Using internet search data to predict new HIV diagnoses in China: a modelling study.

OBJECTIVES: Internet data are important sources of abundant information regarding HIV epidemics and risk factors. A number of case studies found an association between internet searches and outbreaks of infectious diseases, including HIV. In this research, we examined the feasibility of using search query data to predict the number of new HIV diagnoses in China.
DESIGN: We identified a set of search queries that are associated with new HIV diagnoses in China. We developed statistical models (negative binomial generalised linear model and its Bayesian variants) to estimate the number of new HIV diagnoses by using data of search queries (Baidu) and official statistics (for the entire country and for Guangdong province) for 7 years (2010 to 2016).
RESULTS: Search query data were positively associated with the number of new HIV diagnoses in China and in Guangdong province. Experiments demonstrated that incorporating search query data could improve the prediction performance in nowcasting and forecasting tasks.
CONCLUSIONS: Baidu data can be used to predict the number of new HIV diagnoses in China up to the province level. This study demonstrates the feasibility of using search query data to predict new HIV diagnoses. Results could potentially facilitate timely evidence-based decision making and complement conventional programmes for HIV prevention. © Author(s) (or their employer(s)) 2018. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.

This work is one of the first data-driven studies on using search engine (Baidu) data to predict new HIV diagnoses in China.

The proposed models can predict new HIV diagnoses in China with high accuracy.

The proposed models are trained on historical data. Thus, they are ineffective if historical data are unavailable.

This study focuses on predicting the number of new HIV diagnoses, instead of HIV incidence (the estimated number of people newly infected with HIV).

Introduction

HIV is a critical public health issue worldwide.1 There are approximately 36.7 million people living with HIV worldwide (including 0.66 million in China) worldwide at the end of 2016.2 3 The epidemics of HIV has caused huge burden on economy, society, politics and culture. The Chinese surveillance system consists of (1) a sentinel surveillance system, (2) a case-reporting system and (3) a behavioural surveillance and epidemiological survey.4–7 By 2010, the number of sentinel surveillance system reached 1888 across the country for eight key populations, and the system involved various sampling methods: the populations are drug users (snowball sampling in communities or at detention/detoxification centres); men who have sex with men (MSM, stratified snowball sampling at venues or through internet/social networks); female sex workers (stratified sampling at venues or detention centres); sexually transmitted infection (STI) clinic attendees (consecutive sampling); antenatal care clinic attendees (consecutive sampling); long-distance truck drivers (consecutive sampling); mobile population (consecutive sampling); and young students (multistage clustered sampling at colleges).4 The annual funding for HIV prevention and control increased dramatically in the previous decade (average increase of 8% per year).8 Existing HIV prevention and surveillance programmes are based on official statistics from national monitoring authorities, which usually have a lag of 1 month. Recent works conducted a review on HIV prevention and control.9–11

Retrieving up-to-date information of new HIV diagnoses can help raise public awareness of its outbreaks and provide effective prevention efforts.12 Although HIV interventions are not as time sensitive as influenza interventions due to the long incubation period of the virus, precise estimation of new HIV diagnoses can help authorities and public health officials to effectively allocate resources and schedule prevention programmes (eg, national and local campaigns).

In practice, if a model accurately predicts a burst of HIV diagnoses in the current month (nowcasting) or in a few months (forecasting), then decision makers can allocate resources (eg, test kit, fund for campaigns and antiretroviral therapy kit) to help national and local public health services satisfy the upcoming demand. Timely HIV test and early treatment can effectively prevent onward transmission of HIV.7 13 In addition, targeted campaigns could help raise public care for HIV patients and reduce HIV stigma.14 15 Thus, timely and quality treatment in early stages of the infection is important for people who are newly diagnosed with HIV and those who are at risk. Prediction-based campaigns may inform at-risk people of the risk of HIV transmission and allow them to prevent having risky behaviour during the upcoming outbreaks of new HIV diagnoses. These efforts may not directly prevent some at-risk people from being infected but can help them receive better and timely treatment services.

