1. Introduction and background
The frequency of queries in web search logs has been found useful in estimating the incidence of influenza-like illnesses (ILIs) (Ginsberg et al., 2009; Lampos et al., 2015; Lazer et al., 2014; Santillana et al., 2015; Yang et al., 2015). Current methods use two core discriminative features for ILI estimation: (i) past ILI activity, and (ii) the frequency of queries in web search logs that correlate strongly with past ILI activity. There are two problems with this approach.
The first problem is that not all queries whose frequency is strongly correlated to ILI activity are necessarily informative with respect to ILIs, and hence discriminative as a feature for ILI estimation. At the most general level, this is an example of the fundamental issue of correlation not being causation. In the case of estimating ILI, this is exacerbated by the seasonal nature of influenza. In fact, it has been previously observed that previous methods can identify queries that have a very similar seasonality but are clearly not related to ILI. For example, the query “high school basketball” has been found to have a high correlation with ILI activity  even though it is obviously unrelated to ILI. The seasonality of high school basketball accounts for this correlation. Queries unrelated to the ILI activity will not be useful in the case of irregular ILI activity, e.g. an off season influenza outbreak. Additionally, changes in for example the high school basketball schedule would result in changes in the ILI estimates.
The second problem is that by using two types of features that are strongly correlated to each other (past ILI activity, and queries whose frequencies are strongly correlated to past ILI activity), we may compromise diversity in the representations one would expect from the features. Better estimations may be produced by using features that complement each other, regardless of their between–feature correlation.
Motivated by the above issues, we propose an alternative approach to selecting queries. Our approach consists of two steps. (1) We model the seasonal variation of ILI activity, and (2) we select queries whose search frequency fits aspects of this seasonality. Specifically, we present two variations of our algorithm: select queries that correlate with our seasonal model of ILI, and select queries that correlate with the residual between the seasonal model and observed ILI rates.
Our results are two fold. (i) Experimental evaluation of our seasonal query selection models for ILI estimation against strong recent baselines (of no seasonality) show that we can achieve performance that is overall more effective (reduced estimation error), and requires fewer queries as estimation features. With respect to error reduction we see that selecting queries fitting regular seasonal ILI variation is a better strategy than selecting queries fitting ILI outbreaks. (ii) Selecting queries that fit seasonal irregularities result in much more semantically relevant queries. These queries are surprisingly not the ones that result in the best predictions.
Our main results are: (i) We demonstrate that Google Correlate retrieves many non-relevant queries that are highly correlated with a times series of historic ILI incidence, and that the ILI-related queries are not highly ranked; (ii) re-ranking these queries based on their correlation with a residual signal, i.e. the difference between a seasonal model and historic data, strongly favours ILI-related queries; (iii) the performance of a linear estimator is improved based on the re-ranked queries. To our knowledge, the seasonal examination of ILI activity for query selection in automatic ILI estimation is a novel contribution. Seasonal variation has, however, been studied for other medical informatics tasks, such as vaccination uptake estimation (Hansen et al., 2017, 2016).
2. Problem Statement
The goal is to estimate ILI activity at time , denoted , using observed historical ILI activity (reported e.g. by the Centers for Disease Control and Prevention (CDC) in US) and query frequencies in web search logs. This is most commonly done by (i) submitting to Google Correlate111https://www.google.com/trends/correlate a file of historical ILI activity, and receiving as output web search queries (and their frequencies) that are most strongly correlated to the input ILI data. Then, can be estimated with a linear model that uses only web search frequencies (Ginsberg et al., 2009) as follows:
where is the number of queries, is the frequency for query in the web search log at time , the s are coefficients, and is the estimation error.
Including historical ILI activity data can improve the estimations of Eq. 1
, for instance with an autoregressive model(Yang et al., 2015), as follows:
Most ILI estimation methods (exceptions include (Lampos et al., 2017)) that use web search frequencies use all queries found to be correlated to ILI activity, i.e. in Eq. 1 and Eq. 2 corresponds to all strongly correlated queries, and query selection is typically left for the model regularisation, for example using lasso regularisation. In the next section we present a novel way of selecting which among these correlated queries to include in the estimation of according to how well they fit the seasonal variation of ILI activity.
3. Seasonal Query Selection
We reason that among the queries whose frequency is correlated with past ILI activity, some queries may fit the ILI seasonal variation better than others. This is supported by the literature (Lazer et al., 2014). We further reason that this fit of queries to seasonal ILI variation may not be sufficiently captured by simply measuring the correlation between the frequency of those queries and ILI activity. Based on this, we (i) present two models to represent seasonal variation of ILI activity, and (ii) select queries based on these seasonal models.
