E-cigarette use and onset of first cigarette smoking among adolescents: An empirical test of the ‘common liability’

E-cigarettes have become the most commonly used tobacco Background: products among youth in the United States (US) recently. It is not clear whether there is a causal relationship between e-cigarette use and the onset of cigarette smoking. The “common liability” theory postulates that the association between e-cigarette use and cigarette smoking can be attributed to a common risk construct of using tobacco products. This study aims to investigate the relationship between ever e-cigarette use and cigarette smoking onset in the US using a structural equation modeling approach guided by the “common liability” theory. The study population is non-institutionalized civilian adolescents Methods: living in the US, sampled in the longitudinal Population Assessment of Tobacco and Health study. Information about tobacco product use was obtained via confidential self-report. A structural equation modeling approach was used to estimate the relationship between e-cigarette use at wave 1 and the onset of cigarette smoking at wave 2 after controlling for a latent construct representing a “common liability to use tobacco products.” After controlling for a latent construct representing a “common Results: liability to use tobacco products”, ever e-cigarette use does not predict the onset of cigarette smoking (β=0.13, 95% CI= -0.07, 0.32, p=0.204). The latent “common liability to use tobacco products” is a robust predictor for the onset of cigarette smoking (β=0.38; 95% CI=0.07, 0.69; p=0.015). Findings from this study provide supportive evidence for the Conclusions: ‘common liability’ underlying observed associations between e-cigarette use and smoking onset.


Introduction
The prevention of underage cigarette smoking is an essential component to curtail the substantial disease burden associated with cigarette smoking 1 . The prevalence of underage cigarette smoking has been declining in the US over the past two decades 2 . E-cigarettes (or e-vapor products) were introduced to the market as potentially reduced-harm alternatives to combustible cigarettes and have gained popularity since they became generally accessible around 2009 3,4 . In the US, the prevalence of youth e-cigarette use increased sharply between 2011 and 2015 and, after a brief decline, increased again in 2018 and 2019 3,4 . Multiple national surveys have shown that the majority of e-cigarette use is infrequent or experimental 4-6 . Despite this, the existence of exclusive e-cigarette users who do not use other tobacco products raises concerns about whether e-cigarettes may play a causal role in the uptake of cigarette use and, therefore, offset the decline in underage cigarette use.
A review of existing literature revealed some inconsistencies in evidence about the relationship between e-cigarette use and cigarette smoking. The largest body of literature comes from individual-level observational studies showing a consistent positive association linking e-cigarette use with a higher risk of cigarette smoking onset, even after adjusting for a range of variables known to be associated with cigarette smoking in a generalized linear regression framework 7-11 . Nonetheless, in the context of observational studies, it is almost impossible to control for an exhaustive list of confounders; the positive relationship can be attributed to unmeasured confounders associated with e-cigarette use, which would produce a spurious relationship between e-cigarette use and cigarette smoking without the presence of a causal relationship [11][12][13] . Propensity scoring is a statistical method to reduce biases due to confounding in observational studies to provide more robust evidence for causal inference 14 . Recent studies using propensity scoring method have found either null or inverse association between e-cigarette use and smoking among youth 15,16 .
To infer causality, studies with an experimental design arguably provide the best evidence. Nonetheless, a randomized controlled trial of e-cigarette use among nonusers is not feasible 12 . In this context, Vasiljevic and colleagues evaluated the impact of exposure to advertisements promoting e-cigarettes on appeal and susceptibility of tobacco smoking using an experimental design. They found no differences in appeal, susceptibility, or perceived harm of cigarette smoking between youth who were randomized to the exposure group and the control group 17 . Despite the lack of direct behavioral measures, this study suggests that the exposure to e-cigarette advertisement had no acute effect on the measures related to cigarette smoking.
Ecological prevalence trends are inconsistent with the notion that e-vapor use increases cigarette smoking. At the country level, e-cigarettes emerged and gained popularity during the period when the sharpest decline in adolescent cigarette smoking was observed in the US and other countries 5,18,19 . Total nicotine use have remained stable since the introduction of e-cigarettes 20 . In an interrupted time series analysis, Dutra and Glantz found no difference in the rate of decline in ever (p=0.57) or current (p=0.23) cigarette smoking before and after 2009, when e-cigarette became available in the US market 2 . In another study, Levy and colleagues found strong inverse associations between the prevalence of e-cigarette use and the prevalence of cigarette smoking among adolescents and young adults, which confluence with all US national surveys identified via a systematic literature search 21 . Similar findings have been documented in a recent study by Foxon and Selya 20 .
Similarly, a few studies that compared youth cigarette smoking prevalence between states with and without regulations to prohibit sales of e-cigarettes to minors have produced inconsistent findings with two studies documenting lower youth cigarette smoking in states without an e-cigarette age restriction 22,23 , and one study documenting the opposite 24 .
One potential explanation of the consistently observed association between e-cigarette use and cigarette smoking from individual observational studies is the "common liability" theory, which postulates that any observed relationships between e-cigarettes and combustible tobacco cigarettes is attributed to the "liability" to use tobacco products of the individual; once this "common liability" is controlled for, there is no causal relationship between e-cigarette use and cigarette smoking 25-28 . This 'common liability' that encompasses a range of genetic and behavioral factors may not be directly observable but gives rise to the use of various tobacco products (various psychoactive substances in the original theory). Several lines of evidence align with the "common liability" theory. First, the relationship is not unique to e-cigarettes. Various studies showed that the use of any type of tobacco products (e.g., cigar, hookah, etc.) and/or other substances (e.g., alcohol and cannabis) predicted cigarette smoking onset (e.g., 9,10,28,29). Moreover, the risk of cigarette smoking onset increases with the number of types of tobacco product used 9 . Findings from a recent study using a propensity scoring approach found supportive evidence that the frequently observed association between e-cigarette use and smoking is largely attributed to shared risk factors, using data from Monitoring the Future, a national school survey of 8 th , 10 th , and 12 th graders 15 , Kim and Selya found that the association between e-cigarette use and current smoking became null after taking into account a range of variables encompassing demographic characteristics, use of other psychoactive substances, perceived peer cigarette use, risk-taking, socially maladaptive behaviors, attitude toward smoking, and parental education using propensity scoring 15 . Another study using data from NYTS, another national school survey, found inverse relationships linking e-cigarette use and subsequent cigarette smoking after propensity score matching

