I found the review by Hein Putter to be clarifying on how the risk set in a subdistribution PH model is handled and the distinction between the subdistribution hazard and a cause specific hazard (section 3.3.2 specifically). The key is that failures from competing events, e.g., death, remain in the risk set for the primary event of interest and are given a censoring time that is larger than all event times. In this way, death is worst in terms of time to event and is still counted in the submodel for the primary event of interest. The 1999 Fine and Gray paper gives a more technical description, although tbh I found that paper to be a bit of a slog.
I misspoke on the call about how the CIF is modified by treatment in a subdistribution PH model. I should have said that the model assumes proportional subdistribution hazards (easily relaxed), and the effect of a covariate on the CIF of a particular event is given in equation (1) here. The interpretation is that if a covariate is associated with an increase in the subdistribution hazard for a particular event, it will also be associated with an increase in the CIF for that event. In the subdistribution hazard framework, the CIF functions for absorbing events sum to less than 1, so the interpretation is clean unlike with a cause specific hazard framework. The results can also be reported out visually if the entire CIF curve is of interest, analogously to stacked probability plots.
In a simplified analysis where we look at time to re-epithelialization (or re-epi + discharge?), I think we’re not so worried about non-absorbing states. This is good. Once we introduce transient states we have entered multistate model land. I haven’t actually tried to fit these models using the survival package, although I suspect that it actually is possible even with transient states since the Putter review paper does it. If not, the flexsurv and rstpm2 packages would both be able to accommodate. The situation is definitely more complicated if you have panel data (as I suspect is the case with your version of the ACTT-1 data), but not intractable, same for semi-Markov models.
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