Simulation models can be used to estimate trends in the HIV epidemic and explore the effectiveness of interventions in preventing its spread.16–18 Despite numerous studies on simulation models of HIV epidemics and transmissions, current decision makers do not always use them in practice partly because of the lack of confidence in them. In general, simulation models can be fitted well by using historical data. However, using these models to analyse future scenarios remains challenging given the limited information of future epidemics. If we can develop accurate prediction models for timely estimation of epidemics (such as new HIV diagnoses), then simulation models can be calibrated and applied to actual decision making. Hence, it is important to tune the parameters in simulation models using real-time prediction, so that decision makers could develop effective intervention plans.17 18 As a result, new data sources are highly needed to complement conventional report of incidence statistics from Centers for Disease Control and Prevention (CDC), particularly in low/middle-income countries, such as China, where HIV prevention programmes targeting key populations have not been well-developed.

Internet data are important sources of abundant information regarding HIV epidemics.19 In particular, internet searches have been found to be associated with the outbreaks of infectious diseases, such as influenza, hand, foot and mouth diseases and dengue fever.12 20–35 Internet search data are relevant to determine HIV incidence because people, especially adolescents and young adults, rely on the internet as their primary source to acquire HIV-related information.36–40 Such internet data are particularly relevant to young (under 18 years of age) people given their high prevalence of using the internet. Young people often encounter barriers (parent’s consent for testing for HIV) in accessing corresponding services and may actively seek information from the internet.41 42

Previous studies used Wikipedia searches and social media data to predict HIV diagnoses.19 43–45 People prefer the internet search engine as platform to obtain information about diseases that are highly stigmatised in the society (eg, sexually transmitted disease (STD) and mental health) because anonymous internet searches can better protect their privacy compared with other social media platforms (eg, Weibo, WeChat and blog).46–50 Therefore, internet search data have strong predictive power for HIV diagnoses. Existing empirical studies reported a strong correlation between Google trends and incidence of other STDs, including HIV in the USA.12 51–53 However, modelling research on using query data of search engines to predict HIV incidence has been rarely reported. Prediction models must be developed to help decision makers monitor HIV epidemics and estimate outbreaks. The requirement is vital in China, where the traditional HIV monitoring system is very costly because of the large population and the stigma towards HIV.41 42 51 52 Therefore, it is sensible for Chinese authorities and decision makers to use internet-based data to supplement traditional surveillance to help with HIV intervention. To date, research on using internet search query data for HIV surveillance in China is scarce and should be further explored.

In this work, we developed six statistical models to estimate the number of new HIV diagnoses in China by incorporating search query data and historical records at the national and provincial levels. At the end of 2016, China had a total of 731 million Web users, among which the majority (82.4%) use search engines to acquire information.54 Existing research suggests that the use of the internet and social media is correlated with HIV testing behaviour among key populations.55 Our hypothesis is that people who suspect that they are infected with HIV (because of their at-risk behaviour or related symptoms) would search for HIV-related information in the internet search engine and subsequently undergo HIV testing. People infected with HIV will be counted as new diagnoses in the official statistics for the corresponding month. The internet searches represent a representative sample of the at-risk population, who are likely to undergo HIV testing.

Data

We retrieved two sets of official statistics as dependent variable. At the national level, we collected the monthly counts of new HIV diagnoses in China from the China CDC (http://www.chinacdc.cn) between 2010 and 2016 (84 months). The robustness of the proposed models should also be evaluated at the local level because public health interventions are usually targeted at specific subgroups in high-risk local geographic areas. Therefore, we retrieved the monthly counts of new HIV diagnoses in Guangdong province, which is the most populous province in China (with more than 100 million people), from the Health and Family Planning Commission of Guangdong Province (http://www.gdwst.gov.cn/) during the same period. These data are published with a lag of approximately 1 month. We did not investigate the difference between gender and age groups because of lack of demographic information.

Internet search query data were obtained from Baidu Index (https://index.baidu.com/), a Google Trend equivalent to the most popular search engine (Baidu) in China. Similar to Google Trends, Baidu Index is a normalised value that measures the search volume of certain keywords at a specific time. Baidu is the largest search engine in China and has a market share of approximately 70% to 83%.56 The majority (82.4%) of Chinese web users use search engines to acquire information.54 Although not all people diagnosed with HIV used Baidu to search for HIV-related information, several lines of evidence indicate that the number of new diagnoses is correlated with the internet searches.12 In particular, Baidu users are a meaningful sample of people diagnosed with HIV in China because we are modelling the number of new diagnoses at the aggregated level (national and provincial).

