Ethics statement
Participation in this opt-in study was voluntary, and all analyses were carried out on anonymised data. The study was approved by the ethics committee of the London School of Hygiene & Tropical Medicine Reference number 21795.
Data
We combined data from the English participants of the UK CoMix survey and information on local and national restrictions from Gov.uk. Details of the CoMix study including the protocol and survey instrument have been published previously [2]. In short, CoMix is an online survey where individuals record details of all their direct (i.e. potentially risky) contacts in the day prior to the survey. A direct contact was defined as anyone who was met in person and with whom at least one word was exchanged, or anyone with whom the participants had any sort of skin-to-skin contact. Contacts of individuals under the age of 18 were collected by asking parents to answer on behalf of their child. Information is collected weekly from two alternating, broadly representative, panels (each about 2500 people in size), with each person surveyed once every 2 weeks.
We extracted the start and end dates of restrictions and their locations from Gov.uk between August 31st and December 7th, 2020. CoMix participants were considered affected by local restrictions if they reported living within a Lower Tier Local Authority (UK administrative zone) that was under different restrictions from those applied nationally. We restricted the data to 16 days before and after each restriction came into place to allow for two full weeks of survey responses. We then extracted the closest survey response before and after each restriction date. Participants with missing survey responses either side of the start of a restriction were removed, giving two records per person.
Details of restrictions
Local restrictions included a range of rules that were inconsistently applied across regions. Most local restrictions fell into four categories: travel restrictions, non-essential closures, preventing indoor mixing, and discouraging overnight stays. Travel restrictions included any of essential travel only, travel being discouraged, and residents banned from leaving their local area. Non-essential closures included places of worship, non-essential retail, gyms, public buildings, personal care services, art venues, and tourist attractions [7].
The Rule of Six prevented individuals from meeting in groups of six or more indoors and outdoors. The 10 pm closure stipulated that hospitality venues must be closed with customers having left the premises by 10 pm. Work from home relates to individuals being encouraged to work from home where possible.
The three-tier system was created on the 14th of October, each tier built upon the previous tier with Tier 1 being the least stringent and Tier 3 the most [10]. Tier 1 (medium risk) roughly equated to the Rule of Six, work from home, and 10 pm rule, with the addition of closing businesses with music and dancing that opens at night. Tier 2 added no gatherings in indoor space between households, restricted travel, and increased the number of venues that closed. Tier 3 prevented meeting in private outdoor spacing with non-household members and restricted restaurants and bars to table service only, with serving of alcoholic drinks only allowed when consumed alongside a substantial meal [10].
The second national lockdown was less stringent than the first as schools remained open, but included closing of pubs, restaurants, gyms, and non-essential shops and asking people to stay at home [11].
Study design
Our study is a longitudinal natural experiment. For each participant, we have one observation prior to the implementation of, and one observation after the restriction. Observations are at most 16 days from the date of the start of the restriction. This allows individuals within our study to be their own control and thus reduces the effect of between-person variation as well as the effect of longer-term temporal trends. The types of contact reported were categorised as home-based, work contact, school contact, and in other settings.
We compared the number of contacts before implementation of restrictions to the number of contacts after to assess the impact of (i) local restrictions; (ii) three national restrictions (1) Rule of Six, (2) 10 pm closure, and (3) work from home; (iii) entry into each of Tier 1, Tier 2, and Tier 3; and (iv) entry into the national lockdown from Tier 1, Tier 2, and Tier 3. To assess the effect of the different restrictions, we concentrated on changes in setting-specific contacts. For instance, local restrictions and the Tier system are largely targeted at leisure contacts, and the Rule of Six does not apply for businesses or schools. Hence, for these two restrictions, we analysed changes in contacts excluding work and school. The 10 pm closure rule requires restaurants, pubs, and bars to close early, and is therefore not expected to have a direct effect on contacts made at home, work, or school. Thus, we excluded contacts in those settings as the outcome for this restriction and refer to remaining contacts as Other contacts. To assess the effect of the work from home advice, we focused on the work contacts of respondents who were employed. During the second national lockdown, schools remained open, and therefore, we only excluded contacts made at school in assessing its effect.
Statistical analysis
R version 4.0.0 was used for all analyses and the code and data are available on github (see the “Availability of data and materials” section) [12,13,14]. Descriptive and graphical summaries of participant characteristics for age, gender, employment, and socio-economic status were created for each restriction, for the change in mean contacts, and for the spatial and temporal variation in the restrictions. Uncertainty for the mean contacts was calculated using clustered bootstrapping [15] where sampling was done per person rather than per observation level to preserve the correlation structure of the data.
We compared contacts before and during restrictions by calculating the mean, median, and interquartile range (IQR). The change in contacts was categorised into increased, same (unchanged), and decreased. We calculated the mean of the paired differences in contacts before and after restrictions and assessed uncertainty by constructing a 95% confidence interval (95% CI) from 10,000 bootstrap samples [15] of the paired differences.
For each restriction, we conducted paired permutation tests [16] with 50,000 permutations per test. We chose permutation tests as they are robust to distributional assumptions of the underlying data [14]. In order to preserve the study structure, we calculated the paired difference by subtracting the reported number of contacts during the restriction from the reported number of contacts before the restriction and then randomly changed the sign of each pair. In practice, this means generating a vector of random values taking − 1 and 1 that is of the same length as the number of participants and then multiplying the change in contacts by this vector.
We decided to calculate two test statistics for each permutation and each restriction: (1) the proportion of individuals whose contacts decreased after restrictions were implemented, and (2) the mean of the change in contacts before and after restrictions. The proportion of decreases is robust to large values and skewed distributions treating a difference of − 1 and − 1000 in the same way. This measure tests the relative effect of the restriction but does not estimate the effect size. The mean difference estimates the absolute effect but is affected by skewed data. In order to reduce the impact of the skewness, we restricted the total number of contacts to 200 per person per day for the comparison of the means only.
We conducted further assessment of the restrictions by age group for the Rule of Six and the 10 pm rule as these restrictions are likely to have greater potential of an effect in younger individuals who are more likely to be mobile, asymptomatic if infected, and not be shielding. These analyses were stratified by age groups 5–17, 18–39, 40–59, and 60 +.