Abstract
We present a case study using the negative binomial regression model for discrete
outcome data arising from a clinical trial designed to evaluate the effectiveness
of a prehabilitation program in preventing functional decline among physically frail,
community-living older persons. The primary outcome was a measure of disability at
7 months that had a range from 0 to 16 with a mean of 2.8 (variance of 16.4) and a
median of 1. The data were right skewed with clumping at zero (i.e., 40% of subjects
had no disability at 7 months). Because the variance was nearly 6 times greater than
the mean, the negative binomial model provided an improved fit to the data and accounted
better for overdispersion than the Poisson regression model, which assumes that the
mean and variance are the same. Although correcting the variance and corresponding
test statistics for overdispersion is a standard procedure in the Poisson model, the
estimates of the regression parameters are inefficient because they have more sampling
variability than is necessary. The negative binomial model provides an alternative
approach for the analysis of discrete data where overdispersion is a problem, provided
that the model is correctly specified and adequately fits the data.
Keywords
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Article info
Publication history
Accepted:
January 16,
2003
Received in revised form:
January 10,
2003
Received:
August 16,
2002
Identification
Copyright
© 2003 Elsevier Inc. Published by Elsevier Inc. All rights reserved.