Amendments from Version 2
We have made a few amendments based on reviewers' comments. Specifically, we enhanced the consistency in the description of statistically non-significant estimates, added a new citation, relabelled model numbers, and revised the title of Table 2.
Any further responses from the reviewers can be found at the end of the article REVISED (i.e., evidence of 'gateway out') 16 . Second, the relationships between cigarette smoking and e-cigarette use are often reciprocal. Numerous studies have documented that cigarette smoking is associated with higher risk of e-cigarette use 10,30-32 . Indeed, a few studies have found that smoking is a stronger predictor for e-cigarette use compared to e-cigarette use as a predictor for cigarette smoking 10,16 . Third, e-cigarette use predicts the onset of a range of other substance use behaviors, not limited to cigarette smoking 8,29 . These lines of evidence support the notion that the relationship is not limited or specific to e-cigarettes, and common risk factors may underlie the use of various tobacco products 33 .
Poorer inhibitory control and elevated impulsivity are phenotypes of externalizing problems, which has been linked to precocious use of various substances 34-37 . A study found similar levels of inhibitory control and impulsivity between youth e-cigarette users who never smoked a cigarette and youth smokers who never used an e-cigarette. Both groups showed poorer inhibitory control and elevated impulsivity compared to youth not using any tobacco products 38 .
Given this background and guided by the 'common liability' theory, the aim of this study is to estimate the prospective relationship between e-cigarette ever use and the onset of cigarette smoking after controlling for a "common liability" to use tobacco in US adolescents using a structural equation modeling approach. In essence, we first created a unidimensional construct to represent the 'liability' to use tobacco products, and then regressed the onset of cigarette use on antecedent e-cigarette use taking into account the latent 'liability' to use tobacco products.

Study population and sample
The study population consisted of non-institutionalized civilian adolescents 12-17 years of age living in the US, sampled in the longitudinal Population Assessment of Tobacco and Health (PATH) study. A multi-stage sampling method was used to draw nationally representative samples after Institutional-Review-Board-approved parent consent and youth assent 39 . In contrast to school surveys of adolescents, the PATH sample includes young people irrespective of school attendance, and its sampling frame includes college dormitories and children of active-duty military living in the US. More details about the PATH methodology is provided elsewhere 39 .
In this study, PATH wave 1 (2013-2014) and wave 2 (2014-2015) data were used. Participation levels were 54% at the household level and 78% at the individual level for the youth survey at wave 1. Wave 2 follow-up rate was 88% for youth. Because the outcome in this study is the onset of cigarette smoking, the study sample consists of wave 1 never smokers who were followed up at wave 2. We did not include "aged-up" adolescents (i.e., those who became 18 at wave 2) to retain a sample relevant for underage smoking (n=9,045).

Assessments
PATH confidential assessments were audio computer assisted self-interviews (ACASI), with standardized multi-item modules on use of various tobacco products, including cigarettes, e-cigarettes, cigars (including traditional cigars, cigarillos, and filtered cigars), smokeless tobacco, snus, hookah, pipe, dissolvable tobacco, bidis, and kretek. Survey questions about ever use of these tobacco products are typically in the format of "Have you ever smoked/used …, even one or two puffs/times?" In this study, the outcome is the onset of ever cigarette smoking at wave 2, which is defined as smoking cigarettes (even one or two puffs) for the first time between wave 1 and wave 2 assessments among adolescents who had never smoked cigarettes at wave 1. PATH also assessed lifetime history (i.e., ever use) of alcohol, cannabis, Ritalin ® or Adderall ® , Painkillers/sedatives/ tranquilizers, cocaine, stimulants, and other drugs, respectively. Sex (male or female) and age categories (12-14 or 15-17 years of age at baseline) were included as covariates. (The PATH Public Use File only included a binary variable for age.) Information about these covariates is from survey items in the Demographics module. When these items are missing, information from the household screening roster is drawn. Other covariates include race/ethnicity (non-Hispanic White, non-Hispanic Black, Hispanics, and non-Hispanic others), availability of tobacco products in the household (yes/no), and a measure of novelty seeking ("agree" or "strongly agree" to the question "I like new and exciting experiences, even if I have to break the rules. Do you…"), participant's self-rated health (excellent/non-excellent), harm perception of cigarettes ("a lot of harm" to the question "How much do you think people harm themselves when they smoke cigarettes"), and participant's school performance (mostly A's or A's and B's vs. others).

