5
Review of the Social Network Analysis for Policy on Directed Graph Networks Model
The U.S. Food and Drug Administration (FDA) commissioned the development of an agent-based model (ABM) through an interagency agreement with Sandia National Laboratories (SNL), with model development beginning in May 2010.1 A major component of the statement of task provided by the FDA to this committee was to review the model, identify its strengths and weaknesses, and make recommendations for its improvement. This chapter describes this model, entitled Social Network Analysis for Policy on Directed Graph Networks (SnapDragon), and, where appropriate, applies the evaluation framework for policy-relevant ABMs presented by the committee in Chapter 4 to the model. Some of the model evaluation criteria cannot be applied in this chapter because the activities either happened before the committee’s review (including many of the inputs) or else have not yet taken place, as the model is still undergoing development (many of the outputs and outcomes).2 This chapter provides an analysis of the model and discusses its usefulness for informing tobacco control policy.
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1SNL is a federally funded research and development center, operated and managed by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation. SNL functions as a contractor for the U.S. Department of Energy’s National Nuclear Security Administration. The lab supports federal, state, and local government agencies, companies, and organizations. For more information, see http://www.sandia.gov/about.
2The framework presented by the committee in Chapter 4 was developed to assist FDA in the future development of policy-relevant ABMs and to provide a framework for the committee to use for its assessment of SnapDragon. As such, the evaluation framework captures all stages of the model development process, but not all of these can be used to assess SnapDragon at this time.
The committee’s review is based on the SnapDragon model as it existed in July 31, 2014. The modeling team has continued to develop and test the model since that point,3 but the committee did not review any features the modeling team added after July 2014 and did not base its review on changes the development team plans to incorporate in the future.
The SnapDragon model was developed for use by FDA to examine the impact of smoking control policies on certain population smoking metrics, such as prevalence as well as initiation and cessation rates. FDA first directed the model development team to use the model to explore the potential effects of various public education campaigns on the prevalence of tobacco use to help inform its public education efforts. To date, the work on SnapDragon has focused primarily on studying the effects of multiple competing high- and low-opinion messages in a network, illustrated through the study of education campaigns (SNL, 2014a).4 The early stages of conceptual model development began in May 2010. Between the initial conception and the review of the model by this committee, the model development team developed both a single- and multiple-product model (see details below in model description), identified data needs, conducted sensitivity analyses, and presented their model at various conferences.5 The model development team continues to develop SnapDragon, as the model is still in exploratory stages. The SnapDragon model has not yet been published in a peer-reviewed journal, but two manuscripts on the model were undergoing peer review in two different journals during the writing of this report.6 In addition to the draft manuscripts, the committee received more
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3In July 2014 and January 2015, draft descriptions of the committee’s technical understanding of the model were sent to SNL for technical review. In their January 2015 response, the developers noted several changes to the model that occurred after July 31, 2014, and identified additional changes they planned to make. However, the review by the committee is based on the model as it existed on July 31, 2014. These documents are available upon request from the project public access file: http://www8.nationalacademies.org/cp/ManageRequest.aspx?key=49612.
4E-mail communication between the Institute of Medicine (IOM) and FDA staff, June 10, 2014. Available upon request from the project public access file: http://www8.nationalacademies.org/cp/ManageRequest.aspx?key=49612.
5E-mail communication between the IOM and SNL staff, July 14, 2014; available upon request from the project public access file: http://www8.nationalacademies.org/cp/ManageRequest.aspx?key=49612.
6Both manuscripts were accepted for publication at the end of this study. However, the manuscripts reviewed by the committee are available in the project public access file: http://www8.nationalacademies.org/cp/ManageRequest.aspx?key=49612. One manuscript, Modeling Education and Advertising with Opinion Dynamics, is dated May 2013 and was revised November 2013 (Moore et al., in press a); the second manuscript is titled An Opinion-Driven Behavioral Dynamics Model for Addictive Behaviors, dated November 2013 and revised February 2014 (Moore et al., in press b).
information on SnapDragon from in-person presentations by the development team during two open meetings in February and June 2014 (SNL, 2014a,b) as well as from written question-and-answer documents produced by the committee and the model development team (draft manuscripts and other supporting documents are available upon request from the project public access file).7
SnapDragon Model Description
Based on the materials the committee received from the SnapDragon model developers (as outlined above), the committee offers the following description of SnapDragon.8 SnapDragon is an ABM designed to study the effect of tobacco control policies in a single- or multiple-tobacco-product environment. The model distinguishes individuals by any number of characteristics, and in particular, according to their use of a variety of tobacco products, allowing for the investigation of the simultaneous use of different products. Currently, the model classifies individuals as either “users” or “nonusers” for each tobacco product under consideration. The user status is determined by an underlying construct termed “opinion.” An opinion is an aggregate concept that captures the overall positive or negative attitude of a person toward a tobacco product. It is represented as a continuous variable with values between 0 and 1, with 0 standing for the most negative attitude a person can have toward a tobacco product, and 1 the most positive. Each individual carries an opinion about each tobacco product under consideration.
Opinions about a product can vary over time, influenced by the opinions of other individuals. SnapDragon explicitly models the time trajectory of individuals’ opinions as a result of their interactions with other individuals, and the modeling choice is based on theory stemming from the field of opinion dynamics. In the model, individuals are connected to others through predefined social networks.9 Connected individuals can affect each other’s opinions if such opinions do not differ by more than a specified
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7The project public access file is available at: http://www8.nationalacademies.org/cp/ManageRequest.aspx?key=49612.
