Estimation of transitional probabilities of discrete event systems from cross-sectional survey and its application in tobacco control

In order to find better strategies to control tobacco use, it is often critical to know the transitional probabilities among various stages of tobacco use. Traditionally, such probabilities are estimated by performing longitudinal surveys, which are often time-consuming and expensive. In this paper, we propose a method to estimate transitional probabilities from cross-sectional survey data, which is more cost-effective to obtain and hence abundant. The method is based on a discrete event system framework. We introduce state probabilities and transitional (event) probabilities to the conventional discrete event system models. We derive various equations that can be used to estimate the transitional probabilities. We test the method using cross-sectional data of the National Survey on Drug Use and Health. The estimated transitional probabilities can be used in predicting the future smoking behavior for decision-making, planning and evaluation of various tobacco control programs.