Study design

In collaboration with the Millennium Mathematics Project, an educational and outreach project based at University of Cambridge, we recruited four schools to participate in our public engagement and research project in spring 2014. From the applications received, 4 schools were selected in a purposive sample to include a range of geographical and socioeconomic settings (north/south, rural/urban, single-sex/co-educational, fee paying/non-fee paying). For context, 83% of the UK population live in urban areas [28], 4% of schools in England are single-sex [29] and around 7% of children in Britain attend fee paying schools [30].

In the four schools, we worked with year 10 (i.e. 14-15 years old) students on the study design and logistics. Year 7 students (aged 11-12) within each school were the target population for data collection. As with previous projects [23, 31], we used public engagement with schools to facilitate data collection as part of a wider programme of curriculum-relevant scientific activities [32]. We did this using a combination of two school visits per school and six joint video conferences. These video conferences were particularly useful in enabling interaction between the four school classes involved in the project. In particular, all four schools collaborated to design the final questionnaire and obtain consent from study participants, as well as data collection, and analysis and discussion of findings. This provided students with first hand experience of working on a research project from hypothesis to conclusion.

The final survey aimed to ascertain which people year 7 students spent the most time with on a given day. We used a process of peer nomination as a method for data collection [33]: students were asked, via the research questionnaire, to list the six other students in year 7 at their school that they spend the most time with. The choice of six for the number of named contacts follows from a previous study [23], which selected six to balance the risk of right-censoring (i.e. if students had more than six contacts) with the potential for deliberate over-reporting of contacts if there was no upper limit (i.e. as a result of ‘competitive naming’ via peer pressure). Students were also asked to report their gender, school class, as well as non-year group contacts. The specific question asked was ‘how many people not in your year group (including family and teachers) did you have a conversation with yesterday?’ The respondent could select one of five possible categories: 0-5 people; 6-10; 11-15; 16-20; 21 or more.

Collecting data in schools can be challenging for external researchers; we tried to mitigate these logistical constrains by having the students in year 10 administer paper questionnaires to year 7 students at regular intervals throughout the second half of the academic year 2014-15 (Table 1). This allowed the questionnaires to be carried out at suitable times based on student researcher’s knowledge of the school, but also attempted to mitigate external intervention in participant decision making. We encouraged the school participants to carry out the surveys at similar time periods (i.e. at monthly intervals) but there was some variation in timing of survey between schools, based on student availability linked to term times, exam periods, and timetabled registration sessions (Table 1), as well as number of participants (S1 Table).

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Table 1. Summary of survey data from the four schools.

Additional characteristics are given in parentheses: R = rural, U = urban; S = single-sex, C = co-educational; F = fee paying, N = non-fee paying. No. unique denotes the number of uniquely identifiable students who completed the survey across all rounds. Total contacts gives the number of identifiable contacts reported across all participants.

https://doi.org/10.1371/journal.pone.0200090.t001

Two types of informed consent were required for each of the year 7 participants completing the questionnaires. First, their parents or guardians were invited to sign a written consent form to allow their child to participate in the study. Second, the students themselves were asked to verbally consent to undertake the questionnaire each time. The project was approved by the London School of Hygiene & Tropical Medicine Observational Research Ethics Committee (ref 8769).

Data cleaning and processing

Once the survey forms were completed, the data were digitised and cleaned (S1 Data). We compiled a clean list of unique participants and contacts by using the stringdist R package [34] to match each reported name in the survey database to names in a year group list. We matched names using a ranking based on the Jaro-Winkler distances between first name and surnames in the two lists. This measures the minimum number of single-character transpositions needed to convert one word into the other. We ranked potential matches based on the combined distance between first name (d₁) and surname (d₂), with first names given a larger weighting: . This criteria was obtained following several rounds of manual validation, with an additional round of validation performed after names were matched to identify erroneous matches. If d_both > 2, or the best match could not be validated manually, the participant or contact was not included in the analysis. Once the reported names had been cleaned and validated, all subsequent analysis was carried out on anonymised data, with each student name replaced by a unique code. Our analysis focused on two types of contacts. For each pair of participants in a specific round of data collection, a single link was defined if either one of the participants reported a contact between the pair (i.e. there was at least one uni-directional link, in either direction); a mutual link was defined if both participants reported contact with each other (i.e. a bi-directional link). Code and data required to reproduce all the analysis are available at: https://github.com/adamkucharski/schools-networks-15.

Network metrics

We used the igraph R package [35] to visualise the contact networks and examine five specific network metrics. These captured key aspects of network structure, as also examined in previous studies of contact patterns within schools [4, 23, 36]. The global clustering coefficient, which ranges from 0 to 1, is defined as the number of closed triplets in the network divided by number of connected trios of nodes, whether closed or not. Highly clustered networks have a coefficient value near one. The clustering coefficient for a specific round of data collection was calculated using all uni-directional links in the directed network generated from that round. The diameter of a network for a specific round was calculated from the shortest distance between the two nodes that are most distant, where the network included all uni-directional links. Given a categorical variable associated with each node, such as gender or school class, nominal assortativity measures how much nodes with the same categorical value are connected with one another [37]. Nominal assortativity, denoted r, is defined as: (1) where e_ij is the proportion of edges that connect nodes of category i and j. Again, this was calculated using all uni-directional links in the network.

We also estimated how individuals were grouped within the network. We used two different community metrics. The first of these was the common benchmark method of community detection based on edge betweenness, which uses the Girvan–Newman algorithm [38]. This works by defining the ‘edge betweenness score’ for each edge in the network (i.e. the number of shortest paths between nodes in the network that pass through this edge), then the edge with the highest score is iteratively removed until a rooted tree remains, with each clade representing a community. As a sensitivity analysis, we also considered community detection based on propagating labels [39]. In this algorithm, a unique label is attributed to each node at the start, then each node iteratively adopts whichever label the majority of its neighbours have, until the labelling converges to identify communities.

Bootstrap sampling

To assess the consistency of the network metrics for each school over time, we used bootstrap sampling [40]. In each iteration, we randomly sampled a subset m of participants from the full set of unique participants, where m is the mean number of participants across the four rounds (S1 Table). For each sampled participant, we then randomly selected one of the rounds they participated in, and used this round as their reported contacts. This generated a bootstrap network from which we could calculate the relevant network statistics. The variation in these network statistics reflected the level of consistency in responses between rounds. If student participation and responses were identical across rounds, we would have obtained exactly the same network in each bootstrap sample. We performed 10,000 iterations of bootstrap sampling to estimate the median and 95% confidence interval for each network metric.

Out-of-sample prediction

Collecting social contact data can be extremely time consuming. It would therefore be useful to establish whether multiple rounds of data collection generate a more consistent estimate of which individuals are linked. To examine how closely networks based on data collected in each round of surveys could predict the networks generated from data in subsequent rounds, we used an out-of-sample prediction approach. We focused on individuals who had participated in all four rounds of data collection. For each round, we calculated whether each possible pair of individuals were connected by a single link (i.e. at least one uni-directional link) in that round. We analysed single links rather than mutual links because we had already heavily thinned the networks by focusing only on participants who appeared in all rounds. We generated predictions using networks constructed from one or more rounds of training data; if a single link was present between two individuals in the training dataset, we predicted it would exist in later rounds. We then compared our predictions with test datasets, i.e. networks generated from later rounds of data collection. In the case where there was disagreement in the training datasets (e.g. a single link was present in two rounds of training data, but absent in the third), we defined the probability of this pair being connected by a single according to the proportion of training rounds that included a link. This make it possible to calculate expected numbers of true positives (TP) and true negatives (TN) and false positives (FP) and false negatives (FN). Specifically, these numbers were defined as: where p_ij is the proportion of training sets that have a single link between i and j, and s_ij = 1 if there is a single link between i and j in the test network. For example, in the situation where a single link is present in 2/3 of the training rounds, it would predict a single link in the test data with probability 2/3; if the single link had been present in all training rounds, it would have probability 1 of being predicted in the test data. Using the expected values of TP, TN, FP and FN, we calculated precision (), recall (), accuracy () and F-score ().