8In addition, the model developers reviewed this section (SnapDragon Model Description) for technical accuracy.
9Erdős–Rényi (ER) graphs “were selected as a neutral illustrative framework for the results presented to the IOM. SnapDragon currently includes multiple classes of graphs, including scale-free, forest fire, community structure graphs drawn from Lancichinetti et al. (2008), transitivity-based graphs as proposed in Jackson and Rogers (2005), dynamic graphs, and regular graphs such as rings and lattices” (e-mail communication between the IOM staff and SNL staff, August 1, 2014; available upon request from the project public access file).
tolerance range. As time progresses, individuals continuously adjust their opinions toward a weighted average of the opinions of the individuals who can influence them. The weights (or plasticity values) represent the importance given to the opinion of particular individuals.10 These plasticity values are not necessarily reciprocal, meaning that each individual in a connected pair can assign a different weight to the opinion of the other.
In the model, opinions drive tobacco use behavior, which is defined as being either a user or a nonuser of each of the specific tobacco products under consideration. Nonusers whose opinions about a tobacco product increase beyond a certain level (termed the initiation threshold) become users of that tobacco product. Users of a particular product whose opinions about such product fall below a certain level (termed the cessation threshold) become nonusers of the product. The initiation threshold is assumed to be above the cessation threshold, and the difference between these two levels indicates the degree of addiction of an individual to that particular product. An individual whose opinion is above the initiation threshold is a user; an individual whose opinion is below the cessation threshold is a nonuser; an individual whose opinion falls between the initiation and cessation thresholds could be either an addicted user if he or she has previously crossed the initiation threshold or else a nonuser if he or she has not.
Thresholds and opinions are determined by multiple factors. These determining factors, or determinants, can be identified to isolate their effect on policy interventions. In particular, SnapDragon test runs have been conducted to examine the effects of two particular determinants—risk perception and risk affinity—for hypothesized tobacco control policy interventions. Risk affinity is a personal attribute that defines the tendency of an individual to engage in risky activities. Other things being equal, the greater an individual’s risk affinity is, the lower the initiation and cessation thresholds of a product will be. Risk perception is a component of an individual’s opinion that measures the degree to which the individual perceives the product as harmful. Other things being equal, the greater the risk perception, the lower the individual’s opinion of the product.
The SnapDragon model allows for the investigation of multiple tobacco products in the market, either by considering an individual to use different products simultaneously or by allowing an individual to switch between products. The model handles multiple product use by considering opinions and thresholds for each product simultaneously, with each product use determined by its own dynamics. Switching between two products is
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10“Weights can therefore represent the closeness of the relationship (e.g., a best friend can be more highly weighted than friend), as well as the effectiveness of a media campaign” (e-mail communication between the IOM staff and SNL staff, August 1, 2014; available upon request from the project public access file).
handled in the following way: An individual can switch from product A to product B if the user’s opinion of product A is between the initiation and cessation threshold for such a product. In such a case the difference between the product A initiation threshold and the user’s opinion of product A (a “regret” factor) is added to (reinforces) the individual’s opinion of product B. If this reinforced opinion exceeds the initiation threshold for product B, the individual switches from product A to product B.11
Interventions that can potentially influence individuals’ behavior, such as tobacco control efforts, are modeled as modifying either the opinions of individuals about a certain tobacco product or the opinion thresholds that delimit possible user status. For example, price increases can be modeled by raising the initiation and cessation thresholds for a product. In contrast, a public health education campaign can be represented by adding a fictitious individual to the model’s network (a “media node”) who has a fixed low opinion of the product. This media node can influence the opinion of a certain number of individuals within the social network, but it is not influenced by them. In this case, the media node influences the opinions of the individuals it reaches, lowering the individuals’ opinions of the product and potentially triggering a behavioral change.
Other types of interventions can be modeled in a similar way. For example, a tobacco product’s advertising campaign can be represented by adding to the model a media node with a positive opinion about the product, while promotional price discounts can be modeled by lowering the product’s initiation and cessation opinion thresholds. “SnapDragon is designed to incorporate multiple interventions in a scenario in order to model interactions and to analyze complementary and conflicting effects. Interventions can precede one another sequentially or run in parallel.”12
The modeling team uses 2014 data from Tom Valente’s high school networks study13 to evaluate the empirical validity of two assumptions within the SnapDragon model: (1) that opinion influences behavior; and (2) that people are more likely to be friends with others who share their opinions about smoking. With regard to the former, the modeling team asserts that
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11“The ‘regret’ factor can also be scaled (up or down) to reflect product characteristics such as substitutability. For example, if Product B is a less suitable replacement for Product A, then the additional opinion boost should be scaled down” (e-mail communication between the IOM staff and SNL staff, August 1, 2014; available upon request from the project public access file).
12E-mail communication between the IOM staff and SNL staff, August 1, 2014; available upon request from the project public access file.
