From another reviewer for a paper submitted to Circulation CV
Outcomes:

A problem in current "state of the art" reporting of cardiovascular
trial results in major clinical journals (and in the wording of the
CONSORT statement) is the failure to appreciate the importance of
competition between events. By nature, a clinical trial follows closed
cohorts of treated and control patients. If treatment reduces
(relative to control) the risk of, say, cardiovascular (CV) death, but
does not affect non-CV death, the risk of non-CV death among treated
subjects will be higher than among controls even if the rate of non-CV
death is the same in both groups. This is so because the subject-time
of follow-up for treated subjects exceeds that for controls due to the
lower CV mortality. 

This has consequences for trial reporting that are not always
appreciated. A Kaplan- Meier (KM) curve for death of any cause is
interpretable (i.e. shows proportion of subjects alive over
time). Censoring in the data needed to construct this curve occurs
only when follow-up is terminated in a patient who is still "at risk"
of death. On the other hand, a KM curve for CV death is not
interpretable (does not show proportion of subjects alive over time)
because the data used to construct this curve are censored for (i)
termination of follow-up in a patient who is still "at risk" of any
death, and also for (ii) occurrence of non-CV death. Note that in the
latter case the subject concerned is no longer "at risk" of CV death,
and that this type of censoring is "informative", something that is
not allowed in KM analysis. 
Outcomes that combine non-fatal and fatal events are subject to this
problem too. For example, the combined outcome MI, stroke or any death
can be compared between treatment groups by an interpretable KM
analysis, with all censoring being non-informative. 

The corresponding KM-curves can be interpreted as event-free
survival. On the other hand, the combined outcome MI, stroke or CV
death cannot be compared between treatment groups by an interpretable
KM analysis. The analysis is subject to informative censoring for
non-CV death, and the corresponding KM-curves can therefore not be
interpreted as event- free survival. It would have been useful to
confront the readership of Circulation with this problem in current
"state of the art" reporting of cardiovascular trial results. The
example from the BARI trial chosen by the authors might have served
this purpose because the KM-analysis for non-fatal MI is by definition
informatively censored for any death before non-fatal MI. Clinically
this is not a very straightforward example however, the reason being
that "any death before non-fatal MI" is difficult to define. If a
subject dies on the same day that the diagnosis of MI is made (not an
unusual sequence of events...), does one classify this as "any death
before MI", or as "non-fatal MI"? This problem of 
definition does not affect the interpretation of the KM analysis for
the combined outcome MI or death as shown in figure 2, but surely
affects the definition of MI in Figure 1B (I come back to figure 3
later). This paper in its present form fails to clearly define the
problems posed by competing risks in a manner that is understandable
to a general clinical readership. Introducing the problem as one of
multiple clinical states, with one (or more) state(s) as absorbing,
and one(or more) other(s) as potentially reoccurring is
appropriate. But the model in figure 1B is an (perhaps acceptable)
oversimplification in the sense that it does not allow for another
non- fatal MI after the occurrence of a first one. The paper suggests
that analysing data appreciating that there are multiple outcomes by
multistage modelling and Markov modelling are similar concepts. This
is unfortunate and a clear distinction should be made. 

Markov modelling is a very powerful tool to generate the expected
sequence of clinical events in defined subjects, using data on
transition probabilities that may come, among others, from clinical
trials such as BARI. It is not doable to correct the flaws in this
paper by line-by-line suggestions for correction. Nonetheless, here
are (in addition to the above) suggestions to consider in a rewrite: 


----------------------- Reporting competing risk analyses
http://onlinelibrary.wiley.com/doi/10.1002/sim.7501/abstract