Abstract
In spite of recent contributions to the literature, informative cluster size settings are not well known and understood. In this paper, we give a formal definition of the problem and describe it from different viewpoints. Data generating mechanisms, parametric and nonparametric models are considered in light of examples. Our emphasis is on nonparametric and robust approaches to the inference on the marginal distribution. Descriptive statistics and parameters of interest are defined as functionals and they are accompanied with a generally applicable testing procedure. The theory is illustrated with an example on patients with incomplete spinal cord injuries.
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Acknowledgments
The authors are grateful for the use of data from the NeuroRecovery Network, and thank the directors of centers participating in the NRN: Steve Ahr (Frazier Rehab Institute, Louisville, KY), Steve Williams, MD (Boston Medical Center, Boston, MA), Daniel Graves, PhD (Memorial Hermann/The Institute of Rehabilitation and Research, Houston, TX), Keith Tansey, MD, PhD (Shepherd Center, Atlanta, GA), Gail Forrest, PhD (Kessler Medical Rehabilitation Research and Education Corporation, West Orange, NJ), D. Michele Basso PT, EdD (The Ohio State University Medical Center, Columbus, OH) and Mary Schmidt Read, PT, DPT, MS (Magee Rehabilitation, Philadelphia, PA). This research was supported by the Academy of Finland and by NIH Grants 1R03DE020839-01A1, 5R03DE020839-02 and 1R03DE022538-01.
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Nevalainen, J., Datta, S. & Oja, H. Inference on the marginal distribution of clustered data with informative cluster size. Stat Papers 55, 71–92 (2014). https://doi.org/10.1007/s00362-013-0504-3
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DOI: https://doi.org/10.1007/s00362-013-0504-3