Abstract
How long does a treatment take to reach maximum effect? Is the effect maintained or does it dissipate or perhaps even reverse? Do certain sorts of people respond faster or stronger than others? Is the treatment more effective in the long run for those that respond quickly? We describe a continuous time dynamic modelling approach for addressing such questions, with discussion and example code for simple impulse effects, persistent changes in level, treatments where the effect may reverse in direction over time, treatments that change a trend, assessing mediation in treatment effects and examining individual differences in treatment effects, duration and shape and correlates of such individual differences.
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Notes
- 1.
For the sake of simplicity, we generate and fit data without stable between-subjects differences, but in real-world analyses of multiple subjects, it may be advisable to account for such effects. With ctsem this can be done either via the MANIFESTTRAITVAR or TRAITVAR matrices in frequentist configuration or by allowing individually varying parameters with the Bayesian approach—discussed briefly in Sect. 4.4.5.
- 2.
In a model with between subjects differences in the trend, variability in this parameter can be accommodated via the TRAITVAR matrix (for frequentist ctsem) or by simply setting the parameter to individually varying (in the Bayesian approach).
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Driver, C.C., Voelkle, M.C. (2018). Understanding the Time Course of Interventions with Continuous Time Dynamic Models. In: van Montfort, K., Oud, J.H.L., Voelkle, M.C. (eds) Continuous Time Modeling in the Behavioral and Related Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-77219-6_4
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