Analysis approach
Guided by the "common liability" theory, we used a structural equation modeling approach to test whether there is a specific association between e-cigarette ever use at wave 1 and the onset of first cigarette smoking at wave 2 holding constant a latent construct for the "liability to use tobacco products." Structural equation modeling is a collection of statistical techniques that allows simultaneous estimation of relationships of various independent and dependent variables. Compared to conventional single-equation linear models, SEM has several major advantages including a) the flexibility to incorporate various direct and indirect paths simultaneously based on theories or hypotheses, b) the ability to construct latent variables, c) evaluation of how well the specified model fits data via model fit indices, and d) minimization of measurement error via the construction of the latent construct. SEM has been used in tobacco research and yielded valuable insights 40,41 . It is particularly useful when a certain condition (e.g., depression, addiction, or, in this study, the liability to use tobacco products) cannot be directly observed but can be derived from a set of observable behaviors that often happen as a cluster because of the underlying condition. We consider SEM a suitable method to evaluate the common liability theory because the common liability is hypothesized as a latent construct that encompasses various genetic and environmental causes for tobacco use.
in the first analysis steps, we built a latent construct for the common liability to use tobacco products using confirmatory factor analysis methods. The observed variables were lifetime ever use of specific tobacco products. All tobacco products assessed in PATH wave 1 were included to create the latent construct. Snuff and chewing tobacco, snus, and dissolvable tobacco products were combined to create a "smokeless tobacco products" variable due to the considerations that a) youth participants may not differentiate these oral tobacco products well, and b) low occurrence of dissolvable tobacco use (n=9) and high correlation between smokeless tobacco use and snus use (i.e., 69% of snus users had also used smokeless tobacco). All observed variables were treated as categorical variables. The variance of the latent construct was fixed to one in order to obtain factor loading and threshold estimates for each observed variable. After ensuring a good fit of the measurement model (as described in the next paragraph), we built the structural portion of the model to assess the relationship between e-cigarette ever use at wave 1 and the onset of first cigarette smoking at wave 2. Specifically, we drew a path from the latent construct to the onset of first cigarette smoking as well as a direct path from e-cigarette ever use to the onset of first cigarette smoking. Figure 1 provides a conceptual description of the model. If the direct path from e-cigarette to cigarette smoking is statistically robust, it provides evidence that e-cigarettes plays a role for cigarette smoking onset over and beyond the common liability to use tobacco products. If not, it supports the notion that the frequently observed association between e-cigarettes ever use and smoking is attributed to a common liability to use tobacco products.
A series of models were fit to explore the sensitivity of the main model. First, we expanded the measurement model to include other substances measured in PATH (i.e., alcohol, cannabis, prescription Ritalin and Adderall, cocaine/crack, stimulants, and other drugs (heroin, inhalants, solvents, and hallucinogens) in order to further test the model with a latent construct for the liability for use of psychoactive substances (as was originally proposed by the 'common liability theory'). Second, we included additional sociodemographic and individual characteristics variables related to tobacco use in the model as covariates, including race/ethnicity, availability of tobacco products in the household, a measure of novelty seeking, participant's self-rated health, harm perception of cigarettes, and participant's school performance. In the last step of exploratory analyses, we repeated the main model with PATH wave 2 and 3 data as PATH wave 3 data became available soon after the initial analysis was conducted.
Several model fit indices were used to assess the goodness of fit of the measurement and the final structural models. These fit indices include root mean square of approximation (RMSEA) 42 , comparative fit index (CFI) 43 , and Tucker-Lewis index (TLI) . A RMSEA<0.08 and CFI/TLI > 0.90 are considered as indications of reasonably good model fit 44,45 .
Analysis weights were used to adjust for selection probability, nonresponse patterns, possible deficiencies in the sampling frame, and attrition. The PATH User Guide provides details about the calculation of weights 39 . A robust weighted least square mean and variance (WLSMV) adjusted estimator, which uses a full weight matrix, was used to accommodate categorical variables and complex survey design. For all tobacco use variables, there were <3% missing values. None of wave 1 never smokers had missing values in all tobacco use variables, so we are able to include all never smokers in the main model. Balanced repeated replication method was used to generate standard errors and 95% confidence intervals (CI). Analyses were conducted using

Results
Among 13,651 participants at wave 1, there were 11,792 never smokers, among whom 9,045 remained youth (12-17 years of age) and were followed up for wave 2 assessment. Of the 9,045 participants, 51% were males; 64% were 12-14 years of age at wave 1; and 54% were non-Hispanic whites. Table 1 presents the estimated ever use of tobacco products as well as factor loadings and thresholds from confirmatory factor analysis among youths who had never tried a cigarette at wave 1 (n=9,045). Among the sample of youth never smokers, e-cigarette was the most common tobacco product ever tried (3.7%), followed by hookah (2.5%), with bidi and kretek being the least common tobacco products ever tried (0.1%). The measurement model fits reasonably well (RMSEA=0.019, 90% CI=0.014, 0.024; CFI=0.963; TLI=0.945); all factor loadings were greater than 0.4 and statistically significant (p<0.001). Each individual's factor score, a score reflecting the latent liability to use tobacco products, was calculated based on both the threshold and the loading of each item. Therefore, an individual who used bidi, kretek, or pipe (items with greater thresholds) would have a higher factor score compared to an individual who used e-cigarette or hookah only (items with lower thresholds). An individual who used multiple products would generally have a higher factor score than an individual who used a single product. This factor score represents an individual's liability (unobserved) to use tobacco products.
Of the 9,045 never cigarette smokers at wave 1 assessment, 338 adolescents smoked a cigarette for the first time between wave 1 and wave 2 assessments (weighted incidence= 3.8%). The structural equation model shown in Figure 1 fits data well (RMSEA=0.015, 90% CI=0.011, 0.020; CFI=0.969; TLI=0.954). The model shows that after accounting for the general liability to use tobacco products, the association between e-cigarette ever use at wave 1 and cigarette onset at wave 2 is not statistically significant (M1 in Table 2: β=0.13; 95% CI= -0.07, 0.32; p=0.204). The latent general liability variable is positively associated with wave 2 onset of ever cigarette Table 1. Estimated occurrence (%) of lifetime ever use of tobacco products, alcohol, cannabis, and other psychoactive drugs at wave 1, factor loadings, and thresholds from confirmatory factor analysis among never smokers. Data  smoking (β=0.38; 95% CI=0.07, 0.69; p=0.015). Because sex and age are the two most important exogenous variables that are related to tobacco use behaviors, they were introduced as covariates in the next step to assess any potential changes in estimates and statistical inference. Including sex and age as covariates introduced little change in estimates, and statistical inference remained the same (M2 in In the first exploratory step, we expanded the measurement model to include other substances measured in PATH (see Table 1 for factor loading and thresholds In the next exploratory step, we included two sets of sociodemographic and individual characteristics variables related to tobacco use in the model as covariates. First, we included race/ethnicity, availability of tobacco products in the household, and a measure of novelty seeking as covariates in the model. Inclusion of these covariates introduced little change in estimates, and statistical inference remained the same (M5 in Table 2). Next, we additionally included participant's self-rated health, harm perception of cigarettes, and participant's school performance. Again, inclusion of these additional covariates introduced little change in estimates (M6 in Table 2).
In final exploratory analysis steps, we repeated the main structural equation model with PATH wave 2 and 3 data as PATH wave 3 data became available soon after the initial analysis was conducted. Fit indices indicate that the model fit the data well (RSMEA=0.010, 90% CI=0.004, 0.015; CFI=0.992, TLI=0.988).
Estimates are similar to those in the wave 1 and wave 2 model. That is, after accounting for the general liability to use tobacco products, the association between e-cigarette ever use at wave 2 and cigarette onset at wave 3 was not statistically significant (β=0.15; 95% CI= -0.06, 0.35; p=0.157). Possibly due to a reduced sample size of never smokers at wave 2 (n=8,668), the association leading from the latent general liability variable to wave 2 onset of ever cigarette smoking became statistically non-significant (β=0.34; 95% CI=-0.03, 0.71; p=0.074), although the point estimate is similar to that from the corresponding model using wave 1 and wave 2 data. As shown in Table 2, estimates for the e-cigarette-to-cigarette path is highly consistent across the series of models that we tested, which highlights the robustness of these structural equation models.

