Causal Loop Diagram
A causal loop diagram showing the minimal essential set of relationships describing cigarette use, e-cigarette use, their hypothesized relationship between them, and the policy under examination is shown in Figure 1. This conceptual diagram guides the development of the subsequent simulation model (see below). The causal loop diagram shows primarily feedback loops, either positive/reinforcing (whereby a change in one variable accelerates its own future change through the chain of causal relationships) or negative/balancing (whereby a change in one variable limits its own future change).
Loop B1 and B2 describe the central dynamic in this model: that established cigarette use leads to an unacceptable number of preventable deaths (relative to some goal). The term “tobacco-related deaths” is an umbrella term meant to include deaths from both cigarettes and e-cigarettes; though e-cigarettes are not derived from tobacco, this terminology reflects the FDA’s designation of e-cigarettes as a tobacco product. The unacceptably high number of tobacco-related deaths motivates a harm reduction policy, which in this case is twofold: 1) implementing an informational campaign which promotes e-cigarettes as a less risky alternative to cigarettes (B1); and 2) removing existing flavor bans (which are in effect in many places) (B2). This in turn increases e-cigarette initiation. Increasing e-cigarette initiation has 3 intended effects: 1) decreasing the cigarette progression rate by offsetting of cigarettes with e-cigarettes (B1), 2) reducing the cigarette initiation rate by diversion away from conventional cigarettes (B3), and increasing the smoking cessation rate (B4). An important unintended consequence is also included: progression to established e-cigarette use will increase the preventable deaths (though not as much as conventional cigarettes), which can counteract the policy to some degree (R1).
Based on the CLD above, a stock-and-flow diagram (Figure 2) was constructed in Stella Architect, version 1.9.5 (32), which consists of “aging chains” for both cigarette and e-cigarette use (a structure consisting of stocks in series, here representing different stages of use, with appropriate inflows and outflows, representing transition rates). Each aging chain has an initial inflow dependent on the rate of individuals maturing into adolescence (i.e. turning 12 years old), which occurs continuously throughout the length of the simulation. The cigarette aging chain has three stocks: experimenters, established users, and former users; while the e-cigarette aging chain only has the first two. Ex-e-cigarette users were intentionally excluded from the model because there is lack of available data on this group to calibrate parameters. Instead, a simplifying assumption was made (e.g. due to the hardening hypothesis) that once a person becomes an established e-cigarette user, they remain there for life. This is a conservative assumption (see Limitations). The flows from one stock to another are assumed to encompass two mechanisms: 1) a “social-recruitment” mechanism, in which the new initiation rate is positively affected by the proportion of established users; and 2) a “self-recruitment” mechanism in which there is a stable base of nicotine users regardless of usage in the population, consistent with the hardening hypothesis (2). The social recruitment mechanism parameter was set to 2, meaning that each user influences 2 other users per year (see Calibration Testing below).
The two aging chains feed into the Goal-Gap of Tobacco-Related Mortality Module, which calculates the discrepancy between the actual tobacco-related deaths (from both cigarettes and e-cigarettes, based on the respective stocks of established users, as this is the relevant measure from a health perspective (33)) and a goal value. Since it is unrealistic to entirely eliminate tobacco-related deaths, a goal value approximating the death rate from accidents of any type in the general population was chosen (1%/year), below the death rate due to poor diet/physical inactivity and alcohol consumption (34). The discrepancy in the actual vs. desired deaths in turn affects the policy implementation, as a much higher-than-desired tobacco-related death rate motivates regulatory policy.
The policy itself, captured in the Policy Implementation Module, consists of removing existing flavor bans (as one type of policy which increases access to e-cigarettes) as well as an educational campaign promoting e-cigarettes as a less harmful alternative. The effect of the policy is to increase the e-cigarette initiation rate, which has a 3-pronged effect on the cigarette aging chain: increasing diversion away from conventional cigarette initiation, reducing smoking and thus progression rates to established use, and increasing smoking cessation. E-cigarette initiation rate can be increased beyond that of cigarette initiation, indicating that the model allows for never-smokers to initiate e-cigarettes; the e-cigarette and cigarette initiation rates are both capped at the maximum of individuals becoming adolescents each year (maturation rate into adolescence). The Policy Implementation Module includes pragmatic considerations, such as political resistance to overturning a flavor ban, and resources for implementing an informational campaign (both budgetary and workforce-related). The structure of this model allows for ideal, best-case scenarios (no resistance and sufficient resources) as well as more realistic, limited scenarios through changing corresponding parameters (i.e. the likelihood of removing a flavor ban; the proportion of required funding that is approved, and time delays). The overall initiation of the policy is linked to a binary “switch” that can be turned on or off. It is important to note that, while the decision to initiate the policy is a binary variable, the policy itself once switched “on” can still cover a range of specific implementations, including uncertainty of further approval in the case of flavor bans.