13These data were collected as part of National Institutes of Health (NIH)/National Cancer Institute (NCI) grant 3R01CA157577-02S1 (Extending a School-Based Cohort to Improve Longitudinal Modeling), Thomas W. Valente, principal investigator. This data collection was a follow-up to the Social Network Study cohort in 2010 through 2012 (Valente et al., 2013). The data are not yet published.
these preliminary data are “consistent with opinion-to-behavior mapping in SnapDragon” (SNL, 2014b). With regard to the latter, the team members assert that the data are “consistent with the influence-network hypothesis” of SnapDragon (SNL, 2014b). “The data and analyses are considered preliminary, and ongoing analyses will be compared with analyses of Add Health and other data sets.”14
In the remainder of this chapter the committee offers its assessment of the SnapDragon model. The committee focuses on two major evaluation categories outlined in Chapter 4—model suitability and technical best practices—as these are the categories for which the committee had adequate information with which to conduct an analysis. These two categories encompass the “activities” in the logic model presented in Chapter 4, particularly the conceptual development of the model, the model’s implementation, and model testing. Some of the evaluation categories (such as communication and translation) are not yet relevant, as SnapDragon has not yet reached the later phases of model development. Before the model evaluation is presented, the chapter offers an overview of opinion dynamics, as opinion dynamics is the conceptual framework that drives the implementation of SnapDragon. Following this overview, the committee assesses the suitability of the opinion dynamics approach, as implemented in SnapDragon, to inform to tobacco control policy. (For example, does the opinion dynamics approach, as used, have face validity? Does the model incorporate relevant results from the literature in tobacco control?) Finally, the committee evaluates the technical aspects—namely the platform, parameters, and data use—of the model. (For example, has opinion dynamics been empirically validated for use in this context? Does it have predictive validity outside the field of tobacco control? Does the SnapDragon implementation have empirical validity? Have the developers demonstrated that the model’s results agree well with known trajectories of smoking patterns following real-world interventions?) This assessment is based on the committee’s collective expertise and on its interpretation of the supporting literature.
SnapDragon Model: Conceptual Overview
As noted earlier, opinion dynamics provides the underlying conceptual framework for the SnapDragon model. By basing SnapDragon on opinion dynamics, the modelers are making the explicit assumption that the
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14E-mail communication between the IOM staff and SNL staff, August 1, 2014; available upon request from the project public access file.
dynamics that govern smoking initiation, cessation and, in general, product use are mainly dependent on the users’ opinions about tobacco products and, further, that those opinions are influenced mainly by the interaction among individuals. The following section provides a brief overview of the opinion dynamics modeling approach.
Background on Opinion Dynamics
The goal of modeling opinion dynamics is to determine the opinion states in a population and the transitional processes between such opinion states (Castellano et al., 2009). Therefore, a common aim of opinion dynamics models is to identify how the opinions of individual agents are influenced by the opinions of neighboring agents and how they all converge to consensus.15 Conceptually, opinion dynamics stems from sociological and social psychology theories (Cartwright and Harary, 1956; Heider, 1946) and studies (Asch, 1956; French, 1956) that focus on collective behavior and social influence and suggest that individual attitudes and behaviors tend to conform to the majority of the belonging group. The mathematical basis of opinion dynamics is derived from Ising spin models in statistical physics (Galam and Moscovici, 1991; Galam et al., 1982). Given that physics methods are being applied to describe social phenomena, opinion dynamics is generally regarded as an area of sociophysics (Castellano et al., 2009; Galam, 2008).
Over the past 15 to 20 years, as sociophysicists have actively worked in opinion dynamics (Castellano et al., 2009), they have developed several different implementation approaches. Some examples of these implementation approaches are the voter model (Clifford and Sudbury, 1973; Holley and Liggett, 1975), the majority rule model (Galam, 2002; Krapivsky and Redner, 2003), the Snzajd model (Stauffer, 2002; Sznajd-Weron, 2005), the cultural dissemination model (Axelrod, 1997), and the bounded confidence model (Deffuant et al., 2000; Hegselmann and Krause, 2002). (For more information on all of these models, see Castellano et al., 2009, and Xia et al., 2011). These distinct types of opinion dynamics models can differ in the way that they represent opinions (e.g., continuous versus discrete), in their local rules of interaction (e.g., averaging of opinions), and in their underlying structure (e.g., regular lattice, dimensions, and networks). Using various implementations of opinion dynamics–based rules, sociophysicists have incorporated opinion dynamics into models across a number of domains. For instance, opinion dynamics has been applied to voter be-
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15This is not always the case, as shown in some reports in the literature, such as the study by Yildiz et al. (2011) in which the aim is to model stubborn agents that never come to an agreement.
havior (Ben-Naim et al., 2003) and consensus building in politics (Galam, 2008), the diffusion of agricultural practices in Europe (Weisbuch et al., 2002), the spread of propaganda (Carletti et al., 2006), tribal and gendered leadership in Afghanistan (Moore et al., 2012; Schubert et al., 2011), extremist group dynamics and terrorism (Backus and Glass, 2006; Deffuant et al., 2002), and marketing strategies (Martins et al., 2009; Schulze, 2002; Sznajd-Weron et al., 2008). However, opinion dynamics models have not yet been applied to tobacco control or to the wider field of public health.
Opinion dynamics has brought new perspectives to the social sciences and has pointed to new questions and directions for research (Castellano et al., 2009; Galam, 2008; Lorenz, 2007; Xia et al., 2011); however, several opinion dynamics experts have noted that opinion dynamics has not been properly empirically validated and that most attempts to do so have only used election data (Moss, 2008; Sobkowicz, 2009; Weisbuch, 2007). Castellano et al. (2009) argued that the field needs to focus on the development of better defined quantitative models of consensus formation, which can describe this phenomenon in a more objective way, beyond addressing the mere qualitative question of when and how people agree/disagree. Furthermore, as Moussaïd et al. (2013, pp. 1–2) wrote, “it is difficult to track and measure how opinions change under experimental conditions, as these changes depend on many social and psychological factors such as the personality of the individuals, their confidence level, their credibility, their social status, or their persuasive power.” Existing opinion dynamics models tend to start either from plausible criteria on the effect of social interactions on opinion changes or from established social theories, but there has been a minimal effort to compare the predictions of the models with data on real social dynamics. This makes it difficult to model opinion changes or to propose a meaningful validation of the basic mechanisms in opinion dynamics.
