrhagic fever zations can log in. We extracted the monthly reported with renal syndrome [4], coronavirus disease 2019 [5], number of pulmonary TB (PTB) cases in the study sites and hand, foot and mouth disease [6]. Te ARIMA with between 2005 and 2018. We also collected local meteor- exogenous variables (ARIMAX) model exhibits superior ological factors at the same time from the China Mete- prediction performance by adding other event-related orological Data Network (https ://www.nmic.cn/). Tese factors as input variables. Another commonly used time meteorological factors included monthly average temper- series analysis model is based on an artifcial neural net- ature (MAT, °C), monthly average atmospheric pressure work (ANN), which is designed to simulate the way the (MAP, hPa), monthly average wind speed (MAS, m/s), human brain analyzes and processes information. Te monthly average relative humidity (MAH, %), monthly ANN has been applied to construct time series models to precipitation (MP, mm), and monthly sunshine time forecast human diseases [7, 8]. Te recurrent neural net- (MST, h). work (RNN) is a specifc ANN with the ability to trans- fer information across time steps, as it can remember Construction of the ARIMA model previous information and apply it to the current output As described in our previous study [13], we constructed a calculation. Te ability to model temporal dependencies seasonal ARIMA model, which was expressed as ARIMA makes it particularly appropriate to analyze a time series, (p, d, q)(P, D, Q)s. Te variables p, d, and q represent the which consists of a sequence of points that are not inde- autoregressive model order, the number of ordinary dif- pendent [9, 10]. ferences, and the moving-average model order, respec- Time series analyses have been used to predict TB mor- tively. Te variables P, D, and Q represent the seasonal bidity or mortality, but most were conducted in one city or one region and based on one or two models that did not incorporate meteorological factors [11, 12]. Our pre- vious study has revealed that the incidence of TB exhibits seasonal fuctuations, indicating a potential relationship with meteorological factors [13]. Tus, in the current study, we performed a time series analysis in three cities of Jiangsu Province, China, and applied diferent models (ARIMA, ARIMAX, and RNN) to explore whether the inclusion of meteorological factors can improve the per- formance of prediction modeling. Methods Study areas Jiangsu Province is located on the eastern coast of China, with an area of 107 200 square kilometers. It governed 13 cities and had a permanent population of 80.7 mil- lion at the end of 2019. We randomly selected one city Fig. 1 Geographical locations of the three cities in Jiangsu Province from northern, central, and southern Jiangsu and fnally Li et al. Infect Dis Poverty (2020) 9:151 Page 3 of 11 autoregressive model order, the number of seasonal dif- the degree to which the residual series of the model was ferences, and the seasonal moving-average model order, demonstrated to be white noise by the Ljung-Box test; (c) respectively. Variables represent the length of a periodic the performance of the model in predicting PTB cases in pattern (s = 12 in this study). Te number of PTB cases 2018. predicted at time t (Y t ) was determined by the for- θ s q(B)�Q(B )at Construction of the RNN model Yt = θq(B) mula: � (Bs)φ (B)(1−B)d (1−Bs)D , where is the P p Te ANN usually consists of an input layer, a hidden layer, � ( s) operator of the moving-average model, Q B is the and an output layer. Te layers of the traditional ANN φ ( ) operator of the seasonal-moving average model, p B is are fully connected, but the neurons in each layer are not � ( s) the operator of the autoregressive model, P B is the connected. Te RNN is diferent from the ANN in that it (1 − )d operator of the seasonal autoregressive model, B is adds connections between the neurons in the hidden layer (1 − s)D the component of the ordinary diferences, B is (Fig.