Sinking lid on tobacco supply
 Tobacco consumption/ supplyTobacco sales data for the baseline year (2011) were derived from the NZ Treasury (eg, 3.3 billion cigarette equivalents).36 To estimate the number of cigarettes consumed at baseline by each sex by ethnicity group, commercial tobacco sales data and self-reported smoking intensity data from the NZ Health Survey 2006/2007 were matched and combined with baseline smoking prevalence data.
For each sex by ethnicity group, the tobacco sales volume was then assumed to reduce by 10% (absolute percentage points) in the first 5 years, and by 5.6% per year in the remaining 9 years (50%/9), with supply eventually equalling zero in 2025.
Uncertainty of ±20% SD, gamma, around the baseline number of tobacco cigarettes supplied to the market.
 Year-specific proportional smoking uptake and cessation ratesEach year, the total number of tobacco cigarettes supplied to the commercial market was reduced. We thereby assumed that 50% of the yearly reduction was met by people reducing the number of cigarettes consumed per day, and 50% by people quitting smoking (based on the principal of price elasticities of tobacco demand).19 With the end date for tobacco sales approaching, we furthermore assumed that this 50/50 proportion would incrementally shift each year with the proportion of quitting eventually representing the total percentage reduction in supply.
The following plausible responses from the NZ public were thereby taken into account: (1) with a clear end date for commercial tobacco sales approaching, most smokers would realise quitting would be the only viable option, (2) further denormalisation of smoking triggered by media and public discourse may increase smokers’ motivation to quit and (3) quitting smoking may become easier over time as most smokers would have reduced daily cigarette consumption over time.
To determine by what proportion the number of smokers would reduce by each year following a reduction in supply of tobacco cigarettes, the proportional difference was taken between the reduced amount of cigarettes supplied to the commercial market for that year and the total amount of cigarettes that would have been consumed had supply not reduced. The latter was a function of daily cigarette consumption in the previous year and the number of smokers who had survived (taking annual mortality statistics into account). In other words, for each intervention year the difference between the total demand for cigarettes based on the previous year and the actual amount of cigarettes supplied in the current year was taken. The difference was then multiplied with the year-specific proportion due to quitting (ranging from 0.5 to 1). The following formula was used to calculate the year-specific proportional reductions in smoking prevalence in each sex by ethnicity group:
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where Cthe year-specific cessation rate at year t, St = the total amount of tobacco cigarettes supplied to the commercial market under the sinking lid scenario at year, Dt −1 = the total demand for cigarettes based on consumption in the previous year and P=the proportion of the annual reduction in the total number of cigarettes due to quitting at year t (varying between 0.5 and 1.0).
Uncertainty of ±20% SD, beta, around the baseline 50/50 proportions (Pt) of people quitting or reducing consumption due to the reduction in supply.
We ran scenario analyses around the proportions (Pt) by which we assumed that people would quit or reduce daily cigarette consumption. In one scenario, these proportions started at 30% (quitting)/70% (reducing daily consumption) and then shifted towards 100% quitting over time, and in another scenario they were kept constant at 50%/50%, except in the last year when supply ends (ie, 100% quitting).
The year-specific uptake and cessation rates under the sinking lid on supply and their estimated SDs (as estimated in the forecasting model with the different data inputs and specified uncertainty) were used as direct inputs for the tobacco multi-state life-table model to estimate health gain and cost impacts of a sinking lid on supply. Uncertainty SD beta correlations 1.0 between sex by ethnic groups.
 Illicit tobacco market dynamicsThe potential impact of a growing illicit tobacco market on the impact of a sinking lid on supply was only considered in a scenario analysis.In a scenario analysis, we assumed an increase of 1% in the market share of the illicit market for every 10% reduction in the total supply of tobacco. Consequently, every 1% growth in the illicit market share was assumed to result in a 10% reduction in the year-specific proportional reductions in smoking prevalence in each sex by ethnicity group.