To ensure the quality of search query data, we adopted a data-driven approach for identifying HIV-related terms in Baidu searches. In addition to ‘艾滋病’ (HIV/AIDS), we used the Baidu Index toolkit to retrieve terms searched by users immediately before and after searching for ‘艾滋病’ (HIV/AIDS). The retrieved terms were manually cleaned to exclude ambiguous terms and those associated with other diseases, such as ‘途径’ (ways) and ‘症状’ (symptom). We finally collected data on the monthly frequencies of Baidu searches for the following eight HIV-related terms from 2011 (its inception) to 2016: ‘艾滋病’ (HIV/AIDS), ‘艾滋病检测’ (HIV testing), ‘艾滋病初期症状’ (initial symptoms of HIV), ‘艾滋病窗口期’ (HIV test window period), ‘艾滋病试纸’ (HIV test kits/strips), ‘艾滋病潜伏期’ (incubation period of HIV/AIDS), ‘艾滋病能活多久’ (how long can HIV patients live) and ‘艾滋病传播途径’ (ways of HIV transmission). We collected search query data generated by users located in the entire country and those in Guangdong province.

We performed a cross-correlation test with search query data and HIV statistics to filter terms that are not significantly correlated with new HIV diagnoses at the national level (correlation coefficient lower than 0.3).28 29 35 For Guangdong province, all terms are correlated. We included seven terms in the composite search index at the national level and eight terms in the composite search index for Guangdong province (table 1). The composite search index is the weighted summation of the query data of the selected terms, where the weight of a term is the correlation coefficient between the new HIV diagnoses curve and the frequency of the search curve. This composition of search queries/terms produces the most correlative predictor of internet searches and has been widely used for disease surveillance.29 35 57 We normalised the composite search indices according to the actual counts of new diagnoses by using equation (1) and present their time series in figure 1. The normalised composite search index is calculated as follows:

Table 1

Terms included in the composite search indices at the national and provincial levels

Chinese	English translation	Correlation coefficient (China)	Correlation coefficient (Guangdong)
艾滋病	HIV/AIDS	0.54 (p<0.001)	0.43 (p<0.001)
艾滋病初期症状	Initial symptoms of HIV	0.44 (p<0.001)	0.49 (p<0.001)
艾滋病试纸	HIV test kits/strips	0.36 (p<0.01)	0.42 (p<0.001)
艾滋病检测	HIV testing	0.35 (p<0.01)	0.41 (p<0.001)
艾滋病窗口期	HIV test window period	0.34 (p<0.01)	0.36 (p<0.01)
艾滋病能活多久	How long can HIV patients live	0.33 (p<0.01)	0.43 (p<0.001)
艾滋病传播途径	Ways of HIV transmission	0.31 (p<0.01)	0.37 (p<0.01)
艾滋病潜伏期	Incubation period of HIV	Excluded	0.31 (p<0.01)

Figure 1

Number of new HIV diagnoses (black) and composite search index (red) from 2011 to 2016 in China (A) and Guangdong province (B).

Patient and public involvement

The patients and the public were not involved in this study.

Model development

The counts of the new HIV diagnoses generally follow a negative binomial distribution. We examined the relationship between new HIV diagnoses and the search query data (composite search index, figure 1). Similar patterns were obtained over time and had yearly seasonality. The search query data could effectively capture the outbreaks of new HIV diagnoses. Hence, search query data could be used to estimate new HIV diagnoses before official data are published (commonly named as ‘nowcasting’ task).

Although both curves show a continuous increase over time, the search query data curve increases faster, indicating the growing awareness of HIV in China and Guangdong province. Chinese authorities and non-governmental organisations (NGOs) provide significant resources towards national and local HIV prevention programmes. In particular, huge campaigns are conducted during World AIDS Day (December 1) every year. Such campaigns greatly help people learn about HIV. Many newly diagnosed people were educated by these campaigns before they realised their risk of contracting HIV. These campaigns are also the reason for the burst of new HIV diagnoses in December each year. In addition, efforts are exerted to provide test kits to young adults. For example, in a recent practice, the introduction of vending machines of HIV test kits in universities was found to increase the availability of self-testing among college students (goo.gl/k6E65). In general, the rapid increase in HIV-related internet searches is a result of the increasing effort and resources of authorities and NGOs for HIV prevention. The different increasing rates indicate that the prediction models should be calibrated frequently over time to capture the changing associations between the search query data and the count of new HIV diagnoses.

