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st: log-transformed variable in Cox PH


From   Jenkins S P <[email protected]>
To   [email protected]
Subject   st: log-transformed variable in Cox PH
Date   Sat, 4 Feb 2006 17:56:09 +0000 (GMT)

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 <[email protected]>
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 <[email protected]>
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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