Opinion Dynamics and SnapDragon
The model developers use opinion dynamics as the conceptual foundation of SnapDragon, but have made some adjustments in its implementation. In traditional opinion dynamics models, opinion is a general term for beliefs (Carletti et al., 2006; Martins, 2008) or attitudes (Huet et al., 2008; Jager and Amblard, 2005) that are held by individuals. In SnapDragon, “opinion” represents an integrated value of positive and negative attitudes and perceptions of an individual toward a tobacco product.16 Additionally,
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16“‘Opinion’ is an integrated view of a product that is the result of multiple influences and perceptions. In our model it is an acquired behavioral disposition toward smoking which is based upon an aggregation of salient conceptual components and evaluations. Opinion is unidimensional and can range from 0 (lowest opinion of a product) to 1 (highest opinion of
the SnapDragon development team chose to incorporate certain technical elements from various opinion dynamics models. These features include a bounded confidence approach within a social network topology and also media and behavior components, as detailed below.
The SnapDragon development team applied the bounded confidence approach to the model. A widely known bounded confidence opinion dynamics model has been developed by Deffuant and Weisbuch (Deffuant et al., 2000; Weisbuch et al., 2002). In bounded confidence opinion dynamics models, the opinions of agents are represented as continuous variables, ranging between 0 and 1. As in many other types of opinion dynamics models, the opinions of agents in SnapDragon can, over time, be influenced by other agents in the environment, either through random connections in a well-mixed, non-networked population or else by interactions within a social network topology, with the latter being what the SnapDragon model uses. However, in bounded confidence models, agents interact with each other only when their opinions are close together—that is, within certain tolerance bounds; if their opinions are very different from one another, they do not interact (see Equation 1). In the final stationary state, one, two, or more clusters emerge, signifying consensus, polarization, or a fragmentation of opinions, respectively. Eventually, the opinions of all agents within a given cluster converge to the same value.
|xi (t) − xj (t)| ≤ εi
EQUATION 1 i represents an individual, and j represents a neighbor to i. ei is the opinion tolerance bound for individual i. The equation specifies the range of opinion to which individual i might be receptive to interact with a given neighbor (Moore et al., in press b).
The model developers apply these general concepts of bounded confidence to SnapDragon but alter specific elements from the Deffuant–Weisbuch model. Although the Deffuant–Weisbuch model uses a bounded confidence model of non-directed interactions in well-mixed populations, the modeling team implemented directionality imposed by a network topology, so that the interaction between two agents is not necessarily reciprocal. Within this network structure, opinion clusters are formed based on the tolerance values of various individuals (see Equation 1). As time goes by,
a product). While opinion represents an aggregation of factors, it is not a mathematical summation of measured quantities. It is a model parameter used to represent positive and negative affective and utilitarian components that might influence a person’s view of using a tobacco product” (e-mail communication between the IOM staff and SNL staff, April 3, 2014; available upon request from the project public access file).
networks that contain agents with low tolerance (that is, who are less open to influence) will spur the formation of many small fragmented clusters, and networks that contain agents with high tolerance (more open to influence) will move toward a large cluster consensus value.
The SnapDragon developers also deviated from the Deffuant–Weisbuch model in their use of an averaging function, which determines how an agent updates its opinions when interacting with other agents. Specifically, instead of applying a pairwise averaging function that captures randomized discrete interactions, the modelers implemented a rule that calls for agents to average the opinions (weighted by the plasticity values) of all the neighboring agents that satisfy the bounded confidence condition, a technique used in Hegselmann and Krause’s bounded confidence opinion dynamics model (2002). In other words, with the model’s averaging rule, agents move their opinions toward the weighted (by the plasticity values) average opinion of all agents that lie within their tolerance range (see Equation 2).
EQUATION 2 Where xi and xj are as described in Equation 1, xi (t) is i’s current opinion, and xj (t) is the current opinion of neighbor j. xi (t + 1) is the opinion value of individual i at the next time step. When applied to a directed social network, Si consists of the out-degree neighbors of individual i with cardinality. µij is the plasticity value associated with the relationship between individual i and neighbor j (Moore et al., in press a,b).
In addition to using bounded confidence, the modeling team also incorporated media nodes into SnapDragon. In particular, they relied on the work of Carletti and colleagues (2006), who extended the Deffuant–Weisbuch model to model the effects of propaganda, in which the media act to target opinions and influence tolerance levels. The SnapDragon modeling team adopted this idea of media influence, but again, as described above, instead of assuming a well-mixed population in which the media interact with all individuals in the population at the same time, they defined those interactions within the constraints imposed by a social network. Thus, the media are integrated into the social network topology. A media node may have an effect on an influential member of a social network who, subsequently, will have an impact on other members of that social network. However, while the media nodes in SnapDragon have the ability to influence agents, they are not themselves subject to influence.
Another major component of SnapDragon is the connection between opinions and behavior. The model developers reference the Continuous Opinions and Discrete Actions (CODA) model through an update rule
used by Martins (2008). The CODA model assumes that agents update their opinions by observing the actions of surrounding neighbors. The SnapDragon model adopts this notion of linking opinions to behavior, but instead of the agents observing the behaviors of others and subsequently changing their opinions, agents’ opinions (which are susceptible to the influence of other agents) drive behavior change. Therefore, the modeling team integrates a concept reminiscent of CODA into SnapDragon, but it makes significant changes conceptually and does not apply the same implementation strategies.