Basing on the empirical observations, we propose six competing models to estimate the number of new HIV diagnoses by using search query data. The first two models are a negative binomial generalised linear model (nbGLM) with a log link and autoregressive terms (nbGLM-AR) and a Bayesian negative binomial generalised linear model (BnbGLM) with the same variables (BnbGLM-AR). The third and fourth models are nbGLM and BnbGLM with a variable representing the composite Baidu Search Index (nbGLM-Baidu and BnbGLM-Baidu). The fifth and sixth models are nbGLM and BnbGLM with autoregressive terms and composite search index (nbGLM-AR-Baidu and BnbGLM-AR-Baidu). Here, we selected nbGLM as the base model because the data of HIV diagnoses followed a negative binomial distribution. The difference between nbGLM-based and BnbGLM-based models is the coefficient estimation approach. nbGLM uses least squares fitting approach, which might lead to overfitting problem.58 BnbGLM uses Bayesian inference approach, which could fully use prior information for training and resolving the overfitting problem.59 These two sets of models can be represented as follows: nbGLM-AR and BnbGLM-AR:

nbGLM-Baidu and BnbGLM-Baidu:

nbGLM-AR-Baidu and BnbGLM-AR-Baidu:

where represents the number of new HIV diagnoses in month . As we found a monthly seasonality with a circle of a full year, a 12-month autoregressive component is adopted to determine the trend of the overall curve. represents the normalised composite search index of month . represents Gaussian white noise.

We split the data into two sets, namely the training set (January 2010 to December 2014 for new HIV diagnoses data for search query data) and the test set (January 2015 to December 2016). We estimated the parameters of the statistical models using the training set and evaluated the prediction performance using the test set. MASS and BRMS packages in R were used for model fitting. We focused on two main tasks: (1) using search query of a certain month to predict the number of new HIV diagnoses in the same month (‘nowcast’ task) and (2) using search query data of a certain month to predict new HIV diagnoses in the upcoming 1 and 2 months (‘forecast’ task). For the nowcast task, we used equations (2)–(4). For the forecast task, we modified the models as follows:

nbGLM-AR and BnbGLM-AR (forecast):

nbGLM-Baidu and BnbGLM-Baidu (forecast):

nbGLM-AR-Baidu and BnbGLM-AR-Baidu (forecast):

where is equal to 1 or 2, indicating 1-month or 2-month ahead forecast. For both tasks, we used an adaptive time window for model training; that is, each estimate was based on the model trained using the data of all previous months. This adaptive method is more appropriate than fixed time window method60 or shifting time window method23 because it can take advantage of all available training data and the seasonality of the data is consistent over the years. To confirm the robustness of the proposed models, we evaluated their performances by using fixed and shifting time windows. We obtained consistent but slightly less accurate results (see online supplementary materials).

We used commonly adopted tools, namely root mean square error (RMSE) and normalised root mean square error (NRMSE), to evaluate the accuracy of the nowcast and forecast results. RMSE calculates the SD of prediction errors (the smaller, the better), and NRMSE is a normalised version of RMSE for comparing performance at different scales:

where represents the forecasted values of the corresponding observed value . and represent the maximum and the minimum observed values, respectively.

Results

We present the prediction results in figures 2 (China) and 3 (Guangdong province) and compared the performances of different models in tables 2 (China) and 3 (Guangdong province). All models performed reasonably well in predicting the number of new HIV diagnoses of the current month, 1 month in advance and 2 months in advance. The models with only the composite search index (nbGLM-Baidu and BnbGLM-Baidu) were less accurate than those with autoregressive terms. This finding is expected because the number of new HIV diagnoses exhibits a clear seasonality within a 12-month cycle. Our results indicated that using search query data only could generate a reasonable prediction for nowcasting tasks, with normalised RMSE ranging from 23% to 24% at the national and provincial levels. The prediction results in figures 2 and 3 indicated that the composite search index-based models can accurately capture the outbreaks of HIV diagnoses. Furthermore, we found that the variable of the composite search index is only statistically significant in the nowcasting tasks. Hence, internet search query data are useful in estimating the number of HIV diagnoses for the current month as well as in modelling the outbreaks of HIV diagnoses. A full list of the estimates of regression coefficients for all models is presented in online supplementary materials.

