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Background and aims Reports of youth e-cigarette use often do not disaggregate by underlying smoking status. This study compared annual 2014–19 youth estimates of past 30-day e-cigarette use prevalence and frequency by smoking status in the United States. Design Nationally representative, cross-sectional, school-based survey [National Youth Tobacco Surveys (NYTS)]. General linear models accounting for complex survey design compared e-cigarette use prevalence by smoking status by year, overall and stratified by frequency, separately for high school (HS) and middle school (MS) students. The 2019 survey was analyzed separately because of its change in survey methodology. Setting MSs and HSs in the United States. Participants A total of 116 704 students from 1268 schools, ages 9–19. Measurements Students self-reported (paper 2014–18, electronic 2019) ever and past 30-day (current) use of e-cigarettes and cigarettes, as well as frequent use (20–30 days of month). Findings From 2014 to 2018, current e-cigarette use prevalence increased among never, current and former smokers in HS, but only among never and current smokers in MS (each P-value < 0.001). E-cigarette use increases for current HS smokers were primarily among frequent e-cigarette users. In 2018, the absolute number of HS frequent users who were never or former smokers (420 000 combined) surpassed current smokers (370 000). In 2019, current e-cigarette use prevalence for never, former and current smokers was 17.5% [95% confidence interval (CI) = 16.0–19.0], 53.6% (95% CI = 45.2–61.9) and 85.8% (95% CI = 81.6–89.9) for HS students, respectively, and 6.8% (95% CI = 5.9–7.7), 40.8% (95% CI = 34.7–47.0) and 78.0% (95% CI = 71.9–84.2) for MS students. That year, the number of HS never (420 000) and former smokers (570 000) using e-cigarettes frequently eclipsed that of current smokers (390 000). Conclusions E-cigarette use prevalence and frequency among youth vary by smoking status, with highest levels of use among current smokers. However frequent e-cigarette use among never smokers and former smokers has increased.

The supplementary material includes (i) the parameterizations of the time-varying shedding model calibration tests, (ii) models of infectiousness as a function of shedding concentration, (iii) model equations, (iv) comparison of the variable shedding and constant shedding model fits to the PCR CT data, and (v) the data and model fits for each of the seven sampling sites.

Additional details on population characteristics, model identifiability and the single-outcome models

Human pathogens transmitted through environmental pathways are subject to stress and pressures outside of the host. These pressures may cause pathogen pathovars to diverge in their environmental persistence and their infectivity on an evolutionary time-scale. On a shorter time-scale, a single-genotype pathogen population may display wide variation in persistence times and exhibit biphasic decay. Using an infectious disease transmission modeling framework, we demonstrate in both cases that fitness-preserving trade-offs have implications for the dynamics of associated epidemics: less infectious, more persistent pathogens cause epidemics to progress more slowly than more infectious, less persistent (labile) pathogens, even when the overall risk is the same. Using identifiability analysis, we show that the usual disease surveillance data does not sufficiently inform these underlying pathogen population dynamics, even with basic environmental monitoring. These results suggest directions for future microbial research and environmental monitoring. In particular, determining the relative infectivity of persistent pathogen subpopulations and the rates of phenotypic conversion will help ascertain how much disease risk is associated with the long tails of biphasic decay. Alternatively, risk can be indirectly ascertained by developing methods to separately monitor labile and persistent subpopulations. A better understanding of persistence--infectivity trade-offs and associated dynamics can improve risk assessment and disease control strategies.

The interactions between parameters, model structure, and outputs can determine what inferences, predictions, and control strategies are possible for a given system. Parameter space reduction and parameter estimation---and, more generally, understanding the shape of the information contained in models with observational structure---are thus essential for many questions in mathematical modeling and uncertainty quantification. As such, different disciplines have developed methods in parallel for approaching the questions in their field. Many of these approaches, including identifiability, sloppiness, and active subspaces, use related ideas to address questions of parameter dimension reduction, parameter estimation, and robustness of inferences and quantities of interest. In this paper, we show that active subspace methods have intrinsic connections to methods from sensitivity analysis and identifiability, and indeed that it is possible to frame each approach in a unified framework. A particular form of the Fisher information matrix (FIM), which we denote the sensitivity FIM, is fundamental to all three approaches---active subspaces, identifiability, and sloppiness. Through a series of examples and case studies, we illustrate the properties of the sensitivity FIM in several contexts. These initial examples show that the interplay between local and global and linear and non-linear strongly impact the insights each approach can generate. These observations underline that one's approach to parameter dimension reduction should be driven by the scientific question and also open the door to using tools from the other approaches to generate useful insights.

Many cancers are understood to be the product of multiple somatic mutations or other rate-limiting events. Multistage clonal expansion (MSCE) models are a class of continuous-time Markov chain models that capture the multi-hit initiation–promotion–malignant-conversion hypothesis of carcinogenesis. These models have been used broadly to investigate the epidemiology of many cancers, assess the impact of carcinogen exposures on cancer risk, and evaluate the potential impact of cancer prevention and control strategies on cancer rates. Structural identifiability (the analysis of the maximum parametric information available for a model given perfectly measured data) of certain MSCE models has been previously investigated. However, structural identifiability is a theoretical property and does not address the limitations of real data. In this study, we use pancreatic cancer as a case study to examine the practical identifiability of the two-, three-, and four-stage clonal expansion models given age-specific cancer incidence data using a numerical profile-likelihood approach. We demonstrate that, in the case of the three- and four-stage models, several parameters that are theoretically structurally identifiable, are, in practice, unidentifiable. This result means that key parameters such as the intermediate cell mutation rates are not individually identifiable from the data and that estimation of those parameters, even if structurally identifiable, will not be stable. We also show that products of these practically unidentifiable parameters are practically identifiable, and, based on this, we propose new reparameterizations of the model hazards that resolve the parameter estimation problems. Our results highlight the importance of identifiability to the interpretation of model parameter estimates., Author summary Parameter estimation from data is an important part of mathematical modeling, and structural identifiability is the study of what parametric information exists, for a given model, in ideal data. Unfortunately, for a variety of reasons, there is often less information available in our real data sets. The study of these problems is called practical identifiability. In this study, we consider a family of models of cancer biology that are commonly used to explain cancer incidence in terms of underlying biological parameters. Using profile likelihoods, a widely applicable numerical tool, we demonstrate that even though the more complex models we consider have theoretically more identifiable parameters, the data contains only three pieces of practically identifiable information for each model: the product of the initiating mutation rates, the net cell proliferation rate, and the scaled malignant conversion rate. This result can be interpreted biologically: we can determine only the product of cell mutation rates not the intermediate rates themselves. Our result limits the interpretability of previous work, but we propose a novel parameterization to resolve the identifiability issue. Ultimately, our analysis demonstrates the importance of verifying the practical identifiability of parameters before assigning too much weight to the interpretation of their estimated values.

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes.