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Using a shared parameter mixture model to estimate change during treatment when termination is related to recovery
Nisha C Gottfredson1, Daniel J Bauer2, Scott A Baldwin3
1Center for Developmental Science, University of North Carolina at Chapel Hill.
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.
Method:
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.
Conclusion:
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.
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