Notation pi-tilde sub ia at time 00 and 01 denotes the predicted probability of substance use in 2000 and 2001 for State i, age group a; is obtained from simultaneously fitting the three annual models; and is computed as a ratio of two quantities. The quantity in the numerator is a sum of two terms. The first term is calculated as the product of the population projections for State i and age group a in 2000 (N sub ia at time 00), and the predicted probability of substance use for State i and age group a in 2000 (pi-tilde sub ia at time 00). The second term is calculated as the product of the population projections for State i and age group a in 2001 (N sub ia at time 01) and the predicted probability of substance use for State i and age group a in 2001 (pi-tilde sub ia at time 01). The denominator is the sum of the population projections for State i and age group a in 2000 and 2001, i.e., (N sub ia at time 00) and (N sub ia at time 01).