In order to better inform such estimates, a population based contact survey has been carried out in Belgium over the period March-May In contrast to other European surveys conducted simultaneously, each respondent recorded contacts over two days. Special attention was given to holiday periods, and respondents with large numbers of professional contacts.
Participants kept a paper diary with information on their contacts over two different days.
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A contact was defined as a two-way conversation of at least three words in each others proximity. The contact information included the age of the contact, gender, location, duration, frequency, and whether or not touching was involved. For data analysis, we used association rules and classification trees. Weighted generalized estimating equations were used to analyze contact frequency while accounting for the correlation between contacts reported on the two different days.
A contact surface, expressing the average number of contacts between persons of different ages was obtained by a bivariate smoothing approach and the relation to the so-called next-generation matrix was established. People mostly mixed with people of similar age, or with their offspring, their parents and their grandparents.
By imputing professional contacts, the average number of daily contacts increased from The number of reported contacts depended heavily on the household size, class size for children and number of professional contacts for adults. Adults living with children had on average 2 daily contacts more than adults living without children.
These findings can be used to estimate the impact of school closure. We conducted a diary based contact survey in Belgium to gain insights in social interactions relevant to the spread of infectious diseases. The resulting contact patterns are useful to improve estimating crucial parameters for infectious disease transmission models. Peer Review reports.
Mathematical models of person to person transmission of infectious agents require assumptions of social contact patterns between these persons. Such assumptions, in combination with the age-specific cumulative incidence of infection for instance based on seroprevalence data [ 1 — 4 ] , enable estimating the so-called "Who Acquires Infection From Whom" WAIFW matrix [ 1 ]. The WAIFW matrix is central to dynamic transmission models, as are closely related parameters like the basic reproduction number and the force of infection. Over the last decade, some small and unrepresentative studies have explored ways of collecting data on social mixing behaviour relevant to the spread of close contact infections [ 5 — 9 ].
Alternatively, mixing patterns between age groups were estimated in a social network context [ 10 ]. First, each participant registered contacts during 2 random days one week day and one weekend day , enabling more refined coupled analyses on weekend versus week days. Second, participants could be linked to their geographical location enabling the comparison of contact behavior between regions. Third, a school holiday period was included in the sampling period, enabling more refined analyses on weekend versus holiday period days, and different simulations of the effects of school closure.
Fourth, people with more than 20 professional contacts were requested to estimate these separately in terms of number and age to reduce reporting bias for persons with many professional contacts.
In the current paper, we aim to describe and analyze the complete Belgian contact survey in depth. The next section outlines the data collection procedure. We then explain the different methods of data analysis applied in this paper, starting from standard data mining techniques to simulations of the spread of newly emerging infections and the impact of school closure. Finally, we end with a discussion on how these contact data can be used to improve estimation of infectious disease parameters.
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Over the period March — May , persons living in Belgium were recruited by random digit dialing on fixed telephone lines. Only one person per household could participate. In line with the total Belgian population Chi-square test for equality of distributions, p-value 0.
The contact survey conducted as part of this study required participants to complete a survey anonymously, without changing their usual behaviour. No persons were subject to interventions and no physical samples were collected as part of this study. The study protocol was approved by the ethical committee of the Antwerp University Hospital. Two types of physical contacts were defined: 1 two-way conversations during which at least three words were spoken; 2 contacts which involved skin to skin touching.
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Each participant was asked to fill in a paper diary recording their contacts during one randomly assigned weekday and one randomly assigned day on the weekend not always in that order. Teenagers 9—17 y filled in a simplified version of the diary, and were closely followed up to anticipate interpretation problems all surveyors had received identical training instructions to accomplish this.
In addition to a pilot test in Luxemburg, specific Belgian Dutch and French language versions of each type of diary were made and tested in Belgium see also [ 6 , 11 ]. Information recorded in the diary included the exact or estimated age and gender of each contacted person, the duration of contacts per person over the entire day, frequency habitual nature and location or circumstance of contact multiple options possible.
A list of variables used for our analysis is given in Table 1.
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The diaries were sent and collected by mail. Each participant was reminded by phone that they had to fill in the diary, one day prior to each assigned day, and was followed up after the first day to check whether they had. If they had not filled in the diary, they were assigned to a new random day.
If they had not returned the diary, they were reminded by a maximum of three follow up calls to send it in. If participants repeatedly failed to fill in the diary on their assigned day, they were excluded, and replaced by a new recruit. Each participant received a small token of appreciation for the amount of 5 Euro. All diaries were double entered in a computer database and checked manually.
These characteristics of the sample are all broadly in line with general Belgian population statistics National Institute for Statistics, , Belgium. Although in order to keep the diary manageable, we intentionally did not record the relationship with the contacted persons, we extracted household-like contact data from the database by identifying those contacts with the same age as the registered ages of the household members knowing that the contacts occurred at home and that an exact age was given, and not an estimated age range as for the ages of contacted persons from whom the exact age is unknown.
