[R] prediction based on conditional logistic regression, clogit

[peter dalgaard]

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
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