Discussion
In this study, we found that the latent 'common liability to use tobacco products' construct is sufficient to explain later onset of smoking among US adolescents. In our exploratory analysis, we included various sets of covariates that have been shown to be associated with smoking onset. Estimates from these exploratory M1 is the model depicted in Figure 1. M5 includes the following covariates: race/ethnicity, availability of tobacco products in the household, and novelty seeking. M6 includes the following additional covariates: self-rated health, harm perception of cigarette smoking, and school performance.
analyses are almost identical to the estimate from the main model, providing evidence that the model and the latent 'common liability' construct are robust.
Interpretation of findings, implications, and future directions A few hypotheses have been developed to provide theoretical grounds and underlying mechanisms for the relationship between e-cigarette use and subsequent cigarette smoking among youth. Here, we highlight three main theories as cited by the Academies of Sciences Engineering Medicine: the 'diversion theory', 'catalyst theory', and 'common liability theory' 47 . In brief, the 'diversion theory' hypothesizes that e-cigarette deters tobacco cigarette use by diverting 'high-risk' individuals to e-cigarette from combustible cigarettes 26,48 . The 'catalyst theory' postulates that e-cigarette use increases the risk of combustible cigarette use by first attracting 'low-risk' individuals to e-cigarettes, as a reduced-harm product, and then increasing proclivity to try combustible tobacco cigarettes 49 . The 'common liability theory' proposes that any observed relationships between e-cigarettes and combustible tobacco cigarettes is completely attributed to shared risk factors such as impulsivity and novelty-seeking (e.g., common liability to use tobacco products; 25-28 ). If the 'diversion theory' is true, e-cigarette use should decrease the onset of cigarette smoking (or accelerate the declining trend of smoking); if the 'catalyst theory' is true, e-cigarette use should increase the onset of cigarette smoking; if the 'common liability' theory is true, a null relationship should be observed. Our findings provide supporting evidence for the 'common liability' theory for the US youth population as a whole. Recent studies using propensity scoring methods found supportive evidence that the observed association between e-cigarette use and current cigarette smoking was attributed to shared risk factors for tobacco use 15,16 . In this study, we found converging evidence using a different approach (i.e., SEM vs. propensity scoring), which accentuates the possibility that shared causes give rise to both e-cigarette use and cigarette smoking. Nonetheless, it is possible that different hypotheses apply to heterogeneous groups of individuals or contexts. For example, e-cigarettes may provide an alternative to cigarette smoking for some adolescents, whereas they may expose some other adolescents to a more smoking-prone environment. The onset of cigarette smoking is a complex interplay between micro-, meso-, and macro-level factors. Future studies with assessments of a breadth of these relevant factors and due attention to potential heterogeneities may provide more insights about the role of e-cigarette in smoking onset to guide targeted prevention and intervention efforts among youth. Applications of similar approaches in other cultures will help assess the reproducibility and consistency of the evidence, which is required for causal inference. It is noteworthy in this context that tobacco use behaviors in youth are often experimental and highly dependent on the availability of tobacco products 6,50-52 , and an infrequent use pattern (1-2 days during the past 30 day) is more pronounced among exclusive e-cigarette users compared to youths who use other tobacco products concurrently 51 . In this context, future studies incorporating the frequency of e-cigarette use and examining the relationship between e-cigarette use and the progression to more established cigarette smoking will provide useful insights about the e-cigarette-use-and-smoking relationship.

