Table 2. Cross-tabulations of frequency (expected frequency, Eij) of group membership in tobacco use trajectories and marijuana use trajectories We tested observed versus expected cell selleck kinase inhibitor frequencies in the trajectories of tobacco and marijuana use contingency table to determine those trajectory pairs that occur more frequently than expected under independence (Lienert & Krauth, 1975; von Eye, 2002). A pair of trajectories (i, j) was selected when , where Oij is the observed value of ith row and jth column and Eij is the expected value of ith row and jth column with 3.72 chosen to set p < .0001. For each selected pair of tobacco and marijuana use trajectories, first, we predicted Yk, the indicator of the selected marijuana use trajectory group for participant k from the indicator of the selected tobacco use trajectory group for participant k, Xk.

The logistic regression model is Yi = ��0 + ��1Xi + ?i, i = 1, �� ,475, where ?k is the residual error for kth participant under the model. The overall odds ratio (OR) for the selected pair of trajectories is (Agresti, 1996). These ORs are reported in the first line of Table 3. Table 3. Adjusted odds ratios of selected pairs of tobacco use trajectories and marijuana use trajectories from logistic regression analyses after controlling each specified risk factor We then conducted further logistic regression analyses to see whether a risk variable, R, reduced the OR in the pair of trajectories. That is, we fit the logistic regression model Yk = ��0 + ��1Xk + ��2Rk + ��k, k = 1, �� ,475, where Rk is the value of the risk variable R, Yk and Xk are defined as above, and ��k is the residual error for kth participant under this model.

The value is the OR between trajectory groups controlling for risk variable R. We compare the OR controlling for R with the overall OR using the test statistic (Clogg, Petkova, & Haritou, 1995). Under the null hypothesis of no change in OR, T is approximately standard normal. We then examined the five sets of variables specified in Table 4. The logistic regression of the trajectory of marijuana use was estimated with control on the tobacco use trajectory and all variables in each of the sets (see Table 4). We also estimated the logistic regression of the trajectory of marijuana use with control on the tobacco use trajectory and with control on all the psychosocial variables simultaneously.

We then tested whether the OR with a given tobacco use trajectory Entinostat variable was significantly reduced when a set of predictors was added as a control. Table 4. Adjusted odds ratios and 95% CI for selected pairs of tobacco use trajectories and marijuana use trajectories from logistic regression analyses with control on each of 5 sets of risk factors, and on a set of all the risk factors Results Mixture modeling: Extracting trajectories There were four tobacco use trajectory groups.