Dear List, 
 
I have no idea why my last post was not formatted as I intended. 
Hopefully this will fare more successfully.  My apologies for the last
post.
 
**
Earlier last week I posted a request for assistance with gaining a
better understanding of the criticisms levied against the K-M approach
to survival analysis when competing risks may be a consideration.  I
received several responses which offered genuinely helpful insights and
references.  Others contacted me with a request that I share what I've
learned.  So, with grateful appreciation for all who responded, I offer
this summary.  I hope it is both accurate and useful, and welcome
further input, corrections or continued discussion (what better way to
solidify what I've learned!) 
 
The criticism against K-M survival analysis under certain scenarios *
e.g. when competing risks are to be considered - is that it artificially
inflates the estimates of the actuarial incidence of a critical event. 
K-M ignores the presence of competing risks (CR), whereas the cumulative
incidence model does not.  K-M is therefore not appropriate if competing
risks are to be considered.   
 
My initial concern was whether this was a valid criticism, and
according to several who responded, indeed it is.  From one respondent,
"there is a very strong theoretical background about estimating
incidence of event in competing risk situation and the theory does not
point at KM but on the cumulative incidence function".  That is, the CR
model bases its estimates on actual rates relative to the critical
event, and so more accurately estimates the percentage of events
expected to occur, whereas the actuarial incidence given by the
Kaplan-Meier method is much larger. 
 
It seems that the issue really has to do with the interpretation of the
quantities one is estimating.  So essentially, it boils down to a
question of defining the outcome or the critical event, which then
implies the definition for censoring.  Essentially, censored cases are
those for which we have incomplete information relative to the outcome
or critical event.  Censoring means we will never know if the critical
event would have occurred, and that may be due, for example, to the
death of a case before the end of the study, or its loss to follow up.  

 
A competing risk, on the other hand, means that the critical event
would never have occurred in the first place.  So, it is essential that
we separate those cases which report a competing event from those who
are genuinely censored.  Following are a couple examples: 
 
* Cardio-thoracic surgery - if the critical event is defined as the
replacement of a valve implant, "replacement-free survival" is defined
as the time to replacement or death.  If you are interested in
estimating the proportion of valves still able to function after a
defined period of time, then death is defined as a censoring event.
(Miller, 1999). 
 
* Fertility - If the critical event is miscarriage or stillbirth, then
a live birth is defined as a competing risk; and elective termination is
a censoring event because we know that the critical event would never
have occurred. 
 
The K-M approach estimates the actuarial incidence, which is based on
censoring cases that leave the analysis due to causes other than the
critical event.  In other words, this approach estimates the probability
of being free of a critical event, *if* a patient should live so long. 
By contrast, actual rates give the cumulative incidence of an event up
to a specific point in time, accounting for competing events such as
death. In other words, whether a patient lives or not, the actual rate
gives the likelihood that the critical event will occur. If a patient
dies or experiences an event which prohibits the critical event from
occurring, then the patient is not counted as having experienced the
critical event.  Actual rates assume that only active cases (e. g.,
living patients) continue to be at risk for a future event.   
 
I received one suggestion to consider a method called "relative
survival" which apparently also incorporates competing risks. (Dickman,
2004).  However, at this point, I have not yet looked into this method,
so I can not address it here. 
 
One point of clarification from my initial post, though: I wrote that
the artificial inflation of the estimates, confidence intervals, and SE
in K-M is the result of the decreasing n of cases at risk at later time
points. However, one respondent pointed out that the effects of the
decreasing n of cases at risk ought to be considered independent of the
notion of competing risks. 
 
I hope I've been able to summarize the information accurately and in a
way that's useful and informative.  Unfortunately, there is still one
issue that was not addressed in any detail - whether a statistical
package exists which supports the CR approach to survival.  One
respondent offered, "You should think seriously about competing risks
and [using] SPSS.  They are a very difficult match."  I did locate one
package * NCSS * which seems to support this method.  Might anyone know
of others? 
 
Additional suggested references: 
 
Dickman, et al, "Regression models for relative survival" Statistics in
Medicine (2004), Vol. 23, #1, pp 51-64.)   
 
Freidlin B, and Korn EL, "Testing treatment effects in the presence of
competing risks" Statistics in Medicine (2005), Vol. 24, #11, pp
1703-1712 
 
Kalbfleisch,J.D. and Prentice, R.L. The statistical analysis of failure
time data (1980) Wiley, New York, (chapter 8). 
 
Miller, et. al., "Actual versus actuarial analysis for cardiac valve
complications: the problem of competing risks" Curr Opin Cardiol. 1999
Mar;14(2):79-83.) 
 
 
 
 
John Norton
Biostatistician
Oncology Institute
Loyola University Medical Center(708) 327-3095
[log in to unmask]"
 
Everything that can be counted isn't worth counting,
and everything that is worth counting isn't always countable." 

 - Einstein