Figure 2

Actual number of new HIV diagnoses and prediction results of the six proposed models (China). The black curve represents the actual data of new HIV diagnoses. The red curve represents the fitted values. The blue curve represents the prediction result. BnbGLM-AR, Bayesian negative binomial generalised linear model (BnbGLM) with autoregressive terms; BnbGLM-AR-Baidu, BnbGLM with autoregressive terms and the composite Baidu Search Index; BnbGLM-Baidu, BnbGLM with a variable representing the composite Baidu Search Index; nbGLM-AR, negative binomial generalised linear model (nbGLM) with autoregressive terms; nbGLM-AR-Baidu, nbGLM with autoregressive terms and the composite Baidu Search Index; nbGLM-Baidu, nbGLM with a variable representing the composite Baidu Search Index.

Table 2

Accuracy in predicting the number of new HIV diagnoses in China

Model	Nowcasting		One-month ahead forecasting		Two-month ahead forecasting
	RMSE	NRMSE	RMSE	NRSME	RMSE	NRMSE
nbGLM-AR	473.35	11.71%	484.21	11.98%	528.38	13.08%
nbGLM-Baidu	957.58	23.7%	1166.38	28.86%	1176.06	29.1%
nbGLM-AR-Baidu	420.68	10.41%	482.79	11.95%	539.37	13.35%
BnbGLM-AR	455.65	11.27%	456.95	11.31%	497.11	12.3%
BnbGLM-Baidu	976.99	24.18%	1176.16	29.11%	1145.23	28.34%
BnbGLM-AR-Baidu	423.17	10.47%	451.75	11.18%	508.31	12.58%

BnbGLM-AR, Bayesian negative binomial generalised linear model (BnbGLM) with autoregressive terms; BnbGLM-AR-Baidu, BnbGLM with autoregressive terms and the composite Baidu Search Index; BnbGLM-Baidu, BnbGLM with a variable representing the composite Baidu Search Index; nbGLM-AR, negative binomial generalised linear model (nbGLM) with autoregressive terms; nbGLM-AR-Baidu, nbGLM with autoregressive terms and the composite Baidu Search Index; nbGLM-Baidu, nbGLM with a variable representing the composite Baidu Search Index; NRMSE, normalised root mean square error; RMSE, root mean square error.

Actual number of new HIV diagnoses and prediction results of the six proposed models (Guangdong province). The black curve represents the actual data of new HIV diagnoses. The red curve represents the fitted values. The blue curve represents the prediction result. BnbGLM-AR, Bayesian negative binomial generalised linear model (BnbGLM) with autoregressive terms; BnbGLM-AR-Baidu, BnbGLM with autoregressive terms and the composite Baidu Search Index; BnbGLM-Baidu, BnbGLM with a variable representing the composite Baidu Search Index; nbGLM-AR, negative binomial generalised linear model (nbGLM) with autoregressive terms; nbGLM-AR-Baidu, nbGLM with autoregressive terms and the composite Baidu Search Index; nbGLM-Baidu, nbGLM with a variable representing the composite Baidu Search Index.

The integration of the composite search index and autoregressive terms led to excellent performance in all tasks at the national level. In particular, nbGLM-AR-Baidu performed the best in the nowcasting task. The performance of nbGLM-AR-Baidu was 11.8% more accurate than that of the nbGLM-AR model. BnbGLM-AR-Baidu performed almost identically (<1% difference) to nbGLM-AR-Baidu in the nowcasting task and slightly better in the forecasting task. BnbGLM-AR-Baidu was 7.2% and 3.9% more accurate than the nbGLM-AR in the 1-month and 2-month ahead forecasting, respectively.

For the study on Guangdong province, BnbGLM-AR-Baidu performed the best in the nowcasting task. The performance was 4.1% more accurate than that of nbGLM-AR. In the forecasting tasks, although BnbGLM-AR performed the best, the difference between BnbGLM-AR and BnbGLM-AR-Baidu was minimal (less than 1%). Thus, search query data are useful for the nowcasting task in Guangdong.

