# Considering competing risk of death in R

I am doing a survival analysis where my event of interest is time to operation, so what I have coded my status variable is as below:

Status 1 0 2, where 1 means operated, 0 means non-operated and 2 means they had no operation and died before end of follow-up.

So, in my cox regression what I do is:

m1<-coxph(Surv(time, status ==1)~exposure+covarite2+covariate3+..., data)

summary(m1)

my question is that inside the

Surv(time, status ==1)

, using status ==1 is correct and means that I am considering for competing risk of death? I should mention that I am aware of competing risk of death using Fine and Gray model, but I am not interested in applying this model. I appreciate any guidance in this matter.

• Sounds like you need to use death as a censoring event and not a competing risk. You seem to understand this well enough, but it's important whether your treatment of death is as a censoring event - not a competing risk. Commented Apr 2 at 16:13

Using Surv(time, status ==1) as the outcome effectively censors both those that died without operation and those who hadn't yet been operated upon at last follow up. One might argue that you aren't really "considering the competing risk of death" in that case, as you are treating death and lack of operation the same.

As the competing risks vignette notes in Section 3.1, however, the Cox regression coefficients for the "operated" event can be the same as you would get for a full multi-state model when you have competing risks. What you lose by proceeding the way you propose is any modeling of covariates that are associated specifically with death, and the ability to evaluate the probability of each outcome over time.

It probably makes sense to use Surv(time, status) as the outcome. Provided that 0 represents the no-operation/no-death censoring status, you can get a more complete and potentially more useful model, depending on how you intend to use the results.

• This means that what I am doing in the code above is not considering competing risk of death as I am censoring that. right? Your suggestion is multi-state modelling? my event of interest is time to operation however, I have individuals who never got operation and died before end of fup. Commented Jan 4, 2023 at 12:58
• @user358238 you are correct. Even if your primary interest is in time to operation, however, you seem already to have the data for a full model for both operation and death as events. Why not do that? It's a pretty simple competing-risks form of a multi-state model. That will provide the same information you would get with a single model for time to operation, plus provide information about the factors associated with the competing risk of death.
– EdM
Commented Jan 5, 2023 at 13:49
• what if to do two cox model 1) Surv(time, status ==1) and 2) Surv(time, status ==2), where status == 1 is the status for operation and Status == 2 for death. This means to have two set of results. Is that same as doing the a multi-state model. Do you agree? And, if so then I need I need of course interpret them separately. Commented Jan 5, 2023 at 18:47
• @user358238 the R competing risks vignette shows this type of model in Section 3.1. Yes, there are two sets of results, one for each event type, but you get the two sets of results from a single multi-state model. The advantage of the combined model is that you can estimate the survival curves properly for each type of event, which you can't do with separate models.
– EdM
Commented Jan 5, 2023 at 19:02
• @ EdM I see your point for suggesting this model. Despite the advantage of estimating the survival curves properly for each event using multi-state modelling, I want to know for association having two separate cox models is wrong or same thing? Let's say model1 = coxph(Surve(time, status ==1) ~age+gender) and model 2 = coxph(Surv(time, status ==2 )~age+gender). And also, how can I interpret each let's say for instance HR of age from each of the models. How can I interpret? I can get the same HRs from multi-state yes? Commented Jan 6, 2023 at 21:24