Assessing Program Effects in the Presence of Treatment-Baseline Interactions: A Latent Curve Approach

The aim of this paper is to explore methods for evaluating the effects of randomized interventions in a longitudinal design. The focus is on methods for modeling the possibly nonlinear relationship between treatment effect and baseline and evaluating the treatment effect taking this nonlinear relationship into account. A control/treatment growth model formulation based on Muthen and Curran (in press) was used as the framework to assess treatment effects. Piecewise linear growth modeling was chosen to study the treatment effects during the different periods of development. A multistage analysis procedure was proposed for assessing treatment effects in the presence of nonlinear treatment-baseline interactions. To avoid biasing effects of measurement errors in the observed baseline scores, initial status factor score estimates from a latent growth model were used in this analysis. Subsets of subjects, based on the form of the nonlinear treatment-initial status interaction, were then used for treatment-control, multiple-group latent growth modeling to assess treatment effects. Standard errors of the estimates from this multistage procedure were obtained by a bootstrap approach. The methods were illustrated using data from the Prevention Research Center at the Johns Hopkins University involving an intervention aimed at improving classroom behavior, the Good Behavior Game (GBG).