st: log-transformed variable in Cox PH

[Jenkins S P <stephenj@essex.ac.uk>]

Ricardo Ovaldia asked about this issue on Fri 3 Feb.

One potential advantage of including a log-transformed explanatory 
variable in a PH regression model (NB in any PH model, e.g. Weibull or 
Gompertz, not just Cox) is that the estimated coefficient on the 
log-transformed variable shows the elasticity of the hard rate w.r.t. the 
untransformed variable.

I.e. for z = log(x) and z used as predictor, the estimated coeff. on z is 
the elasticity: b_hat =  dlog(hazard)/dlogx = [d(hazard)/dx]*(x/hazard)
In words, the coeff. on the log-transformed vble shows the proportionate 
response of hazard to a proportionate change in x. (See the Manual entries 
on -mfx- for more about elasticities.)

Incidentially, the estimated coeff. on a log-transformed vble in an 
Accelerated Failure Time model shows the elasticity of survival time 
w.r.t. the untransformed varaiable.

Derivations at my survival analysis web page in the pdf 'book'

Stephen

==============
Date: Fri, 3 Feb 2006 12:09:05 -0800 (PST)
From: Ricardo Ovaldia <ovaldia@yahoo.com>
Subject: st: Cox PH question

Dear all,

A reviewer of a manuscript that we recently submitted
to a top medical journal stated that the  "independent
variable, known to be positively skewed , be
log-transformed prior to inclusion in a Cox
proportional hazards model". As far as I know there is
no normality assumption for the Cox model,
additionally transforming this complicates the
interpretation of the reported hazard ratios. Am I
missing something or is the reviewer wrong? Other than
for interpretation, is there another reason to
transform an independent variable in the Cox PH model?

Thank you in advance,
Ricardo.
===========


Stephen
=============================================
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research (ISER)
University of Essex, Colchester CO4 3SQ, UK
Phone: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
Survival Analysis Using Stata: 
http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/index.php

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