title: Using a shared parameter mixture model to estimate change during treatment when termination is related to recovery speed.
abstract: OBJECTIVE
  This study demonstrates how to use a shared parameter mixture model (SPMM) in longitudinal psychotherapy studies to accommodate missingness that is due to a correlation between rate of improvement and termination of therapy. Traditional growth models assume that such a relationship does not exist (i.e., assume that data are missing at random) and produce biased results if this assumption is incorrect.
  
  
  METHODS
  We used longitudinal data from 4,676 patients enrolled in a naturalistic study of psychotherapy to compare results from a latent growth model and an SPMM.
  
  
  RESULTS
  In this data set, estimates of the rate of improvement during therapy differed by 6.50%-6.66% across the two models, indicating that participants with steeper trajectories left psychotherapy earliest, thereby potentially biasing inference for the slope in the latent growth model.
  
  
  CONCLUSIONS
  We conclude that reported estimates of change during therapy may be underestimated in naturalistic studies of therapy in which participants and their therapists determine the end of treatment. Because non-randomly missing data can also occur in randomized controlled trials or in observational studies of development, the utility of the SPMM extends beyond naturalistic psychotherapy data.
authors.affiliation: Center for Developmental Science, University of North Carolina at Chapel Hill.
authors.forename: Nisha C
authors.initials: NC
authors.lastname: Gottfredson
authors.affiliation: Department of Psychology, University of North Carolina at Chapel Hill.
authors.forename: Daniel J
authors.initials: DJ
authors.lastname: Bauer
authors.affiliation: Department of Psychology, Brigham Young University.
authors.forename: Scott A
authors.initials: SA
authors.lastname: Baldwin
authors.affiliation: Department of Psychology, Brigham Young University.
authors.forename: John C
authors.initials: JC
authors.lastname: Okiishi
mesh_terms: D000328:Adult; D005260:Female; D006801:Humans; D008137:Longitudinal Studies; D015233:Models, Statistical; D011613:Psychotherapy