3.1. Step 1: Model seasonal ILI variation
We model seasonal variation in two ways. The first model is the Serfling model (Serfling, 1963), chosen because of its simplicity and expressiveness. The Serfling model (Eq. 3) uses pairs of sine and cosine terms to model seasonality, and a term linear in time to model general upward or downward trends. We use this model with weekly data and one yearly cycle (details on data are given in Section 4), resulting in the following ILI estimation model:
where the s denote model coefficients and the error, i.e. residual.
For the second model we use a yearly average (YA). Here the expected value of is calculated as the average value of seasons of ILI activity data,
where is the season length in weeks, in our case 52.
Fig. 1 shows the fit of the two models, i.e. the Serfling model (Eq. 3) and the YA model (Eq. 4) to historical ILI activity data. We see that the Serfling model fits the general seasonality, but not more complex patterns representing higher transmission. It does not, for example, model differences between the start and end of the ILI season. This is better captured by the YA model.
3.2. Step 2: Query selection
Seasonal correlation. We compute the Pearson correlation between the query frequencies and the ILI seasonal model, i.e. Eq. 3 or 4. We then select queries that are most strongly correlated to the ILI activity model.
Residual correlation. We compute the Pearson correlation between the query frequencies and the residual between the ILI seasonal model and the historical ILI activity. We then select queries that are most strongly correlated to the residual, i.e. unexpected variations in ILI activity (possible outbreaks).
The four query selection methods are denoted (i) Seasonal (Serfling), (ii) Seasonal (YA), (iii) Residual (Serfling), and (iv) Residual (YA).
We experimentally evaluate our seasonality-based query selection methods using two types of data: weekly ILI activity data and Google search frequency data. The ILI activity data is from the US CDC for the period 2004-6-6 to 2015-7-11222https://gis.cdc.gov/grasp/fluview/fluportaldashboard.html (inclusive). The CDC reports this in the form of weighted ILI activity across different US regions. ILI activity for a region corresponds to the number of ILI related visits to health care providers compared to non-influenza weeks, e.g. an ILI activity of 2 corresponds to twice as many visits as in non-epidemic weeks.
We retrieve query search frequencies from Google Correlate with the location set to the US. Specifically, we use the 100333This is a maximum number set by Google Correlate.
queries that have the highest correlation with the ILI activity from 2004-6-6 to 2009-3-29 according to Google Correlate. Google normalizes the search frequencies for each query to unit variance and zero mean, i.e. we do not know the actual search frequencies. We use the interval 2004-6-6 to 2009-3-29 because it represents a non-epidemic period (it excludes the 2009 pandemic of H1N1 influenza virus that caused highly irregular ILI activity). The 100 queries are shown in Tab.1. Only 21 of the 100 queries are related to ILI (in bold).
We compare our query selection methods (Section 3) to the following three baselines: (Tab. 2 baseline i) uses the top- queries to estimate ILI activity, where the top- are chosen to minimise the RMSE error, i.e. if we use queries the RMSE increases; (Tab. 2 baseline ii) using all 100 queries to estimate ILI activity; (Tab. 2 baseline iii) using no queries, only past ILI activity, i.e. an autoregressive model. For (i) and (ii), the query ranking is determined by Google Correlate. For (iii), two autoregressive models are fitted: one using 3 autoregressive terms (Lazer et al., 2014; Yang et al., 2015) and one with 52 autoregressive terms (Yang et al., 2015). This setup is similar to the setup of Yang et al. (Yang et al., 2015). We implement baseline (iii) using Eq. 2 where is set to 3 and 52 terms, respectively, and . Similarly to (Lazer et al., 2014; Yang et al., 2015), we evaluate estimation performance by reporting the root mean squared error (RMSE) and Pearson correlation between the estimations and the observed historical ILI activity.
For all runs, we use data from 2004-6-1 to 2009-3-29 for training, and data from 2009-4-1 to 2015-7-11 for testing. The training data is used to fit Eq. 3-4, and to calculate the correlation scores as described in Section 3.2. Estimations are made in a leave-one-out fashion where data prior to the data point being estimated is used to fit the estimation model. Each model is retrained for every time step using the 104 most recent data points (exactly as in Yang et al. (Yang et al., 2015)). We determine the number of queries in Eq. 1-3
by iteratively adding the next highest ranked query, where query rank is given by either Google Correlate (for the baselines), or by the four variants of our algorithm, specifically (i) correlate seasonal (Serfling), (ii) correlate seasonal (YA), (iii) correlate residual (Serfling), and (iv) correlate residual (YA). The models are fitted using lasso regression, where the hyper-parameter is found using three fold cross-validation on the training set.