Limitations and strengths
This study's findings should be interpreted in light of the following limitations.
First, this study is observational in nature. Although we included multiple covariates in this study, unmeasured heterogeneity is possible (variables not accounted for by the latent 'liability' construct and other covariates not included in this study), and no definitive evidence for a causal relationship is warranted. Nonetheless, we observed high consistency in the estimates across models with different configurations, which supports the robustness of the model. Second, the assessment was based on self-report information. There is possible under-reporting of tobacco and other drug use due to socially desirable responding 53 . The use of audio computer assisted self-interviews can help ameliorate this limitation. Measures for ever use of tobacco products have been shown to have good validity based on self-reported information 54 . Third, the response level at the household screening is moderate. Nonetheless, it is comparable to other modern national household surveys in the US 55 , and post-stratification was applied to bring the sample into balance with the US adolescent population.
Strengths of this study include a) the prospective design provides clear temporal relationship, and is less prone to differential recall as compared to cross-sectional surveys; b) compared to prevalence-based measures, newly incident cigarette use focuses on the onset process without any interference of the persistence process 56 ; c) by using nationally representative data, our results are generalizable to the general US adolescent population; and d) the use of audio computer assisted self-interviews and relatively low attrition in PATH enhances internal validity by reducing potential socially desirable responding and bias associated with attrition.
In this study, we observed a much smaller point estimates for the e-cigarette-to-smoking relationship compared to estimates for the common-liability-to-smoking relationship. Together with the fairly large sample size of PATH (which grants reasonable statistical power), it suggests that the "common liability to tobacco use" is sufficient to explain the onset of cigarette smoking among adolescents.
Our approach is driven by the "common liability" theory. To the best of our knowledge, this is the first study to use a structural equation modeling approach to create a latent unidimensional 'liability' variable, which is consistent with the conceptualization of "liability", which denotes "a latent (unobservable) quantitative trait that, when measured, 'would give us a graded scale of the degree of affectedness or of normality' 27,57 ." Tobacco products use is the result of complex genetic-environment interplay. Under the "common liability" conceptualization, the sequence of tobacco product use is opportunistic and depends upon various environmental factors including accessibility, local policies, and social norms. Therefore, the threshold for each product may change from one culture to other. For example, in a cigar-prone culture, the threshold for cigar use may be lower than that for e-cigarettes. The latent 'liability' construct is capable of accommodating these types of environmental variations. (2020) and an explanation of the common liability theory. The methods section now et al. includes more background information on SEM, which will be helpful to readers not familiar with this type of modeling. We were also pleased to see sensitivity analyses using PATH Wave 3 data as well as analyses including a broader set of covariates (age, sex, race/ethnicity, tobacco product availability in the household, novelty seeking, self-rated health, cigarette smoking harm perception, school performance). The authors provided detail about how missing information was handled. The results section now includes some basic demographic information, revisions to the tables, and additional results based on the new sensitivity analyses described in the methods.

Data availability
We have a few minor suggestions: On page 5, the first letter of the first complete paragraph needs to be capitalized. Table 2 provides results for models M1 to M6 using PATH waves 1 and 2 data. The written results describe models M1 and M2 followed by M5 and M6. Models M3 and M4 are described last. Why not change the order of the models in the table so they are described in sequence in the results? Please revisit the title of table 2. You present estimates for e-cigarette use and onset of ever cigarette smoking as well as estimates for the liability to use tobacco and the onset of ever cigarette smoking. The title only explains the e-cigarette piece.
No competing interests were disclosed. Competing Interests:

Reviewer Expertise: Epidemiology
We confirm that we have read this submission and believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.
Author Response 18 Jun 2020 , Altria Client Services, Richmond, USA Hui Cheng We are delighted to see that reviewers are happy about the revision. We appreciate reviewers' constructive comments which have helped us improve the manuscript. We have made additional adjustments based on reviewers' comments. Specifically, we have changed the model labels, and we have changed the title of Table 2 to "Estimated relationships linking e-cigarette use and common liability latent construct to onset of ever cigarette Data from Population Assessment of Tobacco and smoking from structural equation models. Health survey".

© 2020 Selya A. This is an open access peer review report distributed under the terms of the Creative Commons
, which permits unrestricted use, distribution, and reproduction in any medium, provided the original Attribution License work is properly cited.

Arielle Selya
Behavioral Sciences Group, Sanford Research, Sioux Falls, USA Pinney Associates, Inc., Pittsburgh, PA, USA The authors have done an excellent job responding to my concerns. I agree that a latent factor for nicotine use would make sense as a single latent factor, and that additional covariates would add complications. However, the additional exploratory analyses which include such covariates show that the findings are robust. I have a few remaining comments: My biggest concern is that the authors should be careful not to conclude *no relationship* between e-cigarettes and later cigarette use. Using the significance testing here, that cannot be concluded. A couple specific points: Such results should be worded as, e.g. "not significantly associated with" instead of "not associated with" (p. 6). Though the Beta coefficient does not reach statistical significance, it does look like it's trending towards a small but positive value (~0.13) based on most of the confidence interval being above 0. It is possible then, that with larger sample sizes, this could become significant. Therefore it might be helpful to also phrase this as, "common liability is sufficient to explain later cigarette use" if this is backed up by your results. In this vein, it might be valuable to do something like a nested model test of M1 vs. a model where the path from e-cigarettes to later cigarette use is removed; if the model fit does not substantially worsen, then this would support e-cigarettes not having any additional explanatory power in addition to that of the latent factor. An inconsistency with respect to how p-values are treated: in one place, p=.054 is interpreted as "not statistically significant"; but in another place, p=.074 is interpreted as "marginally associated." This highlights the importance of interpreting the effect sizes as well (e.g. Beta coefficients).
It would be more appropriate to use "nicotine" rather than "tobacco" in most instances, as e-cigarettes contain nicotine but not tobacco.
Another recent paper may be relevant in the literature review on common liability: Foxon & Selya, 2020, , which shows that total nicotine use trends (i.e. the use of any nicotine product) Addiction has not changed after the introduction of e-cigarettes.

