Probabilistic discrete event systems modeling of nonlinear transitions between electronic and combustible cigarette smoking with the 2014 National Youth Tobacco Survey data

A growing number of young people smoke electronic (e-) cigarettes, presenting an emerging challenge to tobacco control. Analyses are needed to better understand the dynamics of mutual transitions between e-cigarette and conventional combustible (c-) cigarette smoking to advance evidence-based tobacco control. In this study we modeled the nonlinear dynamics of c- and ecigarette smoking behavior transitions using the 2014 National Youth Tobacco Survey (NYTS) data. A model with five Markov-Chain transition stages linked by 21 transitional paths/probabilities was constructed, guided by the probabilistic discrete event systems (PDES) theory. The Moore-Penrose generalized inverse matrix was used to solve the proposed model that was under-determined. The estimated transitional probabilities indicate that each year, 7-8% of middle school students and 11% of high school students initiated smoking. E-cigarettes were more attractive then c-cigarettes but the behavior of smoking c-cigarettes was more stable than that of smoking e-cigarettes. Female students were more likely to remain as quitters or ex-smokers while male students were more likely to relapse and smoke again. Findings of this nonlinear dynamics modelling indicate potential increases in both e- and c-cigarette smoking among U.S. middle and high school students if no further measures are taken. The PDESbased approach is effective to investigate the nonlinear dynamics of mutual transitions of two risk behaviors in adolescents with one wave cross-sectional data.