# Re: st: Re: reporting log linked, linear, and fractional polynomial results

 From Buzz Burhans <[email protected]> To [email protected] Subject Re: st: Re: reporting log linked, linear, and fractional polynomial results Date Mon, 27 Oct 2003 14:38:05 -0500

Roger,

Thanks very much for your comments; they were indeed helpful. My data exhibits a great deal of shifting and instability in metabolites , with different subjects and different metabolites demonstrating quite different profiles during the same relative time periods, thus making modeling, interpretation, and reporting quite interesting to say the least.

I got your response as I happened to be rereading your Stata Journal 2:45 paper on use of your -somersd- package. I am reminded of your numerous contributions to the Stata community, both in terms of packages like -somersd-, -bspline-, and the -parmest- family, and your frequent responses to statalist. I am sure I speak for many others who have also benefited from your contributions when I express my gratitude for your responses and contributions. I have quite appreciated and benefited from your articulate grasp and communication of underlying methodology and practical application in your various discussions to the Stata community.

Buzz Burhans

At 01:28 PM 10/27/2003 +0000, you wrote:

```At 08:36 23/10/03 -0400, Buzz Burhans wrote:
```
I would appreciate advice on effective ways of reporting on data for similar outcome types from the same trial which have been modeled using different link functions....
If you fit a GLM (or extension of a GLM) with a log link, then the exponentiated parameters are arithmetic means and their ratios. This is true whether the Y-variable is a count variable or a continuous variable. The ratios may be simple between-group ratios (in the case of categorical X-variables) or ratios associated with a unit increase in an X-variable (in the case of continuous X-variables). If the continuous X-variable is itself a log to the base 2 of another variable (eg X=log_2(W)), then the exponentiated parameter is a per-doubling ratio associated with a doubling of W.

An alternative to fitting arithmetic means and their ratios might be to transform the outcome data to logs and then use a GLM (or extended GLM) with an identity link. The exponentiated parameters are then geometric means and their ratios. For instance, the exponentiated intercept is a geometric mean Y for zero X, and the exponentiated slopes are amounts by which the geometric means are multiplied per unit increase in X. The geometric mean is often a better proxy for the median than the arithmetic mean if the data are positively skewed, eg viral loads, plasma triglycerides and house prices. Another possibility is to power-transform the data and use a GLM with the corresponding inverse-power link function to estimate algebraic means and their differences, but I don't know many people who do this.

Either way, it usually makes sense to centre the X-variates at a sensible X-value, so that the exponentiated intercept will represent an arithmetic or geometric mean expected at a sensible X-value instead of an arithmetic or geometric mean expected at a zero X-value (except if a xzero X-value is sensible). And, in general, the parameters presented with confidence limits should be explicable in words to non-statisticians.

I hope this helps.

Roger

--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605
Email: [email protected]
Website: http://www.kcl-phs.org.uk/rogernewson

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

*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
```Buzz Burhans
[email protected]

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```