We performed a sensitivity analysis with respect to the selected contacts of the same age. These contact surveys, although broadly aiming to record similar outcomes, were not quite the same due to dissimilar implementations in each of the countries see [ 11 ]. One important difference between these surveys was the registration of work contacts. In the Belgian diaries, the participants were asked prior to filling in their dairy for the first time the following sequence of questions.
The complete Belgian surveys including diaries are available [see Additional file 1 , 2 , 3 , 4 , 5 , 6 and 7 ]. Although these questions were asked with the common intention to reduce reporting bias for people with many professional contacts eg bus drivers , there are some important differences in how we approached this, in comparison to DE, FI and NL. First, based on information from the pilot studies, we set the threshold value at 20, whereas in DE, FI and NL it was set at Second, we asked first if the participants thought they had many professional contacts, and only if they did subjectively think so, how many they estimated these to be.
Third, we only revealed in the last question what the consequence of their estimate was for the effort required to complete the diary.
Fourth, we did not only ask about the number of professional contacts, but also about their usual age range. In the current paper, we used imputation to complete the full Belgian data set. However, this too had its limitations, since imputation enabled generating data from which reliable inferences can be made, but could not recreate the values that were not recorded [ 12 ].
In order to impute the other contact characteristics, plausible assumptions were made based on the available information from other POLYMOD countries. Mossong et al. The imputation of gender of contacts was performed based on the same reasoning. For the imputation of contact characteristics like duration and usual frequency, we considered it unlikely that a single professional contact in a large set of such contacts would last longer than 4 hours and reoccur daily. This method could also be more widely applied to all characteristics in an attempt to avoid disrupting dependencies, but could just the same also enforce dependencies.
Furthermore, the choice of distribution for the duration of contacts would be subjective since a it was clearly unknown for what was missing and b the distributions varied substantially between countries. For the remainder of the paper, we focus on this augmented data set but note that the results were similar whenever these imputations were left out, except when estimating the number of contacts. This will be illustrated for one of the methods introduced in the next section.
Since the contact survey contains a lot of information, we will, next to some descriptive statistics, use up-to-date statistical methodology to highlight different aspects from the data. We will first describe the use of association rules and classification trees to identify associations and factors related to type, location, frequency and duration of contact. Then we will use weighted generalized estimating equations to properly model the number of contacts taking into account the correlation of contacts recorded by the same participant on two different days. Finally, we relate contact patterns to the spread of infectious disease using the next generation matrix.
While this methodology provides more insight into how close contact infectious diseases are spread, we note that we do not aim to describe the stochastic nature of an emerging epidemic. In this section we present some more detail on the methods used throughout this manuscript and refer to the literature for an extensive description. In large databases, like the contact database, patterns between variables can be discovered by data mining techniques such as association rules [ 13 ].
If A , B denote properties of contacts e. While A could consist of more than one contact property e. The length of a rule is the total number of properties constituting that rule. Since numerous combinations of contact properties exist, various interestingness measures could be studied.
Background
We focused on the support, the confidence and the lift of a rule. The support of a rule expresses the relative frequency of all contacts in that rule and searching for rules with a high support can be seen as a simplification of 'bump hunting' [ 14 ]. The confidence of a rule expresses the conditional probability associated with that rule P B A.
Finding rules with high confidence is similar to finding rules with a high association between the items, as is finding rules with a high lift value. In the latter case, a higher lift value indicates that the support of the rule is higher than the product of the support of the items in that rule expressing independence between items [ 14 ]. To gain more insight in factors determining contact intensity physical contact, location, frequency and duration , the binary classification tree methodology as introduced by [ 15 ] was used.
This is a recursive partitioning method which is nonparametric in nature, simple and intuitively appealing. At each step, the recursive partitioning algorithm determined an optimal cut off point such that all the contacts were split in two subpopulations to achieve high predictive classification with respect to the variable of interest; touching yes or no , location home, school, work, school, transport, leisure or other , frequency daily, weekly, monthly, a few times a year or first time and duration 0—5 min, 5—15 min, 15 min — 1 hour, 1—4 hours, more than 4 hours.
The resulting subpopulations were split repeatedly until no additional partitioning was warranted: either a subpopulation contained only one class or it was too small to divide any further. The program Rpart [ 16 ], implemented in R, was used to generate the decision trees depicting the classification rules generated through recursive partitioning. When growing a tree equal misclassification costs were assigned to the categories of the response variable. Pruning of the trees to correct for overtraining was undertaken using the 1 SE rule described by [ 15 ] in combination with a maximal tree-depth of 4 layers.