Introduction
Cheng and colleagues ask an interesting and timely research question. They include a series of recent publications in their background as they lay out their justification. The introduction, however, is rather long and somewhat unfocused.
I would lead the discussion of the existing literature with the paragraph starting, "The largest body of literature comes from individual-level observational studies showing a consistent positive association…" The Vasiljevic study looking at exposure to e-cigarette advertisements does not seem directly relevant. Although I understand that it utilizes an experimental design, it could be cut to shorten the rather long introduction.
The authors' reference #26 should be discussed more fully in the introduction and discussion sections, as it identifies the components of common liability to use tobacco products and could shed light on the proper covariates to include in the SEM.
The discussion of ecological studies is lengthy and could be shortened. The authors ran two sets of models, one limited to tobacco products and a second, which they call the 'expanded liability model', that includes tobacco products and psychoactive substances. This expanded liability model is not introduced until the results section. It should be described in the methods.
Sex and age were included as covariates. Were any of the other risk factors for smoking available in PATH, such as were identified in authors' reference 26? If so, why not use those?
Please provide additional information on missing information. The only mention of it is as it relates to the covariates of age and sex. The authors report that this information was obtained from the Demographics module, which if missing was taken from the household screening roster. Was there missing information for the questions related to tobacco products, alcohol, cannabis, and other psychoactive drugs. If so, provide numbers and describe how it was handled. If there was limited missing information, that could be noted as a strength. Also, was there evidence that the data were, or were not, missing systematically? This can be assessed by comparing the available information for respondents who answered the substance use questions vs. those who did not.

Results
Please provide the number of eligible participants at Wave 1 and Wave 2 and report numbers and reasons for any that were excluded. This could be done in the form of a figure ending with the final number included in your analysis.
Also, please include a baseline table that provides basic demographic information. This could also be described in text.
The titles for tables 1 and 2 indicate that that data is from Wave 1 and Wave 2. We are interested in ever use of the products listed in the I'd suggest placing the model results described in the text in a table.

Discussion
The authors conclude that "after accounting for the latent 'common liability to use tobacco products' construct, ever e-cigarette use does not predict the onset of smoking among US adolescents." This statement is supported by the results provided, assuming that the variables considered by the authors reasonably captured the common liability they hypothesized exists. This point -whether or not the covariates included were sufficient -needs further explanation and justification.
The authors identify several appropriate limitations and strengths. However, the limitations should address more explicitly the availability of data to describe smoking propensity, as defined in reference 26 or elsewhere. The authors identify lack of recall bias as a strength of the study, but reference 26 or elsewhere. The authors identify lack of recall bias as a strength of the study, but the interval between waves in PATH is quite short, so recall bias is not a major concern.
The discussion section should place the current results into context of what is already known about smoking initiation in youth. The authors note that their findings are in line with a study by Kim et al.
(2019) and they should discuss this reference more fully. Several other observational studies are referenced in the introduction and further description of these observational studies might be useful here as well. Thank you for the opportunity to be a reviewer of this study. It is my recommendation that this paper be approved with reservations.

If applicable, is the statistical analysis and its interpretation appropriate? Yes
Are all the source data underlying the results available to ensure full reproducibility? Yes

Are the conclusions drawn adequately supported by the results? Yes
No competing interests were disclosed. Competing Interests:

Reviewer Expertise: Epidemiology
We confirm that we have read this submission and believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however we have significant reservations, as outlined above. association between e-cigarette use and onset of cigarette smoking in youth between the ages of 12 and 17 years in the U.S. They utilize nationally representative and publicly available data from the PATH study. The research was guided by "common liability" theory, which "postulates that any observed relationship between e-cigarettes and combustible tobacco products is attributed to the liability to use tobacco products of the individual; once this common liability is controlled for, there is no causal relationship between e-cigarette use and cigarette smoking." The authors report that they are the first study to use structural equation modeling to answer this question. e-cigarette use and cigarette smoking." The authors report that they are the first study to use structural equation modeling to answer this question.

Introduction
1.1 Cheng and colleagues ask an interesting and timely research question. They include a series of recent publications in their background as they lay out their justification. The introduction, however, is rather long and somewhat unfocused.
We thank the reviewer for recognizing the value of the research question. We Authors response: have amended the introduction to make it more focused based on reviewers' helpful comments as follows.
1.2 I would lead the discussion of the existing literature with the paragraph starting, "The largest body of literature comes from individual-level observational studies showing a consistent positive association…" The Vasiljevic study looking at exposure to e-cigarette advertisements does not seem directly relevant. Although I understand that it utilizes an experimental design, it could be cut to shorten the rather long introduction.
We have reorganized the discussion of existing literature in the revised Authors response: manuscript. It now begins with observational studies, followed by the experimental study by Vasiljevic and colleagues, and then ecological evidence. The description of the Vasiljevic study has been shortened.

1.3
The authors' reference #26 should be discussed more fully in the introduction and discussion sections, as it identifies the components of common liability to use tobacco products and could shed light on the proper covariates to include in the SEM.
We have added more details of reference #26 (now reference # 15) in the Authors response: revised manuscript (the middle of the 5 paragraph in the Introduction and the middle of the second paragraph in Discussion). During the revision, another study using similar method has been published. In this study, an inverse association was found between e-cigarette use and subsequent cigarette smoking using data from NYTS. We have added this study in the revised manuscript (ref. #16).