Model Suitability of SnapDragon
In this section, the committee reviews the suitability of SnapDragon for its intended use (see the Chapter 4 evaluation framework for details regarding model suitability). Given this model, what sorts of policies and outcomes are amenable to modeling by SnapDragon? Although SnapDragon has been designed to evaluate a wide range of tobacco products, for ease of exposition the committee comments on how the structure of the model can accommodate known facts about smoking behavior. Models that describe smoking behavior have traditionally classified individuals by various demographic characteristics (e.g., age and gender) and smoking characteristics (the widely used tobacco control models to date are compartmental/ aggregate models).17 Usually, individuals in these models are categorized as never-smokers, current-smokers, or former-smokers, further classifying smokers by the number of cigarettes smoked per day and former smokers by years-quit (HHS, 2014; Jeon et al., 2012; Levy et al., 2006; Mendez et al., 1998). These classifications are important because smoking-associated health risks are known to vary by age, gender, smoking status, smoking intensity, and, in the case of former smokers, by years-quit.
Many of the existing tobacco control models follow groups of individuals through time. Up to a certain age, individuals have a certain chance of starting to smoke. As time progresses, a smoker has the opportunity to quit or to continue smoking, while a former smoker has a certain chance of relapsing. In most of these existing models, the rates to start or quit smoking are exogenously supplied. SnapDragon characterizes individuals as being either users or nonusers of tobacco products. Therefore, the model in its current form can track prevalence of product use, but it cannot accurately determine health risks, because often a great proportion of tobacco-related morbidity and mortality falls on former users of combustible products (HHS, 2014). Although determining health risks was not listed as one of
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17For a review of many existing tobacco control models, see the 2014 Surgeon General’s report, Appendix 15.1 (HHS, 2014).
the purposes of SnapDragon, if the Center for Tobacco Products (CTP) plans to use SnapDragon as a stand-alone model, this will be a limitation. If CTP plans to use SnapDragon only to inform population models, it will not be a limitation of the model.
SnapDragon attempts to model the process of initiation and cessation as being driven by social interactions. Instead of inputting initiation and cessation rates that have been determined outside the model, the model tries to derive these figures endogenously, using a hypothesis of how these processes are generated. That is, SnapDragon attempts to explain the dynamics (i.e., how the system changes over time) inherent in tobacco use as a result of a convergence of opinions about specific tobacco products through the interaction among individuals in the population, guided by the opinion dynamics formulation discussed in the previous section. This overarching assumption supports the use of an agent-based framework to implement the model, as individual interactions are unique to the social network structure in which they occur.
Postulating a simple mechanism at the individual level to explain the multiple emergent complexities of tobacco use observed at the macro level is elegant and appealing, but several elements in SnapDragon’s formulation either do not conform to existing knowledge or defy face validity.
First, the model does not consider a feedback mechanism from behavior to opinion. It is almost certain that the experience of using a particular tobacco product would influence the user’s opinion about such product. For example, when individuals first start smoking, their prior opinions about cigarettes are likely to be altered by the particular experiences of the product. About one-third to one-half of all adolescents in the United States have ever smoked part or all of a cigarette (HHS, 2012), but a substantial proportion of those adolescents who ever smoked do not progress to regular smoking (ALA, 2010; CDC, 1998). It is conceivable that a portion of these youths only tried cigarettes for experimentation, without any intention of continuing to use the product, but it is more than likely that a significant number of the youths who tried cigarettes and did not progress to regular smoking were deterred by their personal experiences with the product. It is also known that adolescents who experiment with menthol cigarettes are more likely to become regular smokers than those who start smoking regular cigarettes (Nonnemaker et al., 2013), indicating that a specific feature of the product influences subsequent behavior. Similarly, it is known that cessation rates increase after age 50, when smokers start experiencing the adverse effects of their behavior (Mendez et al., 1998). All these examples point toward product features and use influencing subsequent behavior independently of social pressures. As SnapDragon takes into account only
the modification of behaviors by opinions and not vice versa, it seems likely that the model is missing an important feedback mechanism—that is, from behavior to opinion.
Second, it is very unlikely that opinions about tobacco products are transmitted independently of individuals’ behavior toward such products, as SnapDragon stipulates. This formulation could lead to highly unrealistic scenarios. For example, the model implies that two individuals with the same opinion about a tobacco product could exhibit different behaviors (user and nonuser) because of the addiction factor or personal differences in initiation and cessation thresholds. However, these two individuals with different behaviors will exert the same influence on the agents with whom they connect because they will transmit the same opinion.
It is certainly conceivable that imitation of smoking behavior could play a role in tobacco use adoption. In fact, the Bass model (1969), a well-established marketing model of the diffusion of goods in the market, proposes that the rate of adoption of a new product is determined by a set of independent self-initiator individuals, followed by a “contagion” or imitation process that depends on the volume of the product already in the market. In SnapDragon, however, the imitation component happens indirectly, by individuals sharing their opinions about a product, rather than their behavior. Because opinions are not influenced by behaviors in the model, a growth or decline in the number of tobacco users in the population will not affect the rates at which new adopters are generated. Similarly, observed quitting behavior cannot be imitated directly in the model. For example, if individuals in a group are near their cessation threshold and a slight decrease in their opinion levels (triggered perhaps by a policy) makes them quit simultaneously, their observed behavior would not produce an additional effect on other individuals beyond the initial adjustment of attitudes triggered by the policy.
