Table 1 Estimated percentage point change in the mean prevalence of e-cigarette use among tobacco smokers who endorse the belief that e-cigarettes are less harmful than combustible cigarettes during the study period (2014–2019), based on autoregressive integrated moving average with exogenous input (ARIMAX) models

 Use of e-cigarettes

0.52 (0.30–0.75), < 0.001

0.48 (0.25–0.71), < 0.001

 Current cigarette smokers

–

0.08 (− 0.14–0.31), 0.48

 Tried to quit in the past year

–

0.12 (− 0.11–0.36), 0.31

 National mass media expenditure in millions (£)

–

0.10 (− 0.14–0.34), 0.42

 ARIMAX (p,d,q)(P,D,Q)

(0,1,1)(0,0,0)

(0,1,1)(0,0,0)

 Non-seasonal (p value)

  Autoregressive (AR) term

–

–

  Moving average (MA) term

< 0.001

< 0.001

 Pseudo R²

0.28

0.33