In such cases, the difference in regression intercepts, or the expected outcome when other variables are equal, for the outcome measure among those who were eligible and those who were not eligible provides an estimate of the intervention effect (Cook and Campbell, 1979). Gormley, Gayer, and Phillips (2005) used this design in concluding that a universal statewide prekindergarten program had a large impact on achievement.

ADVANCES IN STATISTICAL ANALYSIS OF PREVENTION TRIALS

At the time of the 1994 IOM report, virtually all published analyses were limited to examining an intervention’s impact on an outcome variable measured at a single point in time at follow-up. Analyses of impact in randomized field trials and longitudinal analyses were conducted independent of one another. Now, however, it is customary to use growth modeling techniques to examine trajectories of change using more extensive longitudinal data, with corresponding gains in statistical power (Muthén and Curran, 1997) and interpretability (Muthén, Brown, et al., 2002). Growth models can be a valuable tool in understanding the impact of interventions.

Using Growth Models

Most theories of change in prevention research posit an evolving effect on the individual that varies over time as new developmental stages are reached. Although it should be possible to detect intervention effects at a critical transition period using an outcome measured at a single time point, it is also possible to examine the impact of interventions using longitudinal data to show differences in individuals’ developmental trajectories or growth patterns (e.g., repeated measures of aggression or symptoms) by intervention condition.

Often the patterns of growth can be summarized with a few parameters. By fitting individual-level data to linear growth curves, for example, an intervention’s effect can be summarized based on the difference in mean rates of growth for intervention and control participants. Other approaches might include latent growth modeling of different aspects of growth using quadratics and higher order polynomials, piecewise growth trajectories, and nonlinear growth models (Muthén, 1991).

The effects of interventions may vary not only as a function of time, but also across individuals. For example, a universal intervention may have a stronger effect over time on those who start with higher levels of risk compared with those with lower levels of risk, as is now found in a number of preventive interventions (Brown and Liao, 1999; Brown, Wang, et al., 2008). Growth models that include an interaction between interven-



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