Hello, my name is David Mendez and I'm an associate professor in the Department of Health Management and Policy at the University of Michigan School of Public Health. Today, I am going to talk about simulation models in health policy, and in particular, I'm going to focus on a specific type of simulation models called compartmental models or macro simulation models in general. In order to explain how macro simulations or compartmental models work, I am going to use a specific example from smoking rates, from trying to use simulation to predict or to project future smoking rates, prevalence, and smoking status at different ages and so on. What is the main issue of a compartmental model? There are actually two features that we need to pay attention to. One is what we call the stock, is how many individuals we have in a certain category at a certain time. That is what we call the present. Now, if we want to know what's the number of individuals we're going to have in different classifications during the next period in the future, we need to know the rules of change. What are the conditions and the rules that make individuals change their classification in the future? In general, we are going to focus in this equation. The smokers at time t plus 1 in the future are equal to the number of smokers at time t, the present, plus change. Now, let's take a look at the present. This is what we call a compartment. We are keeping track of smokers, and let's say that in that compartment of smokers, we have 10 individuals. That's the present. What is that we are going to project? We're going to try to project how many smokers we are going to have in the next period. For example, in this specific compartment, the changes are the individuals who get into the smoker stock or to their smoker compartment in this period and the individuals who go out of that specific compartment in that specific period. That's the change. Who are those individuals? Well, those individuals are the ones who quit smoking, the ones who died, and also the ones that come in to the smoker stock. Those are the ones that initiate smoking and they want that relapse, so those are former smokers. People who quit before that now retook the habit. In this case, I have 10 smokers now the present, but then we have five that left that stock because they quit, four that died, 10 that came in because of started the smoking behavior, so those are initiators, and two that got in because they relapsed. So 10 minus 4 minus 5 plus 2. We have 10 minus 4, 6 minus 5, 1 plus 2 is 3. So the net change will be three. The smokers that we had before, there were 10, we have a net change of three. So in the next period, we should have 13 smokers. That's the future. Now, how do we know that those individuals are going to go out or they are going to get in? How do we project the number of individuals who change? We estimate, we gather either from data or from published literature, we gather parameters that are in red and express in those equations here. We have the initiation rate, for example, which is the probability that an individual starts smoking at a certain age. If we multiply the never smokers, the stock of never smokers, times the probability that any one of them starts smoking, then we have the inflow of new smokers or individuals who initiate into the category of smokers. Another example. If we know and we can estimate, we can take a look at the published data or estimate ourself from data, we should be able to gather what we call the cessation rate, or the probability that a smoker quit at a certain period, at a certain time, at a certain age. If we multiply that cessation rate times the number of smokers that we have in a category, then we know that total number of individuals who leave the smoker stock because they quit smoking. If we have those parameters that are in red, the relapse rate, the initiation rate, the death rate, and the cessation rate, and these parameters can be very specific regarding age, gender and so on, socioeconomic status, as disaggregated as you need, then we have an accurate representation of what's going to happen in the future.
