Model Structure
The SAVM adopts a public health framework (Levy et al. 2017) that has been specifically developed to consider the impact of NVP use on smoking and public health. We focus on the regular (rather than experimental) use of NVPs and cigarettes and the transitions between those uses both to simplify the model and because health outcomes generally depend on regular (i.e. stable) use patterns over time (Jha et al. 2013). The public health impact of NVP use among smokers and non-smokers is estimated by comparing two scenarios: a) the No-NVP Scenario which projects future cigarette use and associated mortality outcomes for each birth cohort in the absence of NVPs, and b) the NVP Scenario which incorporates NVP use patterns into each cohort’s cigarette use trajectory.
The SAVM begins with separate cohorts of males and females by individual age. Within each cohort, the population evolves with age. To simplify the model and focus on the current, former and never smoking and vaping, their rates are translated into population levels using the actual and projected US population (Centers for Disease Control and Prevention 2019a).
The No-NVP Scenario
The No-NVP Scenario projects the prevalence of never, current, and former smokers over time using age and gender-specific initiation and cessation rates for each cohort. The data were developed using an age-period-cohort statistical smoking model (Holford et al. 2014a, Holford, Levy and Meza 2016, Jeon et al. 2018, Tam et al. 2018). Established smoking is measured as having smoked at least 100 cigarettes during one’s lifetime and currently smoking every day or some days. Initiation is based on becoming an established current smoker and occurs through age 40. Current smokers become former smokers after having quit. A two year cut-off is applied to reflect cessation net of relapse, i.e., relapse is not explicitly considered. The initiation and cessation rates are projected forward based on data from the NHIS through the year 2013, before NVPs became popular and thus reflects smoking patterns in the absence of NVPs.
For a given cohort, the projected prevalence of never smokers at age a and time t is composed of the surviving never smokers in the previous year (age a-1, time t-1) who did not initiate smoking. Denoting the initiation rate from never smokers at a-1 and t-1 to smokers at a and t as Inita−1,t−1 and the death rate of never smokers in previous year as DR_nevera−1,t−1, never smoker prevalence at age a and year t is calculated as:
Prev_nevera,t= Prev_nevera−1,t−1 * (1 - DR_nevera−1,t−1) * (1 – Inita−1,t−1). (1)
The prevalence of smokers includes surviving never smokers who initiate smoking and surviving smokers who do not quit. Denoting the cessation rate from smokers at a-1 and t-1 to former smokers at a and t as Cessa−1,t−1 and the smoker death rate as DR_smokera−1,t−1, current smoking prevalence evolves as:
Prev_smokera,t = Prev_smokera−1,t−1 * (1- DR_smokera−1,t−1) * (1- Cessa−1,t−1)
+ Prev_nevera−1,t−1 * (1 - DR_nevera−1,t−1) * Inita−1,t−1. (2)
Denoting DR_former as the former smoker death rate, former smokers include surviving former smokers and surviving smokers who quit smoking for at least two years, former smoking prevalence is:
Prev_formera,t = Prev_formera−1,t−1 * (1 – DR_formera−1,t−1) + Prev_smokera−1,t−1
* (1- DR_smokera−1,t−1) * Cessa−1,t−1. (3)
Since prevalence estimates decline each year due to deaths, each of the prevalence rates is multiplied by the following correction factor to assure that they sum to 100%:
Correction factora,t = 1/[Prev_nevera−1,t−1*(1-DR_nevera−1,t−1) + Prev_smokera−1,t−1*
(1-DR_smokera−1,t−1) + Prev_formera−1,t−1*(1-DR_formera−1,t−1)]. (4)
The NVP Scenario
Starting from the same initial current, former and never smoking prevalence as in the No-NVP Scenario, the NVP Scenario is expanded to include current and former NVP use. The transitions are shown in Fig. 1.
Figure 1 here
A switching parameter allows direct transitions from smoking to vaping. This parameter varies by age and varies over time through an exponential decay process. The model directly relates the NVP Scenario to the No-NVP Scenario by defining the NVP and smoking initiation rates in the NVP Scenario through separate linear multipliers applied to the smoking initiation rate (Inita.t) in the No-NVP Scenario. Using a linear multiplier assures that NVP and smoking initiation follows the same age patterns for smoking initiation as in the No-NVP case, e.g., smoking initiation mostly occurs before age 21 and is minimal after age 30. Similarly, NVP and smoking cessation are modelled as separate linear multipliers of smoking cessation (Cessa,t) in the No-NVP Scenario, so that cessation follows the same age pattern in the No-NVP Scenario and tends to increase with age. With variations by age incorporated via the respective initiation and cessation patterns in the No-NVP Scenario and because current studies do not indicate different patterns, the smoking and vaping initiation and cessation multipliers are simply modeled as independent of age. In addition, these multipliers are assumed to remain constant over time, so that smoking and vaping initiation and cessation in the NVP Scenario follow the same temporal patterns as in the No-NVP Scenario.
