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Biostatistics Advance Access published online on July 14, 2005
Biostatistics, doi:10.1093/biostatistics/kxi044
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.
Received May 19, 2004
Revised June 22, 2005
Accepted July 13, 2005

Article

Estimation in Regression Models with Externally Estimated Parameters

R. Todd Ogden 1* and Thaddeus Tarpey 2

1 Department of Biostatistics, Columbia University, 6th floor, 600 West 168th Street, New York, NY 10032, USA
2 Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435, USA

* To whom correspondence should be addressed.
R. Todd Ogden, E-mail: ogden{at}biostat.columbia.edu


  Abstract

In many regression applications, some of the model parameters are estimated from separate data sources. Typically these estimates are plugged into the regression model and the remainder of the parameters are estimated from the primary data source. This situation arises frequently in compartment modeling when there is an external input function to the system. This paper provides asymptotic and bootstrap-based approaches for accounting for all sources of variability when computing standard errors for estimated regression model parameters. Examples and simulations are provided to motivate and illustrate the ideas.

Keywords: Bootstrap; compartment models; PET imaging.
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