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Assessing the regression to the mean for non-normal populations via kernel estimators
1Division of Biostatistics and Epidemiology, Department of Public Health, Weill Cornell Medical College, New York, USA.
North American Journal of Medical Sciences
|May 5, 2012
Summary
Regression to the mean, a statistical phenomenon affecting longitudinal studies, is now easier to assess. This new kernel-based method improves upon existing nonparametric approaches for non-normal data.
Area of Science:
- Statistics
- Biostatistics
- Longitudinal Data Analysis
Background:
- Regression to the mean (RTM) is a statistical phenomenon where extreme initial values tend to move closer to the average in subsequent measurements.
- This effect is particularly pronounced in longitudinal studies and can influence observed changes in response.
- Das and Mulder previously proposed a nonparametric method to estimate RTM.
Purpose of the Study:
- To adapt Das and Mulder's nonparametric RTM estimation method for empirical distributions using kernel estimation.
- To maintain the original assumptions of the Das and Mulder method while enhancing its applicability.
- To provide a user-friendly and data-adaptive approach for RTM assessment.
Main Methods:
- Utilizing state-of-the-art kernel density and hazard function estimation techniques.
- Implementing nonparametric bootstrap methods for estimating the standard error of RTM estimates.
- Leveraging statistical software packages like SAS and R for practical application.
Main Results:
- The developed kernel-based approach is user-friendly and suitable for practitioners.
- The method effectively estimates RTM in empirical distributions, including non-normal populations.
- Standard errors for RTM estimates are reliably calculated using nonparametric bootstrap.
Conclusions:
- The presented kernel-based method offers a user-friendly way to assess regression to the mean.
- This approach is particularly valuable for analyzing non-normal data in longitudinal studies.
- The data-adaptive nature enhances its applicability in real-world research settings.
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