Because SAVM focuses on regular use, the NVP Scenario does not explicitly incorporate “gateway” effects whereby youth transition from short-term vaping to regular smoking. Any such transitions are however incorporated indirectly through the smoking initiation multiplier in the NVP Scenario. Similarly, the NVP Scenario does not explicitly model short-term NVP use leading to quitting both cigarettes and NVPs, but is indirectly incorporated through the smoking cessation multiplier. In addition, the NVP Scenario does not distinguish dual cigarette and NVP users from exclusive smokers, because dual user have generally been found to either remain dual users or soon transition to either exclusive cigarette or exclusive NVP use (Azagba, Shan and Latham 2019, Borland et al. 2019, Coleman et al. 2018, Robertson et al. 2019, Stanton et al. 2020, Taylor et al. 2020) and the health risks of dual users are similar to those of exclusive smokers (Goniewicz et al. 2017, Shahab et al. 2017a, Shahab et al. 2017b). However, transitions from dual use to exclusive NVP use or to neither cigarette or NVP use are reflected in the switching and smoking cessation parameters.
Never smokers include surviving never smokers who do not initiate into smoking or NVP use, calculated as:
Prev_nevera,t = Prev_nevera−1,t−1 *(1 – DR_nevera−1,t−1)* (1 – αS* Inita−1,t−1– αV * Inita−1,t−1), (5)
where αS and αV are the smoking (S) and vaping (V) initiation multipliers. Smokers include surviving smokers who do not switch to vaping and who do not quit smoking and surviving never smokers who initiate smoking:
Prev_smokera,t = Prev_smokera−1,t−1*(1-DR_smokera−1,t−1)*(1 – σa−1*(1-δ)t−t0–1 – χS* Cessa−1,t−1)
+ Prev_nevera−1,t−1 * (1–DR_nevera−1,t−1) *(αS*Inita−1,t−1), (6)
where σa−1 is the switching rate from smoking to NVP use in the initial year t0 with decay rate δ for each cohort and χS is the smoking cessation multiplier. Exclusive NVP users include surviving never smokers who initiate vaping, surviving vapers who do not quit, and those switching to vaping from surviving current smokers before age 35:
Prev_NVPa,t = Prev_nevera−1,t−1*(1-DR_nevera−1,t−1)*αV*Inita−1,t−1 + Prev_NVPa−1,t−1*
(1-DR_NVPa−1,t−1)*(1– χV * Cess a−1,t−1) + Prev_smokera−1,t−1* I(a-1 < 35)*
(1–DR_smokera−1,t−1)* σa−1*(1-δ)t−t0–1, where I(a-1) = 1 if a < 36, otherwise = 0. (7)
DR_NVP is the death rate of exclusive NVP users and χV is the NVP cessation multiplier. The transition from smoker to exclusive NVP user is conditional on being less than age 35, because mortality risks of smoking are small when quitting before age 35 (Jha et al. 2013).
Former smokers include surviving former smokers, surviving smokers who quit smoking and do not vape, and surviving former smokers who regularly vaped but quit vaping:
Prev_formera,t = Prev_formersa−1,t−1*(1 – DR_formera−1,t−1) + Prev_smokera−1,t−1 *
(1 – DR_smokera−1,t−1) * (χS* Cess a−1,t−1) + Prev_FS-NVPa−1,t−1 *
(1 – DR_FS-NVPa−1,t−1) * (χV* Cess a−1,t−1), (8)
where Prev_FS-NVPa−1,t−1 is the prevalence of former smokers who currently use NVPs and DR_FS-NVPa−1,t−1 is the corresponding death rate. Former NVP users include surviving former NVP users and surviving vapers who quit:
Prev_FNVPa,t = Prev_FNVPa−1,t−1 * (1- DR_FNVPa−1,t−1) +
Prev_NVPa−1,t−1 * (1 – DR_NVPa−1,t−1) * χV * Cessa−1,t−1, (9)
where DR_FNVPa−1,t−1 denotes the former NVP user death rate. Since former smokers using NVPs may quit vaping, former smokers using NVPs (after age 35) includes surviving former smokers using NVPs who do not quit vaping and smokers who switch to vaping:
Prev_FS-NVPa,t = Prev_FS-NVPa−1,t−1*(1- DR_FS-NVPa−1,t−1)*(1 – χV * Cess a−1,t−1)
+ Prev_smokera−1,t−1* I(a-1 > 35) * (1- DR_smokera−1,t−1)*(σa−1*(1 + δ)t−t0–1),
where I(a-1) = 1 if a ≥ 36, otherwise = 0 (10)
As in the No-NVP Scenario, a correction factor is applied as the reciprocal of the sum of prevalence rates for each smoking and vaping category i to ensure that the prevalence rates each period sum to 100%:
Correction factora,t = 1 / ∑i [Prev_ia−1,t−1 * (1 – DR_ia−1,t−1)]. (11)
Public Health Outcomes
The SAVM considers two public health outcomes considered: 1) Smoking- and vaping-attributable deaths, and 2) smoking- and vaping-attributable life-years lost (LYLs).. Both are based on the excess risks of smoking or vaping and the number of current and former smokers and vapers.
In the No-NVP Scenario, smoking-attributable deaths (SADs) for current smokers is calculated by applying the excess risks of smokers relative to never smokers (DR_smokera,t – DR_nevera,t) to the smoking population:
SAD_smokera,t = (DR_smokera,t – DR_nevera,t) * Prev_smokera,t * Populationa,t, (12)
and attributable deaths for former smokers is calculated as:
SAD_formera,t = (DR_formera,t – DR_nevera,t) * Prev_formera,t * Populationa,t (13)
SADs for current and former smokers are summed over all ages in a particular year to obtain total SADs in that year. LYLs are estimated as the number of premature deaths multiplied by the remaining life expectancy (LE) of a never smoker at each age in year t denoted by LE_Nevera,t:
LYLa,t = (SAD_smokera,t + SAD_formera,t ) * LE_Nevera,t. (14)
Summing over ages in a particular year obtains the LYLs in that year.
In the NVP Scenario, SAD_smokera,t and SAD_formera,t are calculated in the same manner as above except using their respective prevalence rates in the NVP scenario. Vaping-attributable deaths for current exclusive NVP users (VADs) and for former NVP users (FNVP) are measured by two similar equations (15) and (16). For current exclusive NVP users, attributable deaths (VAD_NVPa,t) are a product of the number of NVP users and the excess risks of smoking adjusted by NVP relative risk, denoted by RiskNVP, and similarly for former NVP use attributable deaths (VAD_FNVPa,t):
VAD_NVPa,t = RiskNVP*(DR_smokera,t - DR_nevera,t)*Prev_NVPa,t*Populationa,t. (15)
VAD_FNVPa,t = RiskNVP*(DR_formera,t -DR_nevera,t)*Prev_FNVPa,t*Populationa,t. (16)
As a special case in the NVP Scenario, the death rate of NVP users who previously smoked is determined by the portion of excess risk of current relative to former smokers plus the death rate of former smokers:
DR_FS-NVPa,t = RiskNVP * (DR_smokera,t - DR_formera,t) + DR_formera,t (17)
Smoking and vaping-attributable deaths (SVADs) for former smokers who currently use NVPs (FS-NVPs) in the NVP Scenario is measured as a product of the number of FS-NVPs and the excess mortality risk of FS-NVP to never smokers:
SVAD_FS-NVPa,t = [DR_FS-NVPa,t -DR_nevera,t)]*Prev_FS-NVPa,t* Populationa,t (18)
Attributable deaths are calculated by summing SADs, VADs and SVADs over ages each year for a given cohort. LYLs in the NVP Scenario at each age are calculated as:
LYLa,t = (SAD_smokera,t + SAD_formera,t + VAD_NVPa,t + VAD_FNVPa,t +
SVAD_FS-NVPa,t)*LE_Nevera,t (19)
Summing over ages in a particular year obtains the LYLs in that year.
The public health impact of NVP use each year is evaluated as the difference in attributable deaths between the No-NVP and NVP Scenarios, and similarly for LYLs.
Data and Parameters
A detailed description of model parameters is shown in Table 1.
