Impact on sales of adding a smaller serving size of beer and cider in licensed premises: an A-B-A reversal design

Background: Smaller serving sizes of alcoholic drinks could reduce alcohol consumption across populations thereby lowering the risk of many diseases. The effect of modifying the available range of serving sizes of beer and cider in a real-world setting has yet to be studied. The current study assessed the impact on beer and cider sales of adding a serving size of draught beer and cider (2/3 pint) that was between the current smallest (1/2 pint) and largest (1 pint) standard serving sizes. Methods: Twenty-two licensed premises in England consented to taking part in the study. The study used an ABA reversal design, set over three 4-weekly periods, with A representing the non-intervention periods, during which standard serving sizes were served and B the intervention period when a 2/3 pint serving size of draught beer and cider was added to the existing range, along with smaller 1/2 pint and larger 1 pint serving sizes. The primary outcome was the daily volume of beer and cider sold, extracted from sales data. Results: Fourteen premises started the study, of which thirteen completed it. Twelve of those did so per protocol and were included in the primary analysis. After adjusting for pre-specified covariates, the intervention did not have a significant effect on the volume of beer and cider sold per day (3.14 ml; 95%CIs -2.29 to 8.58; p = 0.257). Conclusions: In licensed premises, there was no evidence that adding a smaller serving size for draught beer and cider (2/3 pint) when the smallest (1/2 pint) and largest (1 pint) sizes were still available, affected the volume of beer and cider sold. Studies are warranted to assess the impact of removing the largest serving size. Trial registration: ISRCTN: https://doi.org/10.1186/ISRCTN33169631 (08/09/2021), OSF: https://osf.io/xkgdb/ (08/09/2021)

Impact of health warning labels and calorie labels on selection and purchasing of alcoholic and non‐alcoholic drinks: a randomized controlled trial

Aims: To estimate the impact on selection and actual purchasing of (a) health warning labels (text‐only and image‐and‐text) on alcoholic drinks and (b) calorie labels on alcoholic and non‐alcoholic drinks. Design: Parallel‐groups randomised controlled trial. Setting: Drinks were selected in a simulated online supermarket, before being purchased in an actual online supermarket. Participants: Adults in England and Wales who regularly consumed and purchased beer or wine online (n = 651). Six hundred and eight participants completed the study and were included in the primary analysis. Interventions: Participants were randomized to one of six groups in a between‐subjects three [health warning labels (HWLs) (i): image‐and‐text HWL; (ii) text‐only HWL; (iii) no HWL] × 2 (calorie labels: present versus absent) factorial design (n per group 103–113). Measurements: The primary outcome measure was the number of alcohol units selected (with intention to purchase); secondary outcomes included alcohol units purchased and calories selected and purchased. There was no time limit for selection. For purchasing, participants were directed to purchase their drinks immediately (although they were allowed up to 2 weeks to do so). Findings: There was no evidence of main effects for either (a) HWLs or (b) calorie labels on the number of alcohol units selected (HWLs: F(2,599) = 0.406, P = 0.666; calorie labels: F(1,599) = 0.002, P = 0.961). There was also no evidence of an interaction between HWLs and calorie labels, and no evidence of an overall difference on any secondary outcomes. In pre‐specified subgroup analyses comparing the ‘calorie label only’ group (n = 101) with the ‘no label’ group (n = 104) there was no evidence that calorie labels reduced the number of calories selected (unadjusted means: 1913 calories versus 2203, P = 0.643). Among the 75% of participants who went on to purchase drinks, those in the ‘calorie label only’ group (n = 74) purchased fewer calories than those in the ‘no label’ group (n = 79) (unadjusted means: 1532 versus 2090, P = 0.028). Conclusions: There was no evidence that health warning labels reduced the number of alcohol units selected or purchased in an online retail context. There was some evidence suggesting that calorie labels on alcoholic and non‐alcoholic drinks may reduce calories purchased from both types of drinks

Time scales and exponential trends to equilibrium: Gaussian model problems

We review results on the exponential convergence of multi- dimensional Ornstein-Uhlenbeck processes and discuss related notions of characteristic timescales with concrete model systems. We focus, on the one hand, on exit time distributions and provide ecplicit expressions for the exponential rate of the distribution in the small noise limit. On the other hand, we consider relaxation timescales of the process to its equi- librium measured in terms of relative entropy and discuss the connection with exit probabilities. Along these lines, we study examples which il- lustrate specific properties of the relaxation and discuss the possibility of deriving a simulation-based, empirical definition of slow and fast de- grees of freedom which builds upon a partitioning of the relative entropy functional in conjuction with the observed relaxation behaviour