**2. Methods**

### *2.1. Data Source and Participants*

Data from the UK Household Longitudinal Study (UKHLS) were used [24]. UKHLS is a nationally-representative longitudinal panel survey of UK adults which began in 2009 and included over 40,000 households (57% household and 82% individual response rates) [25]. Details on the study and its sampling strategy are reported elsewhere [26]. In short, participants are surveyed annually to collect demographic, socioeconomic, behaviour and health related information using a computer assisted personal interview. The household questionnaire is answered by a reference person (see Supplementary Materials for sampling strategy, Figure S1) [25].

For this analysis the general population sample was restricted to English households with data reported by an adult (aged 19 years or older) reference person (*n* = 24,711) with complete household food spend for home and away from home sources (*n* = 24,047) (see Supplementary Materials for sample flow diagram, Figure S2.). The full household and analytic sample did not differ significantly on key demographic, socioeconomic, exposure or outcome variables; therefore only the analytic sample is presented. Ethical approval was not required for the analysis of secondary data presented here, but was obtained by UKHLS for data collection.

### *2.2. Exposure: Density of Away from Home Food Outlets to All Food Outlets*

Data on the location of food establishments were obtained from Ordnance Survey's Points of Interest (POI), an administrative dataset for use by governmen<sup>t</sup> and business [27]. The data are created and maintained by PointX, which sources the data from a list of over 150 suppliers, runs verification checks and classifies the features (see the reference for user guide) [28]. POI data has been found to be a viable alternative to accurate local council data in the UK [29]. Each food outlet is provided with geographic coordinates at a stated accuracy of within 1 m. The data is updated quarterly; this analysis used data from June 2014. The use of POI data for determining food environment exposure has been demonstrated in previous studies [30–32]. Away from home food establishments were comprised of three subcategories: 'sit-down restaurants', 'fast food outlets' and 'cafés'. Example sit-down restaurants include Bella Italia, Wetherspoons or Nando's; fast food outlets include McDonald's, Burger King or Kentucky Fried Chicken; and cafés include Café Nero, Starbucks and Costa. Food outlets primarily used as a food source for at home food preparation (e.g., supermarkets, convenience and green grocers etc.) were classified as 'Other' (see Supplementary Materials for food outlet frequency and classification, Table S1). Retail outlets in which food provision is not the primary service or food is not sold directly to the public were excluded (e.g., workplace cafeterias, cinemas and recreation facilities).

Using a geographic information system (ArcGIS 10, ESRI), relative away from home food establishment density was calculated for each household. Relative density is theorised as a spatial metric representing the intensity of exposure to features of the local food environment [33], and consistent with the focus on examining the role of density of away from home food establishments for this analysis [10]. Food outlet counts (away from home and other food outlet types) were made within a 1 mile Euclidean (straight line) radius buffer, centred on household addresses provided through UKHLS secure data access (see Figure 2). This distance is based upon previous work suggesting a behavioural relevance to food shopping among UK adults [34]. Relative density for each household was then calculated as the sum of the count of away from home establishments divided by the count of all food sources, divided into quintiles. Q1 represented those with the lowest proportion of away from home food outlets and Q5 representing those with the highest proportion.

**Figure 2.** Depiction of how exposure was characterised as proportion of away from home food outlets to all food outlets around the home.

### *2.3. Outcome: Household with High Away from Home Food Spend*

Household food expenditure was self-reported using two questions in the UKHLS survey: "About how much has your household spent in total on food and groceries in the last four weeks from a supermarket or other food shop or market? Please do not include alcohol" and "About how much have you and other members of your household spent in total on meals or snacks purchased outside the home in the last four weeks?" Monthly household food spend (£) was equivalised against household size using the OECD modified equivalence scale [35] and top-coded at the limit of the second highest decile (£500/month) that is, all values ≥£500 were recoded at that value. Sensitivity analyses informed the top coding through comparing mean home and away from home food spend to household spend estimates from the UK's Living Costs and Food survey for 2009 [36]. Total away-from-home food spend was divided by total household food spend then stratified into tertiles. The highest tertile (T3) was used to define households with a 'high' proportion of their total monthly household food spend on away from home food (approximately 25% or more). While no validation study of UKHLS data has been performed, previous work has found no significant differences between receipts and self-reported data on total food expenditures, expenditures at food stores, or eating out [37].
