Simulating interventions in graphical chain models for longitudinal data

Simulating the outcome of an intervention is a central problem in many fields as this allows decision-makers to quantify the effect of any given strategy and, hence, to evaluate different schemes of actions. Simulation is particularly relevant in very large systems where the statistical model involves many variables that, possibly, interact with each other. In this case one usually has a large number of parameters whose interpretation becomes extremely difficult. Furthermore, in a real system, although one may have a unique target variable, there may be a number of variables which might, and often should, be logically considered predictors of the target outcome and, at the same time, responses of other variables of the system. An intervention taking place on a given variable, therefore, may affect the outcome either directly and indirectly though the way in which it affects other variables within the system. Graphical chain models are particularly helpful in depicting all of the paths through which an intervention may affect the final outcome. Furthermore, they identify all of the relevant conditional distributions and therefore they are particularly useful in driving the simulation process. Focussing on binary variables, we propose a method to simulate the effect of an intervention. Our approach, however, can be easily extended to continuous and mixed responses variables. We apply the proposed methodology to assess the effect that a policy intervention may have on poorer health in early adulthood using prospective data provided by the 1970 British Birth Cohort Study (BCS70).