The model was run over the period 2000-2100, with e-cigarettes first appearing around 2010, and the policy also being implemented in 2010. The detailed model structure and equations, including the modules, can be downloaded for free (35); the model can be opened and run using the free software isee Player (36).
The model was calibrated to match the “behavior modes” (i.e. the fundamental shape of the trend, such as exponential growth or exponential decline) observed in youth cigarette and e-cigarette use in the US over the period 2000-2019 (most recently available data), based approximately on the National Youth Tobacco Survey (NYTS) (30, 31) for dynamics relevant to youth (i.e. initiation and progression to established use) and the National Health Interview Survey (NHIS) (37) for dynamics relevant to adults (i.e. smoking-related fractional death rates). Since this model is not intended to finely replicate historical behavior or provide precise future projections, calibration to a broad behavior mode was sufficient. Some parameters were selected based on external data (lifetime probability of quitting cigarettes, self-recruitment effect; experimenting and cessation rates; tobacco-related raw death rates and life expectancies; cessation rates; diversion, smoking reduction, and cessation effects, times to established use; and all population numbers), while others (social contagion effects; tobacco-related fractional death rates) were calibrated by running “live” simulations over a range of parameters to determine the optimal value with respect to stocks of established users (cigarettes and e-cigarettes), as these are the stocks relevant for public health. Stocks of established cigarette and e-cigarette users according to NYTS (30, 31) and the NHIS (37) show approximately goal-seeking behavior towards a plateau (based on the proportion who are self-recruiters), and exponential growth for established e-cigarette use. Remaining parameters of flows (i.e. social contagion effect) were calibrated to achieve a reasonable match between simulated and historical data, based on the observed behavior mode and approximate magnitude (e.g. estimates of 46.5 million smokers in the US in 2000 (38). Specifically, the social contagion parameter was tuned over a wide range of plausible range values (0, meaning no social influence, to 10, meaning that each user influences 10 other users), and the value that produces an initial decline followed by a plateau through the end of the time horizon (i.e. year 2100) was selected, consistent with the hardening hypothesis. Values higher than 2 (the final parameter value) produce a continuous decline, while values higher than 2 produce an *increase* in smoking prevalence, both of which are unrealistic.
Parameters for the three-fold effects of e-cigarette use on cigarette smoking (diversion, smoking reduction, and cessation) were quantified as follows. With no existing empirical estimates for a diversion effect, this was quantified based on a separate study (28, under review) as 37.8% of e-cigarette users per year being diverted from initiating cigarettes. No empirical estimates exist for a smoking reduction effect either, and this was quantified using the rationale that, among adolescent tobacco users, about 30% preferentially use e-cigarettes historically (1, 5); therefore, e-cigarettes may offset 30% of ever-smokers who progress to established smoking. The cessation effect was quantified based e-cigarettes having an approximately 20% success rate for smoking cessation in a randomized trial (39).
A range of validation tests were performed on the model, which identified errors that were corrected in the final model. Boundary conditions were examined conceptually to determine which variables and causal relationships were included in the model. Parameter assessment was based on external data sources and calibration to observed data. Extreme conditions testing was conducted by setting inflows and initial values of stocks to 0 and very high values, and ensuring the model behaved reasonably (e.g. stocks do not fall negative).
A base-case model was constructed to replicate approximate trends in cigarette and e-cigarette use among US adolescents and adults across 2000-2019 (26, 36, 37, 40) and projected into the future (year 2100). Several policy scenarios were run, including an ideal-world, best-case scenario (no practical obstacles to implementation), and scenarios where policy implementation is delayed, faces resistance (i.e. low likelihood of removing flavor bans, due to controversy), and faces limited funding for an informational campaign. Specifically, time delays for the best-case scenario were set to 0.1 years (for time to approve both policies, time to approve funding, and time to hire and train workforce) and 10 years (for workforce turnover rate); and in the time-delayed model, were set to larger values (time to approve removal of flavor bans = 2 years, time to approve informational campaign = 1 year, time to adjust workforce = 1 year, time to train workforce = 0.25 years, and time to approve funding = 1 year). With respect to uncertainty in approving the removal of flavor bans, probability of approval was set to 1 and 0.5 for the ideal-case and uncertain-approval scenarios, respectively. With respect to budgetary constraints, the fraction of required budget that is approved is set to 1 (full budget) and 0.7 in the ideal-case and budget-restricted scenarios, respectively. Additionally, the model is publicly available and can be run through a web interface, allowing users to vary policy implementation parameters and other assumptions of the model (e.g. the strength of diversion, smoking reduction, and cessation effects).