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As noted earlier, Google Correlate identifies the top-100 queries, but only 21 of these are ILI-related. Our four algorithms re-rank the 100 queries. Fig. 2 plots the number of ILI-related queries as a function of the number of rank-ordered queries. The solid curve is based on the original ranking provided by Google Correlate. We observe that both the (i) Seasonal (Serfling) and (ii) Seasonal (YA), re-rank the queries such that, in general, the ILI-related queries are ranked worse. The Residual (Serfling) generally performs similarly to or worse than Google Correlate in favouring ILI-related queries. In contrast, Residual (YA) re-ranks the queries such that almost all ILI-related queries are favoured. Of the top-21 queries, 19 are ILI-related. All 21 ILI-related queries are within the top-23. The only two non-related queries in the top-23 are ranked at 19 and 21. Clearly re-ranking queries based on Residual (YA) strongly favours ILI-related queries much more than Google Correlate or our other three variants.
For each ranking of the queries, we select the top- queries that either minimise the RMSE or maximise the Pearson correlation. This is done for the Linear model of Eq. 1 and for the autoregressive model of Eq. 2, Tab. 2 shows the results. For the Linear model (column 1), we observe that Residual (YA) performs best w.r.t. RMSE and Pearson correlation, though the latter is not significant. Note that in both cases, (i) the number of queries needed by Residual (YA) is significantly less than for the other three variants and (ii) the two baselines performed worse.
For the autoregressive models, we observe that the Seasonal (Serfling) model performs best w.r.t. RMSE and Pearson correlation. This is achieved with relatively few queries (5, 9, or 11). However we note that of the top-5, -9 or -11 queries only 3, 3 or 4, resp. are ILI-related. In general, autoregressive models perform well when the signal has a strong autocorrelation. However, should the signal strongly deviate from seasonal patterns, then it is unlikely that the ILI estimates would be accurate.
|RMSE (the lower, the better)|
|Linear (Eq. 1)||#q.||Autoregressive 52 (Eq. 2)||#q.||Autoregressive 3 (Eq. 2)||#q.|
|Not Seasonal||baseline i||0.413||33||0.309||68||0.312||46|
|Not Seasonal all q.||baseline ii||0.416||0.310||0.314|
|ILI History||baseline iii||n/a||0.348||0.333|
|Correlation (the higher, the better)|
|Linear (Eq. 1)||#q.||Autoregressive 52 (Eq. 2)||#q.||Autoregressive 3 (Eq. 2)||#q.|
|Not Seasonal||baseline i||0.942||86||0.968||68||0.967||46|
|Not Seasonal all q.||baseline ii||0.941||0.967||0.967|
|ILI History||baseline iii||n/a||0.959||0.962|
The incidence of influenza-like illness (ILI) exhibits strong seasonal variations. These seasonal variations cause Google Correlate to identify a large number of non-relevant queries ( 80%). Many of the relevant queries are not highly ranked. Estimating the incidence of ILI with non-relevant queries is likely to become problematic when ILI deviates significantly from its seasonal variation.
We proposed a new approach to ILI estimation using web search queries. The novelty of our approach consists of re-ranking queries derived from Google Correlate. We first developed two models of the seasonal variation in ILI. The first is an analytical Serfling model. The second is an empirical model based on yearly averages. Four methods of re-ranking queries were then examined. The first two re-rank the queries based on their correlation with the two seasonal models. The second two re-rank queries based on their correlation with the residual between the seasonal models and historical ILI activity.
Experimental results showed that re-ranking queries based on Residual (YA) strongly favoured ILI-related queries, but re-ranking queries based on the two seasonal models, Seasonal (Serfling) and Seasonal (YA) led to rankings that were worse than those of Google Correlate.
When ILI estimates were based on both queries and autoregression the best performance was obtained when queries were re-ranked based on Seasonal (Serfling). Future work is needed to determine why, but we reason that (i) autoregessive models perform better when the signal has strong autocorrelation, i.e. is strongly seasonal, and (ii) this strong seasonality was present in our dataset, i.e. there was little deviation from the seasonal models. If, however, strong deviations did arise, we expect that models based on autoregression and queries re-ranked based on correlation with seasonal models will perform much worse.
This work complements the use of information retrieval and machine learning methods in the wider area of medical and health informatics(Dragusin et al., 2011, 2013).
Partially supported by Denmark’s Innovation Fund (grant no. 110976).
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