R help - Jun 2014 - prediction based on conditional logistic regression, clogit

I ususally scan the digest for "surv", so missed your question on the
first round.
You caught predict with a case that I never thought of; I'll look into
making it smarter.

As Peter D said, the clogit function simply sets up a special data set and then
calls
coxph, and is based on an identity that the likelihood for the conditional
logistic is
identical to the likelihood of a Cox model for a specially structured data set. 
I
vacillate on whether this identity is just a mathematical accident or the mark
of some
deep truth.  However it did allow us to use existing code rather than write new
routine
from scratch.

In this special data set all of the follow-up times are set to 1 (any constant
value would
do).  For normal Cox regression a predicted "expected number of
events" depends on the
length of follow-up for the subject, so the predict routine expects to find a
follow-up
time variable in your newdata.  In my code, "rep(1, 150L)" is being
mistaken for the name
of the time variable, and failure of the confused routine ensues in due course.

For the interim: in a conditional logistic the "expected number of
events" is just
exp(eta)/(1 + exp(eta)) where eta is the linear predictor.  There is no
follow-up time to
worry about and predict.coxph would have done way too much work, even if it
hadn't gotton
confused.  Use

	risk <- predict(fit, newdata=dat.test, type='risk')
	risk / (1+risk)

Terry Therneau
>
>> >Hi, I am using clogit() from survival package to do conditional
logistic regression. I also need to make prediction on an independent dataset to
calculate predicted probability. Here is an example:
>> >
>> >
>>> >>dat <- data.frame(set=rep(1:50,each=3),
status=rep(c(1,0,0),50), x1=rnorm(150,5,1), x2=rnorm(150,7,1.5))
>>> >>dat.test <- data.frame(set=rep(1:30,each=3),
status=rep(c(1,0,0),30), x1=rnorm(90,5,1), x2=rnorm(90,7,1.5))
>>> >>fit<-clogit(status~x1+x2+strata(set),dat)
>>> >>predict(fit,newdata=dat.test,type='expected')
>> >Error in Surv(rep(1, 150L), status) :
>> >?  Time and status are different lengths
>> >
>> >Can anyone suggest what's wrong here?
>> >

On 17 Jun 2014, at 16:38 , Therneau, Terry M., Ph.D. <therneau at
mayo.edu> wrote:
> As Peter D said, the clogit function simply sets up a special data set and
then calls coxph, and is based on an identity that the likelihood for the
conditional logistic is identical to the likelihood of a Cox model for a
specially structured data set.  I vacillate on whether this identity is just a
mathematical accident or the mark of some deep truth.

My take on this is that it is the latter, but in reverse: The Cox likelihood
works by splitting the event history into a series of conditional experiments:
Given a risk set and that one member must die, work out the likelihood that it
is the member that is observed to die. These experiments are clearly not
independent since the risk set of one experiment depends on the outcome of the
previous ones. However, arguably, it is still sensible to cumulate the
information represented by the log-likelihood contributions.

I.e. you can do condtional logistic regression with a Cox likelihood because the
Cox likelihood _is_ a conditional logistic regression likelihood.

-- 
Peter Dalgaard, Professor
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com