[R] what is the difference between survival analysis and (...)

[Thomas Lumley]

On Wed, 28 Mar 2007, Frank E Harrell Jr wrote:

> Eric Elguero wrote:
>> Hi everybody,
>>
>> recently I had to teach a course on Cox model, of which I am
>> not a specialist, to an audience of medical epidemiologists.
>> Not a good idea you might say.. anyway, someone in the
>> audience was very hostile. At some point, he sayed that
>> Cox model was useless, since all you have to do is count
>> who dies and who survives, divide by the sample sizes
>> and compute a relative risk, and if there was significant
>> censoring, use cumulated follow-up instead of sample
>> sizes and that's it!
>> I began arguing that in Cox model you could introduce
>> several variables, interactions, etc, then I remembered
>> of logistic models ;-)
>> The only (and poor) argument I could think of was that
>> if mr Cox took pains to devise his model, there should
>> be some reason...
>
> That is a very ignorant person, concerning statistical
> efficiency/power/precision and how to handle incomplete follow-up
> (variable follow-up duration).  There are papers in the literature (I
> wish I had them at my fingertips) that go into the efficiency loss of
> just counting events.  If the events are very rare, knowing the time
> doesn't help as much, but the Cox model still can handle censoring
> correctly and that person's approach doesn't.
>

Certainly just counting the events is inefficient -- the simplest example would be studies of some advanced cancers where nearly everyone dies during followup, so that there is little or no censoring but simple counts are completely uninformative.

It's relatively hard to come up with an example where using the total-time-on-test (rather than sample size) as a denominator is much worse than the Cox mode, though. You need the baseline hazard to vary a lot over time and the censoring patterns to be quite different in the groups, but proportional hazards to still hold.

I think the advantages of the Cox model over a reasonably sensible person-time analysis are real, but not dramatic -- it would be hard to find a data set that would convince the sort of person who would make that sort of claim.

I would argue that computational convenience on the one hand, and the ability to exercise lots of nice mathematical tools on the other hand have also contributed to the continuing popularity of the Cox model.


     -thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle