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

[Frank E Harrell Jr]

Thomas Lumley wrote:
> 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
> 
> 
> 

Nicely put Thomas.  I have seen examples from surgical research where 
the hazard function is bathtub shaped and the epidemiologist's use of 
the exponential distribution is very problematic.  I have also seen 
examples in acute illness and medical treatment where time until death 
is important even with only 30-day follow-up.

Frank

-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University