I need to calculate the sample size of a clinical trial in which the outcome is the exacerbation rate that is known has a negative binomial distribution, i already calculate it with Poisson distribution but i found evidence that mentioned exacerbation rate fit better with NB because the variance of the counts is usually greater than the mean resulting in an overdispersion.
The negative binomial regression has an additional parameter to capture the variation - so I don't think it can be over dispersed in the sense that the Poisson regression can be.
Hi,
I met recommend computing dispersion in similar distribution, such as Poisson, and comparing coefficients into index (sensitivity/robustness).
Hope this helps,
Matt
I quote from 'Applied Medical Statistics Using SAS' by G. De & B.S. Everitt, p. 301:
... overdispersion can often be spotted by comparing the residual deviance with its degrees of freedom. For a well-fitting model, the two quantities should be approximately equal. If the deviance is far greater than the degress of freedom, overdispersion may be indicated ...
The authors use the SAS proc genmod. In the output, the 'Value/DF' ratio value indicates overdispersion. If this value is quite positive, they refit the model (Poisson in their example, but this could as well be NB) with the scale=d option, which uses the square root of the deviance divided by its degrees of freedom as the scale parameter. This results in larger standard errors for the parameters. They then compare the models with and without this scale=d option to decide which parameters should be retained.
See: http://support.sas.com/kb/22/630.html
In R:
http://www.statpower.net/Content/MLRM/Lecture%20Slides/Overdispersion.pdf
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