Discussion

An interesting finding is that the number of new HIV diagnoses always surged in December, and dipped in January and February. The surge in HIV diagnoses in December may be due to the national campaign around the World AIDS Day. There are multiple effects61 62: (1) many people become aware of their risk of being infected, and may search for HIV-related information more often; (2) it is easier for at-risk people to assess HIV testing services, thus they may do the test and be diagnosed. The decrease in HIV diagnoses in January and February may be due to the fact that most Chinese have a long break (1–2 weeks for adults, and 3–4 weeks for students) to celebrate the Chinese Lunar New Year (usually between late January and late February) with family members in hometown. In addition, many people who suspected themselves to be with HIV may have already done the test in December because of the national campaign. However, this explanation is only our hypothesis. There are many other potential reasons such as the delay of reports and the accessibility of related services. New survey studies and randomised controlled trials are needed to identify the root cause of this phenomenon.

By incorporating search query data, we can accurately predict the number of new HIV diagnoses for the current month before the official statistics are available at the national and provincial levels. At the national level, incorporating search query data could also improve the performance in predicting the number of new HIV diagnoses in the near future. In addition to the benefits of improved overall accuracy, nbGLM-AR-Baidu and BnbGLM-AR-Baidu could accurately capture the bursts of HIV diagnoses, whereas nbGLM-AR and BnbGLM-AR without the composite search index underestimated the bursts.

Conclusion

This research demonstrated the feasibility of using search query data to predict the number of new HIV diagnoses in China at the national and provincial levels. We provide a basis for developing low-cost methods for prediction. The proposed method could be applied to actual HIV surveillance and prevention programmes. The prediction models can serve as a forward-looking feedback loop to help decision makers respond timely through allocating resources. If the prediction results indicate that an outbreak is going on, then decision makers can allocate resources to initiate national campaigns and increase the inventory of test and treatment kits without having to wait for the official statistics. National campaigns should focus on approaching the at-risk web users by providing HIV-related information to social and mass media. This prediction-enabled online approach could destroy the barriers for people accessing HIV-related services, such as testing and treatment, and reduce the risk of new infections in the long run. To fulfil the potential of using internet search data for HIV prevention and surveillance, future research must complement conventional HIV prevention programmes with internet data for timely evidence-based decision making. In addition to internet searches, we will further research on the value of social media data (eg, Microblog, online discussion forums and online health communities) in HIV surveillance.

This research presents several limitations. First, considering the limited access to HIV diagnosis data at the province and city levels, we only validated the model for the entire country and Guangdong province. Second, the number of new HIV diagnoses is only a portion of the HIV incidence. Our future research will focus on using internet search query data to accurately estimate HIV incidence. Third, the surveillance data are subject to sampling bias.4 For example, the system tends to oversample MSM who are younger and more interested in HIV testing because of continence sampling through the internet or social networks. Moreover, the selection of STI clinic attendees is based on the physicians’ judgement of the risk of patients and the workload of physicians. Patients are less likely to be selected when they are seen during peak hours. Fourth, age disaggregation and other detailed demographic information of the users who searched for HIV-related terms are not available. Fifth, this research is based on data in China. The associations between search query data and HIV diagnoses could be different in other cultural context.

Table 3

Accuracy in predicting the number of new HIV diagnoses in Guangdong province

Model	Nowcasting		One-month ahead forecasting		Two-month ahead forecasting
	RMSE	NRMSE	RMSE	NRSME	RMSE	NRMSE
nbGLM-AR	56.39	21.28%	54.73	20.65%	54.66	20.6%
nbGLM-Baidu	64.08	24.18%	80.65	30.43%	82.84%	31.26%
nbGLM-AR-Baidu	54.64	20.62%	55.09	20.79%	55.25	20.85%
BnbGLM-AR	55.2	20.83%	53.75	20.28%	52.59	19.84%
BnbGLM-Baidu	63.03	23.79%	79.35	29.94%	81.38	30.71%
BnbGLM-AR-Baidu	54.18	20.45%	54.21	20.46%	53.01	20.04%

BnbGLM-AR, Bayesian negative binomial generalised linear model (BnbGLM) with autoregressive terms; BnbGLM-AR-Baidu, BnbGLM with autoregressive terms and the composite Baidu Search Index; BnbGLM-Baidu, BnbGLM with a variable representing the composite Baidu Search Index; nbGLM-AR, negative binomial generalised linear model (nbGLM) with autoregressive terms; nbGLM-AR-Baidu, nbGLM with autoregressive terms and the composite Baidu Search Index; nbGLM-Baidu, nbGLM with a variable representing the composite Baidu Search Index; NRMSE, normalised root mean square error; RMSE, root mean square error.