The committee has not found any references in the health field literature that support the dynamics suggested by the opinion dynamics formulation, which are the underpinnings of SnapDragon (that is, the way SnapDragon describes how opinions evolve over time and how these opinions trigger actions). Diffusion models have been proposed in the marketing literature to explain the dynamics following the introduction of new products in the market (Mahajan et al., 1990), but these models have relied on imitating the adoption of the product rather than the diffusion of the underlying attitude toward such products, which may or may not trigger the adoption behavior.
Third, the rationale behind the modeling choice of making interacting opinions converge to a weighted average is not clear. This is clearly a modeling choice by the developers of SnapDragon, as opinion dynamics offers a number of ways by which opinions of different interacting agents can get reconciled (Castellano et al., 2009; Xia et al., 2011), including
as one possibility the convergence to an average. This modeling choice, when applied to smoking behavior, can lead to inconsistencies between the model’s results and observed facts. For example, studies suggest that there is almost no smoking initiation after age 26 (for example, among 30- to 34-year-olds, 89.8 percent of smokers initiated by age 19, and 99.2 percent by age 26 [HHS, 2012; IOM, 2015]). This indicates, following the logic implied by SnapDragon, that nonsmokers’ opinion of tobacco smoking never rises above their initiation threshold after age 26, regardless of the potential multiple interactions with positive opinions about tobacco use throughout their lifetimes. This implies either that nonsmokers have a substantially higher initiation threshold than smokers or that the assumption of potentially converging opinions about tobacco through social interactions is not likely to be accurate. If it were, we would observe smoking initiation (albeit small) at all ages, due to the individuals’ multiple encounters with positive messages about tobacco use throughout their lives. It is likely that other mechanisms, not reflected in SnapDragon, play an important role in modifying smoking behavior as people age (such as those identified in Chapter 2).
Fourth, another aspect of the model that defies face validity is the lack of a credible behavior for former smokers. The model does not consider relapses, and it is difficult to envision how it would. For individuals to quit, their opinions will have to run below the cessation threshold. It is known that many quitters relapse after a period of time because they continue to crave nicotine. The SnapDragon formulation would imply that former smokers’ opinions about smoking would have to increase beyond their initiation level after quitting, triggered by interactions with other agents, which is a very unrealistic scenario.
Finally, while models based on opinion dynamics have been able to replicate the equilibrium patterns of a number of socially driven processes (Clifford and Sudbury, 1973; Holley and Liggett, 1975), the committee has not found applications in which the specific time path to equilibrium has been empirically validated. Estimation of time paths is important in tobacco control because the evaluation of policies usually involves the determination of discounted benefits and costs wrought by specific interventions. As the dynamics of smoking behavior carry much inertia, the full effects of tobacco control interventions may take a long time to realize, and thus the time trajectory of smoking rates becomes very relevant. As currently designed, the model is not suitable for addressing long-term dynamics but only the short-term impacts of policy interventions. Even for short-term assessments of policies, it is doubtful that SnapDragon will be able to generate more than qualitative scenarios at best, given that a realistic parameterization of the model is not likely to be feasible. For example, it would be very challenging to estimate individuals’ baseline opinions and action thresholds, because
smokers have different levels of addiction that may depend on genetics, smoking intensity, and age, among other factors (HHS, 2010).
Use of Data in SnapDragon
SnapDragon is meant to represent key aspects of the real-world process of tobacco use, particularly initiation and cessation. Data could thus serve as inputs to the model, ensuring that agents are realistic representations of persons. Data could also confirm whether the model is able to replicate or predict real-world patterns of initiation and cessation among individuals or populations. Data are critical at many if not all stages of model development. As discussed below, the current SnapDragon model does not use much data. Although SnapDragon is still in the early stages of development and testing, and the modeling team has outlined some areas where they plan to collect or use existing data (Moore et al., in press b; SNL, 2014a),18 data could have played a more central role in informing the model during its early stages of development.19 At least three types of data could be used to inform SnapDragon or future plans for its parametrization or testing: stylized facts that offer qualitative benchmarks, individual-level data on personal characteristics, and quantitative aggregated data. (Additional data needs for an ABM are discussed in Chapter 6.)
The most basic type of data that could be used in a model is stylized facts20 that offer qualitative benchmarks. The ability to replicate stylized facts is a minimum bar that any model should be able to clear. Although such replication means that a model is able to capture general features of the real world, the qualitative nature of such facts precludes precision of the type that would convince policy makers of a model’s validity. The SnapDragon modeling team mentions a number of known facts about tobacco use that could be used as stylized facts to inform the model (Moore et al., in press a,b), but SnapDragon incorporates only a small range of relevant and salient stylized facts (for example, peer influence in smoking initiation) to inform and validate the model. This is important because it affects the data used to inform the conceptual underpinnings of the model. The modeling team has used opinion dynamics to inform the model, but stylized facts such as varied individual quitting processes at different ages and changing peer influence by age are not included. The model has a great
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18The modeling team noted that the initial stages of model development focused on model structure and that later development will incorporate more realistic data (SNL, 2014a).
19See also communication between the IOM and SNL staff, June 25, 2014; available upon request from the project public access file.
20Stylized facts are structural observations or a “set of properties, common across many instruments, markets and time periods . . . observed by independent studies” (Cont, 2001, p. 223).
deal of flexibility, but the relevant stylized facts are not used to inform the base model. Although these data could be incorporated in SnapDragon at later stages of development, it would have been more informative to do so early in model development.