The discussion of ecological studies is lengthy and could be shortened.
We have shortened the discussion about ecological studies in the revised Authors response: manuscript.
1.5 Common liability theory should be introduced and described in the introduction, as it underlies the whole project. What is it, how is it measured, why is it appropriate for this project?
In the revised manuscript, we have added more details about the common Authors response: liability theory (the beginning of the 5 paragraph of the Introduction). th th 2. Methods 2.1 SEM is not that commonly used by epidemiologists. The paper would be more accessible if it included a brief introduction to SEM, including model selection, model evaluation, and how to interpret the results. The authors should explain why SEM is the right way to analyze a hypothesis based in common liability theory.
We have added a brief introduction of SEM and why we think SEM is Authors response: appropriate for this analysis based on the common liability theory (2 paragraph under Analysis Approach). PATH wave 3 data were not available when we started this project. During the Authors response: course of the project, they became available. We did repeat the analysis using wave 2 and 3 data, and the results are similar. We have added estimates using wave 2 and 3 data in the Results section of the revised manuscript and in the new Table 3. Nonetheless, we consider wave 1 and 2 data our primary focus because it is what we set out to do. Also, PATH wave 1 is the true baseline cohort, which is a representative sample of youth. Wave 2 is a follow-up of the wave 1 cohort with 'shadow' youth (those younger than 12) sampled at wave 1. In addition, for longitudinal studies like PATH, attrition occurs at each follow-up. When using wave 2 and 3 data, attrition may play a larger role.
2.3 Are the questions the same in Wave 2 for those who are 18? If so, have you considered running a sensitivity model that includes the 18-year-olds? Have other authors made this same decision to exclude them? How many Wave 1 youth were excluded because they had aged up by Wave 2? It may make less sense for future studies to make this cut-off considering changes in the minimum legal age to purchase tobacco products.
We did discuss whether we should include aged-up youth in the analysis, and Authors response: we decided not to because the focus of this study is on youth smoking onset. During wave 1 and 2 data collection (2013-2015), cigarettes were legal for 18-year-olds to purchase in most places. Risk profiles and mechanisms may differ for underage smoking from of-age smoking. We wanted to retain a focus on youth smoking onset and, therefore, did not include 18 year olds in the current study.
2.4 The authors ran two sets of models, one limited to tobacco products and a second, which they call the 'expanded liability model', that includes tobacco products and psychoactive substances. This expanded liability model is not introduced until the results section. It should be described in the methods.
We have added a paragraph in the Method section to describe a series of Authors response: models to explore the sensitivity of the main model results, including the model with additional psychosocial covariates and the model with wave 2 and wave 3 data, as suggested by the nd psychosocial covariates and the model with wave 2 and wave 3 data, as suggested by the reviewers (fourth paragraph in the Analysis section).
2.5 Sex and age were included as covariates. Were any of the other risk factors for smoking available in PATH, such as were identified in authors' reference 26? If so, why not use those?
We have added additional covariates in the series of exploratory analysis Authors response: described in the revised manuscript. Please see our response to reviewer #1's comment #2 for a detailed explanation.
2.6 Please provide additional information on missing information. The only mention of it is as it relates to the covariates of age and sex. The authors report that this information was obtained from the Demographics module, which if missing was taken from the household screening roster. Was there missing information for the questions related to tobacco products, alcohol, cannabis, and other psychoactive drugs. If so, provide numbers and describe how it was handled. If there was limited missing information, that could be noted as a strength. Also, was there evidence that the data were, or were not, missing systematically? This can be assessed by comparing the available information for respondents who answered the substance use questions vs. those who did not.
We have added a sentence in the revised manuscript to indicate that for all Authors response: tobacco use variables, there were <3% missing values. In addition, we specified a robust weighted least square mean and variance adjusted estimator which uses a full weight matrix. Therefore, a participant is included in the model unless the participant has missing values in all indicator variables (i.e., tobacco use and substance use variables). None of wave 1 never smokers had missing values in all of these variables, so we are able to include all never smokers in our model. We have added this information in the last paragraph of the Methods section in the revised manuscript.

Results
3.1 Please provide the number of eligible participants at Wave 1 and Wave 2 and report numbers and reasons for any that were excluded. This could be done in the form of a figure ending with the final number included in your analysis.
In the revised manuscript, we added a sentence about the number of Authors response: participants included in the current study: Among 13,651 participants at wave 1, 11,792 were never smokers, among whom 9,045 remained youth (12-17 years of age) and were followed up for wave 2 assessment. The sampling procedure of PATH is described in detail in PATH User's Guide (ref. #39) 3.2 Also, please include a baseline table that provides basic demographic information. This could also be described in text.
In the revised manuscript, we have added basic demographics of the sample in Authors response: Table 1 and a sentence in the first paragraph of the Results section: Of the 9,045 participants, 51% were males; 64% were 12-14 year olds; and 54% were non-Hispanic whites.
3.3 The titles for tables 1 and 2 indicate that that data is from Wave 1 and Wave 2. We are interested in ever use of the products listed in the table at Wave 1 and ever use of cigarettes at  Wave 2. Please clarify what is provided in the table and update the table titles/descriptions. We have adjusted the titles of Table 1 and Table 2 to reflect the estimates are Authors response: among wave 1 never smokers.
3.4 In fact, perhaps tables 1 and 2 could be combined to include demographic data from Wave 1; ever use of e-cigarette, cigar, pipe, hookah, SLT, bidi, alcohol, cannabis, prescription Ritalin and Adderall, cocaine/crack, stimulants, and other drugs at Wave 1; and ever cigarette use at Wave 3.
In the revised manuscript, we have combined the previous Table 1 and 2 into Authors response: one table (new Table 1).
3.5 I'd suggest placing the model results described in the text in a table.
We have added Table 2 which contains model results. Authors response:

4.1
The authors conclude that "after accounting for the latent 'common liability to use tobacco products' construct, ever e-cigarette use does not predict the onset of smoking among US adolescents." This statement is supported by the results provided, assuming that the variables considered by the authors reasonably captured the common liability they hypothesized exists. This point -whether or not the covariates included were sufficient -needs further explanation and justification.
As we indicated above, we have added additional covariates in the model in our Authors response: exploratory analyses, and the estimates were very similar to the one from the main model. We think these additional results suggest a certain degree of robustness of the latent 'common liability' construct and the main model overall. We have added this information and related discussion in the revised manuscript. Please also see our response to comment 2.5 and to reviewer #1's comment #2 for more details.
4.2 The authors identify several appropriate limitations and strengths. However, the limitations should address more explicitly the availability of data to describe smoking propensity, as defined in reference 26 or elsewhere. The authors identify lack of recall bias as a strength of the study, but the interval between waves in PATH is quite short, so recall bias is not a major concern.
Regarding concerns about other covariates, we have conducted additional Authors response: exploratory analyses to incorporate additional covariates related to smoking onset based on previous literature. Please also see our response to comment 2.5 and to reviewer #1's comment #2.
Regarding recall bias, we understand that the follow-up interval is only a year; however, there has been literature showing inconsistencies in the reporting of tobacco use as well as alcohol drinking behaviors in the youth population. In a cross-sectional setting, a smoker may be more likely to recall other tobacco use and vice versa because they can be correlated behaviors. Therefore, we recall other tobacco use and vice versa because they can be correlated behaviors. Therefore, we think it is a noteworthy strength of the current study.

4.3
The discussion section should place the current results into context of what is already known about smoking initiation in youth. The authors note that their findings are in line with a study by Kim (2019) and they should discuss this reference more fully. Several other observational studies et al. are referenced in the introduction and further description of these observational studies might be useful here as well.
We have revised both the Introduction and Discussion to provide fuller details of Authors response: previous studies and their relevance to the current study to help put findings from the current study into context.
In closing, we thank all three reviewers for their helpful and constructive comments. We hope we have provided sufficient information and revision to make the work acceptable for publication.

Arielle Selya
Behavioral Sciences Group, Sanford Research, Sioux Falls, USA Pinney Associates, Inc., Pittsburgh, PA, USA This manuscript focuses on the controversial question of whether e-cigarettes causally lead to later cigarette smoking among adolescents, or whether the use of both conventional cigarettes and e-cigarettes are due to a common liability. The paper uses structural equation modeling to model the pre-existing likelihood of e-cigarette use as a latent factor, finds that e-cigarettes do *not* have a causal effect on later conventional smoking over and above the latent factor. This paper uses an innovative method to address a complicated statistical question. The paper is well-written, and the implications are important.
Major comments: The introduction has an excellent literature review that makes a convincing case for the common liability hypothesis, even using papers that at face value support the "gateway" hypothesis of e-cigarettes but identifying interesting counterpoints in the analyses of these papers.
My main concern is about the choice to include only substance use variables in the latent factor representing liability to use tobacco products. Propensity to use tobacco products includes a variety of other factors as well (socioeconomic, personality characteristics, risk perception, peer group and family substance use, mental health, etc). Are these other variables available in the PATH study, and if so what was the rationale to restrict only to behavioral tobacco use measures? 1 2 cigarettes and e-cigarettes are due to a common liability. The paper uses structural equation modeling to model the pre-existing likelihood of e-cigarette use as a latent factor, finds that e-cigarettes do *not* have a causal effect on later conventional smoking over and above the latent factor. This paper uses an innovative method to address a complicated statistical question. The paper is well-written, and the implications are important. Authors We thank the reviewer for recognizing the significance and novelty of the work response: and the helpful comments. We have revised the original manuscript based on these comments as detailed below. Major comments: 1. The introduction has an excellent literature review that makes a convincing case for the common liability hypothesis, even using papers that at face value support the "gateway" hypothesis of e-cigarettes but identifying interesting counterpoints in the analyses of these papers.
We thank the reviewer for recognizing the value of the research question. Authors response: 2. My main concern is about the choice to include only substance use variables in the latent factor representing liability to use tobacco products. Propensity to use tobacco products includes a variety of other factors as well (socioeconomic, personality characteristics, risk perception, peer group and family substance use, mental health, etc). Are these other variables available in the PATH study, and if so what was the rationale to restrict only to behavioral tobacco use measures? What would the results look like if other covariates were also included?
We agree with the reviewer that the propensity to use tobacco products is Authors response: multifaceted, including important factors mentioned by the reviewers. In this study, we were guided by the 'common-liability' theory and hypothesized that the use of various tobacco products is driven by an unobserved latent liability to use tobacco products. That is, a single-dimension latent variable (i.e., the liability to use tobacco products) gives rise to the use of different tobacco products. This latent liability to use tobacco products likely varies by socioeconomic, personality characteristics, risk perception, peer influence, and familial history of substance use, mental health etc., which can be precedents, consequences, or both (feedback loops) of tobacco use. That is, our expectation is that the latent variable, which represents an individual's liability to use tobacco products, is correlated with these other variables. Practically, one complexity to include various other factors in the structural equation framework is that these variables are not necessarily manifestations of a single dimension, which complicates the structure of the measurement model. Due to the above theoretical and practical reasons, we chose to take a simpler theory-driven approach to define the latent construct by tobacco use behaviors and only included sex and age as covariates because they are exogenous to the liability-and-smoking-onset relationship. In an exploratory step, we further expanded the model to include other substances because it has been shown that adolescent substance use is highly opportunistic and tobacco use is highly correlated with other substance use among adolescents in the original submission. That said, the reviewer's concern is well taken. We have expanded the model to include aforementioned variables as covariates to the extent that they were assessed in PATH wave 1 survey. Specifically, we took a two-step approach to include additional covariates.
we added First, race/ethnicity (non-Hispanic White, non-Hispanic Black, Hispanics, and non-Hispanic others), availability of tobacco products in the household (yes/no), and a measure of novelty seeking ("agree" or "strongly agree" to the question "I like new and exciting experiences, even if I have to break the rules. Do you…").
, we additionally included participant's self-rated In the second step health (excellent/non-excellent), harm perception of cigarettes ("a lot of harm" to the question "How much do you think people harm themselves when they smoke cigarettes"), and participant's grade (mostly A's or A's and B's vs. others) because these variables are more likely to have feedback