Table 1
Data and Initial Parameters for the US Smoking and Vaping Model
Input parameters | Description | Data source or estimate |
Population | Population by age, gender, and year (2013–2100) | US population projections (Center for Disease Control and Prevention 2019) |
Mortality rates | Mortality rates by age, gender, and year for never, current, and former smokers (2013–2100) | CISNET Lung Group,(Holford et al. 2014a, Holford, Levy and Meza 2016, Jeon et al. 2018, Tam et al. 2018) available on the CISNET website (CISNET 2016). |
Expected life years | Expected life years remaining of never smokers by age, gender, and year (2013–2100) | CISNET Lung Group,(Holford et al. 2014a, Holford, Levy and Meza 2016, Jeon et al. 2018, Tam et al. 2018) available on the CISNET website (CISNET 2016). |
Smoking prevalence | Current and former smoking prevalence by age and gender for initial year | CISNET Lung Group,(Holford et al. 2014a, Holford, Levy and Meza 2016, Jeon et al. 2018, Tam et al. 2018) available on the CISNET website (CISNET 2016). |
NVP relative risk multiplier | Excess risk of NVP use measured relative to excess smoking risks (mortality rate of current smokers – mortality rate of never smokers) | NVP mortality risks estimated to be 5% that of smoking excess risk for both genders at all ages, based on multi-criteria decision analysis(Nutt et al. 2016) and independent review (McNeill et al. March 2020). 40% risk is also applied in the sensitivity analysis. |
NVP Switching rate | Rate of switching from smoking cigarettes to exclusive NVP use | Ranges from 0.6%-4.0%, estimated by age group and gender using prospective analysis from PATH data 2013–2018 |
Smoking initiation multiplier in the NVP Scenario | Ratio of smoking initiation rate in the NVP Scenario to smoking initiation in the No-NVP Scenario | 75% of No-NVP smoking initiation rate, based on recent studies (Levy, Yuan and Li 2017, Levy et al. 2018c, National Center for Health Statistics 2019). |
NVP initiation multiplier in the NVP Scenario | Ratio of NVP initiation rate in the NVP Scenario to smoking initiation in the No-NVP Scenario | 50% of No-NVP smoking initiation rate, based on recent studies (Cullen et al. 2019, Hammond et al. 2019, Miech et al. 2019b, Miech et al. 2019c). |
Smoking cessation multiplier in the NVP Scenario | Ratio of smoking cessation rate in the NVP Scenario to smoking cessation in the No-NVP Scenario | 100% of the No-NVP smoking cessation rate |
NVP cessation multiplier in the NVP Scenario | Ratio of NVP cessation rate in the NVP Scenario to smoking cessation in the No-NVP Scenario | 100% of the No-NVP smoking cessation rate |
Notes: NVP = nicotine vaping product. No-NVP Scenario refers to values in the absence of NVP use. NVP Scenario refers to values with NVP use. |
Table 1 here
The No-NVP Scenario
The current, former and never smoking death rates and expected life years of never smokers were developed by Rosenberg et al (Holford et al. 2014a, Holford et al. 2014b, Holford, Levy and Meza 2016, Rosenberg et al. 2012) and are available on the CISNET website (CISNET 2016). Current population, mortality rate and expected life year estimates are from the CDC (Center for Disease Control and Prevention 2019).
The NVP Scenario
The NVP Scenario requires six input parameters: NVP mortality risks, NVP switching rate, smoking initiation, vaping initiation, smoking cessation and vaping cessation.
The NVP relative risk multiplier, RiskNVP, represents the relative risk of death associated with current NVP use as a percentage of the excess mortality risk experienced by current or former smokers as defined above. NVP relative mortality risks are designated as 5% of cigarette excess risks based on a multi-criteria decision analysis (Nutt et al. 2016) and a Public Health England review (McNeill et al. March 2020). Since others have suggested higher risks (de Groot et al. 2018, Nelluri et al. 2016, Tegin et al. 2018, Unger and Unger 2018), an NVP relative risk multiplier of 40% is also considered.