The second type of data that could inform SnapDragon is individual-level data on the distribution of attributes of agents in the population, including the health behaviors of interest (tobacco use) as well as demographic information (age, gender, race, socioeconomic status) and other relevant agent attributes. Individual-level data would include the multiple characteristics of individual agents, which are likely to be correlated to one another. Data might be aggregated (for example, if the joint distribution of agent characteristics were known). Such data are readily available in multiple sources commonly used in health behavior research, such as the National Health and Nutrition Examination Survey21 and the Behavioral Risk Factor Surveillance System (BRFSS).22 Individual level data are commonly used in ABMs to create a one-to-one correspondence between agents and real-world persons (North and Macal, 2007). These data may also be used to monitor individual trajectories, which could serve as ground truth23 against which to compare modeled trajectories. SnapDragon currently does not use individual-level data to specify agent characteristics.
A third type of data is quantitative contextual or aggregated data. Such data might arise from the aggregation of nationally representative surveys of the individuals just described. Data may permit an examination by geographic context, such as with the Tobacco Use Supplement of the Current Population Survey24 or state-level data available in the BRFSS. The social network context of tobacco use is also available in some datasets (such as from Add Health), although such data are harder to come by (as described in greater detail below). As above, such data could be used as an input to initialize the model or as ground truth for model validation.25 State-level comparisons between model outputs and real-world trends would increase confidence in the models’ ability to capture the real-world data-generating process (Windrum et al., 2007). At present, SnapDragon makes limited use of data aggregated at the national level to calibrate initiation thresholds and addiction factors in order to produce smoking prevalence around observed levels. Such data are not used by SnapDragon to model differences seen across geographic regions or social networks. Although the commit-
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21See http://www.cdc.gov/nchs/nhanes.htm (accessed March 2, 2015).
22See http://www.cdc.gov/brfss (accessed March 2, 2015).
23“Ground truth” refers to any data that capture the empirical process under investigation.
24See http://appliedresearch.cancer.gov/tus-cps (accessed March 2, 2015).
25Validation is defined as “the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model” (AIAA, 1998, p. 3).
tee acknowledges that the SnapDragon developers are not yet at the stage of incorporating such data into the model (SNL, 2014a),26 the committee cannot fully assess whether the model is behaving correctly because it does not reproduce observed facts.
SnapDragon is currently implemented at the level of a hypothetical population with 250 agents. One common goal of ABMs is the simulation of higher-level behavior that is emergent, such as the clustering of smoking behavior within networks that arises from peer influence. SnapDragon builds up from individual agents’ behaviors and thresholds to look at patterns of smoking behavior (e.g., the prevalence of smoking) at the aggregate level of a high school in the United States or a small network in a larger community consisting of friends and friends of friends. This may present challenges for validation, especially if ground-truth data are not available at the level of interest. For example, the model may be calibrated to individual-level data of stages of tobacco use initiation, but it may be the case that only population-level data on tobacco consumption are available. Aggregated individual-level data could be compared by county or state to see if the patterns match (Berk, 2008). The Valente data27 include 20 answers to opinion-related questions, some of which are related to attitudes toward tobacco use, but the data are cross-sectional28 and closely tied to smoking behavior itself, and they are not currently incorporated into the model. The Valente data, though confirming that there is a clustering of these attitudes in the network, merely confirm a stylized fact. The SnapDragon development team identified the need for more longitudinal data; however, the type of data needed to inform SnapDragon is generally not available.
The uses of data are most extensively described by the SnapDragon modeling team in two places: on Table 1 of the draft journal manuscript (Moore et al., in press b) and in a presentation to the committee (slide 33, SNL, 2014b). The model developers also discussed some assumptions in a response to committee questions.29 These descriptions show that the initial model is thin on data inputs and validation against external sources.
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26See also communication between the IOM and SNL staff, January 26, 2015; available upon request from the project public access file.
27These data were collected as part of NIH/NCI grant 3R01CA157577-02S1 (Extending a School-Based Cohort to Improve Longitudinal Modeling), Thomas W. Valente, principal investigator. This data collection was a follow-up to the Social Network Study cohort in 2010 through 2012 (Valente et al., 2013). The data are not yet published.
28The data collected by Valente are longitudinal, but the 20 additional questions added on as part of NIH/NCI grant #CA157577-02S1 were collected only during the final year of data collection.
29E-mail communication between the IOM staff and SNL staff, January 21, 2014; available upon request from the project public access file.
Parameters are chosen to demonstrate model dynamics, rather than allowing a single parameter to dominate the model’s behavior. In addition to the parameters specified in the draft manuscripts describing the SnapDragon model (Moore et al., in press a,b), the team has added two more parameters: (1) “risk affinity” to make the agents more heterogeneous and (2) “risk perception” to allow for product switching (SNL, 2014b). These parameters also are not based on data.
Calibration, Verification, and Validation
To ensure that a model is valid and that it accurately represents the real world for its intended use, a model must go through calibration,30 verification,31 and validation processes at various points in model development. At this point in time, SnapDragon is very general and flexible. What the team described as verification entails a comparative analysis with empirical research and sensitivity analysis to determine what drives the model’s behavior (SNL, 2014a).32 These exercises are limited to internal validation or calibration of model parameters to replicate real-world results—what Berk (2008, p. 291) calls “internal quantitative credibility,” rather than confirmation that the model’s data-generating process is the same as the real-world data-generating process (Windrum et al., 2007). The SnapDragon modeling team members report that they have plans to conduct “parameter analysis and uncertainty quantification to make sure the parameters are consistent with knowledge of the system.”33 However, it is not clear whether even these exercises would constitute Berk’s external quantitative credibility—that is, comparisons of model output with real-world test data not used to develop and calibrate the model. The evaluations conducted so far have been “nearly data-free” (Berk, 2008, p. 293) relations between model output and ground truth that use very few stylized facts. Furthermore, these stylized facts are only qualitative rather than, say, quantitative values that draw from actual trends in smoking initiation and cessation over time. Missing so far is the search for areas where the model
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30Calibration is “the process of adjusting numerical or physical modeling parameters in the computational model for the purpose of improving agreement with experimental data” (AIAA, 1998, p. 13).