As well as comparing network links, we measured the consistency of individual-level indegree across rounds. For each participant, we calculated their indegree in the training round, compared these predictions with the test data, then calculated the mean difference across all participants. If there were multiple training rounds, the mean was used. Suppose two rounds of training data were used and a participant had indegree 3 and indegree 4 in the training rounds and indegree 6 in the test round. In this case, the absolute difference was calculated to be |3.5 − 6| = 2.5). We used the same approach to calculate the mean difference in reported contacts outside the year group between training and test rounds.

Discussion

We assessed key features and structural characteristics of social networks in four UK secondary schools, and how these varied over time. As in previous studies [23, 31], the research was embedded within a public engagement project, with students and teachers in participating schools contributing to the study design and data collection. We found that although individual contacts within the year 7 groups studied varied over the five month study period, out-of-sample prediction accuracy of contacts was over 90%. Further, many aspects of the overall network structure, such as extent of clustering and number of communities, remained relatively stable between rounds of data collection.

Children are a key epidemiological group for many directly transmitted infectious diseases [10–12]. Our results show that it is feasible to collect longitudinal self-reported data from a group of year 7 children, and that data collected is reasonably consistent between rounds, which should increase confidence in cross-sectional studies examining self-reported contacts in this age group. We also observed considerable variation in network structure between the schools, indicating that while key network properties may be relatively robust within a school, there may be substantial differences depending on where a study is conducted. The small differences in individual-level indegree across rounds (Fig 4C) suggests that highly or weakly connected individuals remain so over time. However, we did not examine within or between classroom contact patterns in detail, given the low assortativity for classroom mixing within most schools. In future studies, it would be interesting to examine how the physical structure of buildings and timetabling influences social contacts [14], given that the school in our study that set students for all subjects had lower clustering than other schools.

There are some additional limitations to our study. To ensure the questionnaire was straightforward to complete, students were asked to list the names of the six students they spend the most time with. The data may therefore be right censored: if the true number of contacts exceed the limit of six named students, the network will not represent all potential interactions. Moreover, single links may represent peers an individual would like to be friends with, rather than actual contacts. However, similar contact groupings can be observed in the networks with single and mutual links (Fig 3), suggesting that consistent contact patterns were being captured. In self-reported questionnaires there is also the issue of recall bias [26], but it has been shown that children are capable of achieving similar levels of accuracy to adults for simple objective questions [18], and that links between school classes in networks inferred from surveys are consistent with networks measured using wearable sensors [36]. Although we worked closely with the schools to ensure questionnaires were conducted as consistently as possible, the times between rounds of data collection also fluctuated based on logistical constraints, such as term dates. Given that the ‘true’ contact network was never observed, only measured contacts in each round, our analysis of out-of-sample predictions reflects consistency between rounds, rather than comparison to a known baseline network. There was also a low response rate from some classes, mostly as a result of parents either not receiving, completing or returning a consent form. A one off survey may have been more effective in terms of response rate [23], but it would not have been possible to analyse the longitudinal patterns we were interested in. One option for future work would be to extend the data collection period over a year or two, rather than over five months we considered, to see whether the consistency in contact patterns held over multiple school years. Although this would be provide longer term insights, it would also potentially introduce further practical challenges both for researchers and school staff.

We focused on close social contacts in this study, as it has been suggested that these play a key role in transmission of respiratory infections [2, 41]. However, there may other important routes of transmission that are not captured by self-reported social mixing patterns, such as fomites and aerosols [42, 43]. An outstanding challenge for such infections is how to measure social contacts at the time of infection, and hence link transmission events with the interactions that generated them. Bacterial infections, for which there can be high rates of nasopharyngeal carriage, may therefore be a good target for future research into this question [41].