Integrated Data Analysis for Longitudinal Data: Pooled Estimates Based On Multiple Calibrations

Integrative data analysis (IDA; Curren & Bauer, 2009) synthesizes findings (e.g., intervention effects) from multiple studies using individual participants' data to obtain overall parameter estimates. For combining longitudinal studies, current IDA methods use a two-stage approach whereby an initial randomly-selected calibration subsample generates maximum a posteriori(MAP) factor scores (Bauer and Hussong, 2009).  In the second stage, longitudinal analysis (e.g., latent growth curve modeling) of the MAP scores is conducted for the whole sample. A two-stage solution has been practical because existing computer capacity and software cannot accommodate both model complexity (latent mean and variance regression and item DIF) and dependency among observations. This presentation explored single- versus  multiple-calibration approaches. 

 The single-calibration approach draws a calibration sample based on randomly selecting one observation from each participant's repeated measures. However, a single observation per participant does not capture the full range of variability (i.e., within-subject) that exists in all of the observations. For example, in the present study, the single-calibration sample represented only approximately 25% of all potential observations. In order to capture the total variability in the data and achieve stability in the parameter estimates, the present study augmented the estimates derived from a single calibration by drawing multiple, random-calibration samples (with replacement), conducting separate latent growth curve analyses on the factor scores derived from each calibration sample, and in the final stage, combining estimates from the separate growth curve analyses.

 The present study tested the effects of Multidimensional Family Therapy (MDFT, Liddle, 2002), an evidence-based adolescent substance abuse treatment program, on the growth trajectories of adolescents receiving abuse treatment. Data for this study came from five randomized control trials (Liddle, 2008; Liddle & Dakof, 2002; Liddle et al., 2009; Liddle et al., 2011, Dakof et al., 2012).

Initially, each of 10 calibration samples generated individual MAP factor scores for all participants. Each set of MAP scores was then analyzed in a second stage latent growth curve analysis. Growth curve results were combined based on Wang's (2012) procedure. Notwithstanding substantial variability in growth trajectory estimates (i.e., treatment, treatment x gender, treatment x race/ethnicity) across calibration samples, combined results, in contrast with some of the single-calibration samples, indicated a significant (p < .05) main MDFT treatment effect, with significant moderator effects for males and African Americans. Implications for data synthesis in future studies are discussed.