31Verification is “the process of determining that a model implementation accurately represents the developer’s conceptual description of the model and the solution to the model” (AIAA, 1998, p. 3). This includes code verification (Does the code correctly implement the intended algorithms?) and solution verification (accuracy in which the algorithms solve the mathematical-model equations for the specified quantity of interest) (NRC, 2012).
32See also communication between the IOM and SNL staff, June 25, 2014; available upon request from the project public access file.
33E-mail communication between the IOM staff and SNL Staff, January 21, 2014, page 3; available upon request from the project public access file.
does well and where it fails in making predictions and then using these analyses to refine and improve the model.
Specific Issues That Arise in Modeling Networks
In the examples that the modeling team shared with the committee, SnapDragon employed an Erdős–Rényi random graph; the modeling team reports that it plans to employ other stylized networks in future work. Other models have used real-world networks, such as airline routes (Epstein et al., 2007) and traffic patterns (Eubank et al., 2004), which are especially relevant for airborne infectious diseases. The use of real-world networks has the advantage of replacing assumptions about network structure with the actual network. It would be relatively straightforward for SnapDragon to use real networks as an input (e.g., Add Health or the data collected by Valente34), which would have the advantage of including agent attributes within the social network context. The disadvantage of inputting a fixed network is that the network-generative process and dynamics are not captured, which may be important if both peer selection and influence processes operate, as has been suggested for smoking behavior (Schaefer et al., 2012). Network dynamics are increasingly being incorporated in models, for example, to model behavioral changes in response to an epidemic outbreak (Epstein et al., 2008; Meloni et al., 2011) and network-behavior coevolution in smoking (Schaefer et al., 2013).
IMPLICATIONS FOR THE SNAPDRAGON MODEL
Summary of Findings and Conclusions
The SnapDragon model presents a novel framework for dealing with the complexities of tobacco use behavior. The developers of SnapDragon, which uses opinion dynamics methods, have suggested that it could be applied for a number of tobacco control policy applications, but the underlying assumptions of the model (as discussed in this chapter) suggest that this is unlikely. The committee statement of task calls for recommendations for improvement of SnapDragon, if needed, and although some changes could be made to address some of the weaknesses identified in this report, doing so would lead to the creation of a new model. SnapDragon does not encompass essential facts from the tobacco research literature, and many of
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34These data were collected as part of NIH/NCI grant 3R01CA157577-02S1 (Extending a School-Based Cohort to Improve Longitudinal Modeling), Thomas W. Valente, principal investigator. This data collection was a follow-up to the Social Network Study cohort in 2010 through 2012 (Valente et al., 2013). The data are not yet published.
its assumptions lack face validity. In addition, the required data to inform the parameters in SnapDragon have not yet been identified, and the model has not yet reached the stage of model validation for broad application to tobacco control policy.
It is true that SnapDragon has the necessary flexibility to reproduce certain observed facts about tobacco use behavior by manipulating plasticity values and action thresholds. However, this could be problematic because, as Laine (2006, p. 37) writes,
Overly flexible models, for instance ones with many free parameters, can be easily made to fit all these anomalies, byproducts of errors and noise, without capturing the regularities underlying the behavior. A model like this does not really inform us about the interesting patterns that may exist in the population, but just reflects the idiosyncrasy present in each individual sample. This is called overfitting.
SnapDragon is a very flexible model, but it currently lacks sufficient modeling structure to be informative. Therefore, the committee has not included recommendations for improvement. Key findings and conclusions regarding SnapDragon are below:
Conclusion 5-1: As SnapDragon presumes that opinions may modify behavior but that behavior does not modify opinion, the committee concludes that the model is missing an important feedback mechanism from behavior to opinion.
Finding 5-1: The committee finds that the representation of behavior in SnapDragon does not align with what is currently known about tobacco use and dependence.
Conclusion 5-2: The committee concludes that the modeling decision of making interacting opinions about tobacco converge to a weighted average is not supported by evidence and is unlikely to be an accurate representation of tobacco use behavior.
Finding 5-2: Whereas some other models based on opinion dynamics have been able to replicate the equilibrium patterns of socially driven processes, the committee has not found applications in which the specific time path to equilibrium has been empirically validated.
Finding 5-3: The committee finds that there has been no assessment of SnapDragon’s ability to accurately predict initiation, prevalence, or cessation.
Conclusion 5-3: The committee concludes that a realistic parameterization of SnapDragon would be hard to achieve, so it is unlikely that the model will be able to generate credible assessments of policies.
Recommendation 5-1: SnapDragon should not be pursued by the Center for Tobacco Products as an aid for regulatory decision making.
Chapters 2, 3, and 4 offer findings, conclusions, and recommendations to assist CTP in the development of ABMs in the future. Chapter 6 offers guidance on inputs and implementation for ABM at CTP, drawing on lessons learned from the review of SnapDragon and other models.
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