Re: st: Log transform of skewed data

[Roger Newson <roger.newson@kcl.ac.uk>]

At 14:53 02/06/04 -0400, you wrote:
> I have data on the "cost" (actually tranformed hours) of various types of
> caretaking for Alzheimers patients. I'm interested in a regression model to
> test treatment effects in a multisite study. As is usual for cost data, it
> is positively skewed. So, I contemplated a log transform, either through a
> direct transformation of the response, or through a log link in a glm, gee,
> or something similar. I actually am using "xt" commands to allow for
> nonindependence among caretakers treated at the same site.
>
> the problem is that the mode cost is $0, so that the distribution is
> bimodal. This, of course, remains true if I do a lof transform. Any ideas on
> how to analyze such data would be apreciated.
Log-transformed data can often be understood in terms of geometric means 
and their ratios. If in Stata you type

findit gmratio

then you should be taken to my website, where you can download my Stata Tip 
on the -eform- option of -regress- (Newson, 2003), which shows how to use 
this to calculate confidence intervals for geometric means and their ratios.

If there are zeros, however, then there is a problem, because the log of 
zero is not defined. In this case, you either have to transform the zeros 
to something else, or use arithmetic means instead of geometric means, with 
a log link function, in a glm or gee, usually using the -eform- option. The 
parameters will then be arithmetic means and their ratios, instead of 
geometric means and their ratios. Arithmetic means are still defined if the 
outcome is possibly zero, as is the case with loglinear modelling of count 
data, and the principle is the same with non-count data such as your 
caretaker-hours. The trick with the -noconst- option, mentioned in Newson 
(2003) may still be useful if you want a baseline arithmetic mean for a 
baseline patient.

Hope this helps.

Roger

References

Newson R. Stata tip 1: The eform() option of regress. The Stata Journal 
2003; 3(4): 445.


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
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Tel: 020 7848 6648 International +44 20 7848 6648
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Email: roger.newson@kcl.ac.uk
Website: http://www.kcl-phs.org.uk/rogernewson

Opinions expressed are those of the author, not the institution.

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