The NVP switching rate σa is the annual rate at which current smokers switch from smoking to NVP use, leading to a direct reduction in smoking prevalence. Baseline male (female) NVP yearly switching rates are based on prospective data that we collected from the 2013/2014, 2014/2015, 2015/2016, and 2016/2017 Population Assessment of Tobacco and Health (PATH) surveys (U.S. Food and Drug Administration, National Institutes of Health and Abuse. 2019) averaged over years: 4% (2.5%) for ages 18–24, 2.5% (2.0%) for ages 25–34, 2.5% (1.6%) for age 35–44, 1.3% (1.4%) for ages 45–54, 1.2% (1.4%) for ages 55–64, and 0.6% (1.0%) for ages 65 and above. Those below age 18 were assigned the age 18–24 rate. We also consider switching rates that are 50% lower and 100% higher than those baseline estimates. Rates are initially assumed constant over time (i.e., 0% decay), but we also consider a 20% decay rate, δ, to reflect the potential for switching rates to decline in the absence of innovation.
Since the smoking initiation in the NVP Scenario is measured relative to smoking initiation (Inita,t) in the No-NVP Scenario, the smoking initiation multiplier αS is greater than 100% if NVP use increases net smoking initiation beyond the rate at which individuals would have otherwise initiated smoked in the absence of NVPs (i.e., gateway in > gateway out), and is less than 100% if those who would have initiated smoking tend to transition to exclusive NVP use instead of smoking (i.e., gateway out > gateway in). Based on the more rapid downward trend in US youth and young adult smoking as NVP use increased in recent years (Levy et al. 2019a), the age- and time-invariant baseline smoking initiation multiplier is initially set at 75%, i.e. a 25% net decrease in smoking initiation due to vaping. A range of 25–125% is also considered.
The NVP initiation rate multiplier αV reflects the youth and young adult initiation of NVP use relative to smoking initiation rates (Inita,t) in the No-NVP Scenario. If less than 100%, NVP initiation rates are lower than smoking initiation rates in the No-NVP Scenario. i.e., fewer individuals become regular NVP users than who would have become smokers in the No-NVP Scenario. Reflecting the increased US youth and young adults regular NVP users in recent years (Cullen et al. 2019, Hammond et al. 2019, Levy, Yuan and Li 2017, Miech et al. 2019b, Miech et al. 2019c), the age- and time-invariant baseline NVP initiation multiplier is initially set at 50% for all ages. Sensitivity analysis is conducted over the range of 25–75%.
Since smoking cessation in the NVP Scenario is measured relative to smoking cessation (Cessa,t) in the No-NVP Scenario, the smoking cessation multiplier χS is greater than 100% if smoking cessation rates are higher in the NVP Scenario than in the No-NVP Scenario, e.g., if the availability of NVPs leads to increased smoking cessation. A parameter less than 100% implies that smokers on net are less likely to quit smoking in the NVP Scenario compared to the No-NVP Scenario, e.g., NVP use leads to dual use (continued smoking) rather than complete cessation among smokers. The baseline smoking cessation rate multiplier is initially set at 100% with a range of 50%-150% also considered.
The NVP cessation multiplier χV is greater than 1 if NVP cessation rates are higher than smoking cessation rates in the No-NVP Scenario. The parameter is less than 100% if NVP cessation rates are lower than smoking cessation rates in the No-NVP Scenario, e.g., NVPs are less addictive than cigarettes. The baseline NVP cessation multiplier is set at 100%, with a plausible range of 50%-150%.
Model Validation and Analysis
The model estimates the NVP effects over time for the prevalence of current and former smokers, current and former NVP users, and former smokers using NVPs, and for smoking-attributable and NVP-attributable deaths. The model was first validated over the years 2013 to 2018 by comparing model predictions of current smoking prevalence to current smoking prevalence rates from the NHIS (Centers for Disease Control and Prevention 2019b) by age and gender. We focus on relative reductions over the period 2013–2018, because levels in the initial year 2013 in the model differ from those in the NHIS. We also validated NVP use. However, we confine the model comparison to NVP prevalence measures from the 2018 NHIS. Although NVP use was already occurring in 2013, the model itself begins with no NVP use that year and is adjusted to reach the 2018 levels. (Levy et al. 2019b). Consequently, we validate NVP use against NHIS estimates for 2018, the latest year for which data was available rather than rely on prior trend data. We defined NVP users as those who used e-cigarettes at least 10 of the past 30 days to reflect more regular use.
Upon validating the model, we consider how NVP use affects smoking prevalence, smoking- and NVP-attributable deaths and LYLs. We conduct sensitivity analyses for the NVP transition and risk parameters over the plausible ranges specified above focusing on their impact on premature attributable deaths and LYLs.