Study design
This is a retrospective time-series study investigating the association between weekly discounting and sales of five SSB categories in a single supermarket located in Metropolitan Montreal, Canada. The study time period represents the period covered by our beverage transaction data, which is between January 2008 and December 2013, thus consisting of 311 weeks, or 6 years. The unit of analysis is weekly sales transactions for each beverage category. Note that this is not a longitudinal data analysis that uses measurements from multiple stores as seen in our previous studies [16, 17], i.e. these are not panel data. Rather, we performed a time-series (i.e., single store) analysis, which allowed us to explore time-lagged effects while accounting for temporal correlation of sales.
Transaction data
The transaction records were generated by a large supermarket owned by a major Canadian retail chain (the identity of the chain is anonymized) and were purchased from a marketing firm, Nielsen [25].
The data consist of weekly sales quantity of individual beverage items, as uniquely defined by the Universal Product Code and item name, weekly price of sold items in Canadian cents, flyer promotion and retail display promotion (described below). We classified these items into the five non-alcoholic SSB categories based on product name of each beverage item and corresponding food category assigned by Nielsen. For example, soda items were categorised by the company as “carbonated soft drink”, but we manually excluded diet soda i.e., items with artificial sweeteners based on terms such as “diet”, “zero”, “non-sugar”.
Outcome
The weekly sales quantities of each beverage item were standardized to the Food and Drug Administration’s single serving size of 240 ml for beverage (approximately 1 cup). The outcome variable was the aggregated sum of sales from items in each category in each week, where the category-specific average number of distinct items over the entire 6 year period in our store was 109 (soda), 152 (fruit drinks), 36 (sports and energy drinks), 22 (coffees and teas), and 29 (drinkable yogurts). The category-specific sales were natural log transformed to reduce skewness. We did not analyse the disaggregated, individual item-level association between sales and discounting, since such an analysis required us to account for across-item dependency of sales. Since the change of category-level sales is of primary relevance to population nutrition rather than the sales of individual food items or brands, our unit of analysis for both exposure, outcome and covariates was defined at the level of beverage category.
Exposure
The exposure variable is category-specific discounting at each week. Specifically, it is a continuous variable calculated as the weighted average of weekly price discounting of individual items in each category, with weights representing each item’s market share (proportion of serving-standardized sales) within the category to which it belongs. Price discounting of an individual item is a continuous measure and was calculated as percent decrease of the serving-standardized price sold (net price) from the baseline (i.e., non-promoted) price [16, 26]. Detailed calculation of serving-standardized discounting for each item and subsequent aggregation to category is provided in Appendix S1 and Supplementary Fig. S1 in the Supplementary Information File.
Statistical analysis: regression variables to capture lagged association of price discounting and SSB sales
A lagged association between time-varying outcome (log-transformed sales quantity) and exposure (discounting) is commonly captured by a distributed lag model, which is a regression model that contains multiple time-lagged values of an exposure. Regression coefficients for these time-lagged variables have functional constraints (i.e., the value of the coefficients is constrained to change smoothly over lag) as frequently seen in environmental time-series epidemiology and econometrics [27, 28]. One such constraint is the Koyck lag decay [29], which captures the monotonic decay of the effect of an exposure over time by two regression coefficients: β as the immediate effect (at lag zero) and λ as the lag coefficient that quantifies the decaying rate. The functional form of the Koyck decay is represented by a polynomial of form:
$$\beta {\lambda}^0+\beta {\lambda}^1+\beta {\lambda}^2+\beta {\lambda}^3+\dots +\beta {\lambda}^h,$$
where h indicates lag, and βλ0 = β is the immediate effect. An estimated value of the lag coefficient λ closer to 0 indicates the absence of a lag, while its value closer to 1 indicates a stronger lagged effect. The visual interpretation of the lagged effect represented by this polynomial function is provided in Supplementary Figs. S2 a and b (Appendix S2). We pre-specified the range of the estimated value of λ to be 0 < λ < 1 so that the effect of discounting decayed monotonically towards zero over the lag, capturing a diminishing effect.
Statistical analysis: time-series regression model to incorporate Koyck lag model
The Koyck lag variables were added to a linear time-series regression, dynamic linear model [30, 31]. The details of the model, including the intercept and the lag coefficients, are provided in Appendix S3. We accounted for seasonal trends of sales by adding the sine- and cosine-transformed harmonic wave of a week variable as detailed in Appendix S3.
Covariates were weekly varying variables that are likely to temporally correlate with price discounting and sales. These included non-discounting promotion: weekly-varying display promotion and flyers, which often co-occur with price discounting (although not always) and are associated with higher sales [3]. Display promotion is temporarily placement of items into prominent location of stores such as store front. We calculated the value of these variables at the level of SSB category at each week by aggregating binary promotion status across items. Specifically, display promotion was coded as 1 if an item was temporarily placed at any one of prominent retail locations from the original shelf space, such as the end of aisle, entrance to store, or by the cashier. Flyer promotion was coded as 1 if an item was listed in flyer, and 0 otherwise. These item-level binary variables were aggregated to the category-level proportion as the weighted proportion of items promoted in each category at a given week, where the weights represented an item’s serving-standardized market share, as in the discounting variable. Additionally, an indicator variable for whether the week contained national and provincial statutory holidays was added. Other covariates were regular (baseline) price of each beverage categories, mean daytime temperature in each week, and the lagged value of sales itself (autoregressive of order 1).
We fitted a separate model for each of the five food categories independently under the Bayesian framework. We therefore specified prior distributions for regression parameters (Appendix S3). Interpretation of regression coefficients is based on point estimates (posterior mean or median) and uncertainty (95% Credible Interval [CI]) as summarized from the posterior distribution of the parameters approximated by Markov Chain Monte Carlo methods. We used the Stan software, which uses Hamiltonian Monte Carlo methods and accessed through the Rstan package in R software [32]. Model selection, specifically selecting a subset of variables from the covariates described above was guided by the value of the Watanabe-Akaike Information Criterion (WAIC) indicator of model fit [33]. As sales of many food categories are expected to have seasonal trends a priori, we did not perform any selection of the seasonal terms and thus they were retained in all models. A lower WAIC value indicates a better-fitting model. Codes are publicly available in an online repository [34].
As a sensitivity analysis, we tested an alternative shape of promotion decay by changing the constraint of the lag parameter λ from 0 < λ < 1 to −1 < λ < 0. The latter specification implies that, rather than assuming monotonic decay seen in Supplementary Figs. S2 a and b, we allowed the model to capture a so-called ‘post-promotion dip’ (Supplementary Figs. S3), a sharp reduction of sales below pre-discounting period immediately after discounting [3]. Theoretical explanations for the post-promotion dip are provided elsewhere [3, 35, 36].
The study was approved by the Institutional Review Board, Faculty of Medicine, McGill University (IRB approval#: A07-E45-16B), which did not require a written or verbal consent from human subjects, as the study used aggregated (store-level) secondary data. All methods followed the institutional guidelines and regulations.