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I am building a Cox PH model for recurrence-free survival from breast cancer. One of my variables, the number of involved lymph nodes, is highly skewed with many more "0" values than positive integers. It seems to me that this would make any transformation ineffective because this variable cannot be negative. Here is a stem plot of the lymph node data:

 0 | 00000000000000000000000000000000000000000000000000000000000000000000+195
 2 | 00000000000000000000000000000000000000000000000000
 4 | 00000000000000000000000000000
 6 | 000000000000000
 8 | 000000000000
10 | 0000000000
12 | 00000
14 | 0000
16 | 0
18 | 
20 | 0
22 | 
24 | 00
26 | 0
28 | 0
30 | 
32 | 0

A log(X+1) transformation doesn't do anything to normalize the data because there is no data less than 0. How important is it to transform this variable? Would using only values <20 and log-transforming them help more? This must be a common problem; are there any creative solutions to it?

Thanks for your help!

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I think in any modeling the use of transformations should be done primarily if there is reason to believe that the response is most closely related to the variable through the function you use to transform. Usually it is the response that requires transformation to normality and not the covariates. The underlying assumption in regression is that the error term is normally distributed. The covariates are assumed to vary by design and not due to any measurement error and the regression function is the conditional expectation of Y given X. The most important assumption in the Cox model aside from its functional form and the use of partial likelihood is the proportional hazard assumption.

So after all these comments the simple answer is that there is not a real need to transform your covariate. Also i personally do not like rigging up a method to apply a log transformation when the data contains actual zero values.

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    $\begingroup$ Ok that makes sense to me. I was a bit confused because while reading some books on Cox regression, some authors occasionally log-transformed variables in their examples but never really mentioned WHY they were doing it. $\endgroup$ – JJM Jul 12 '12 at 15:05

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