[R] Comparing COXPH models, one with age as a continuous variable, one with age as a three-level factor

[Bond, Stephen]

Totally agreed.

I made a mistake in calling the categorization a GAM. If we apply a step function to the continuous age we get a limited range ordinal variable. Categorizing is creating several binary variables from the continuous (with treatment contrasts).

Stephen B
-----Original Message-----
From: Frank Harrell [mailto:harrelfe at gmail.com] On Behalf Of Frank Harrell
Sent: Thursday, September 02, 2010 4:23 PM
To: Bond, Stephen
Cc: r-help at r-project.org
Subject: Re: [R] Comparing COXPH models, one with age as a continuous variable, one with age as a three-level factor

On Thu, 2 Sep 2010, stephenb wrote:

>
> sorry to bump in late, but I am doing similar things now and was browsing.
>
> IMHO anova is not appropriate here. it applies when the richer model has p
> more variables than the simpler model. this is not the case here. the
> competing models use different variables.

A simple approach is to have the factor variable in the model and to 
formally test for added information given by the continuous variable 
(linear, quadratic, spline, etc).  AIC could also be used.

  >
> you are left with IC.
>
> by transforming a continuous variable into categorical you are smoothing,
> which is the idea of GAM. if you look at what is offered in GAMs you may
> find better approximations f(age) as well as tools for testing among
> different f(age) transformations.

I don't follow that comment.  Smoothing uses the full continuous 
variable to begin with.

A restricted cubic spline function in age is a simple approach.  E.g.:

require(rms)
dd <- datadist(mydata); options(datadist='dd')
f <- cph(Surv(dtime,death) ~ rcs(age,4) + sex, data=mydata)
plot(Predict(f, age))

Note that you can always expect the categorized version of age not to 
fit the data except sometimes when behavior is dictated by law 
(driving, drinking, military service, medicare).

Frank

>
> regards.
> S.