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A priori power analysis in longitudinal three-level multilevel models: an example with therapist effects
Kim de Jong1, Mirjam Moerbeek, Rien van der Leeden
1Research Department, GGZ Noord-Holland-Noord, Heiloo, the Netherlands. k.dejong@ggz-nhn.nl
Summary
Power analysis for three-level longitudinal models in psychotherapy research is crucial. Patient-level randomization is most efficient, and sufficient power can be achieved with smaller sample sizes, though larger samples prevent bias.
Area of Science:
- Psychology
- Statistics
- Psychotherapy Research
Background:
- Three-level longitudinal models are increasingly used in psychotherapy research, especially for therapist-effect and group-effect studies.
- Power analysis for these complex models remains under-explored, hindering robust study design.
Purpose of the Study:
- To investigate the impact of various factors on statistical power in three-level longitudinal models.
- To provide guidance on optimizing study design for psychotherapy research utilizing these models.
Main Methods:
- Utilized data from a routine outcome monitoring study.
- Examined the influence of intraclass correlation, randomization level, sample size, covariates, and participant drop-out on statistical power.
Main Results:
- Randomization at the patient level demonstrated the highest efficiency for power.
- Increasing the number of measurements yielded minimal gains in statistical power.
- Covariates and a 25% drop-out rate had limited effects on power in the analyzed dataset.
- Sufficient statistical power is attainable with small sample sizes, but larger samples are necessary to mitigate estimation bias.
Conclusions:
- Patient-level randomization is recommended for maximizing power in three-level longitudinal psychotherapy studies.
- While small sample sizes can yield adequate power, larger samples are essential for reliable parameter and standard error estimation.
- Researchers should carefully consider these factors when designing studies using three-level longitudinal models to ensure adequate statistical power and accurate results.
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