Survival analysis and competing risks

#1
Hi there, please feel free to move this thread if I've put it in the wrong forum!

Am trying to run some survival analyses for the first time and started with Cox proportional hazard models using SPSS (haven't used R for anything yet but can work out how to do these in R if more sophistication is needed). I have some questions about competing risks and haven't been able to find answers relevant to our situation through various online searches, so hopefully someone here might be able to point me in the right direction!

My question comes down to the assumption of independence between censoring and the event in Cox regression. My understanding is that a competing risk is anything that essentially modifies the probabilities of experiencing the event; technically, you shouldn't censor these people because censoring assumes everyone has the same risk of experiencing the event after the observation period. Various materials on competing risks haven't quite answered the question, and hopefully I'll be able to clearly iterate our situation and my queries here:

- The event of interest is not death, but rather development of a medical condition over a period of time. It seems most of these models were designed to assess death, and so they assume that every person who gets censored will experience this event at some point in the future beyond the study - we can't quite say that assumption holds true with regard to development of disease. Have seen many non-death studies using these models, but am not sure about their appropriateness.
- Everyone who makes it to the end of the study period and does not develop the condition (i.e. remains healthy) gets right censored. Everyone who progresses is marked as having experienced the "event".
- Some people decide to withdraw from the study - they get right censored at the time of withdrawal. (Although some research suggests that people who are lost to follow up in these studies may have various risk factors that put them at greater risk to develop the disease, so we might not be able to treat all of these as "random" withdrawal.)
- Other people withdraw specifically due to ill health - these people might be at greater risk of developing the condition than the average person who withdraws because, say, they moved interstate.
- Some people die during the study period. I've seen other papers right censor these people, but obviously their risk of developing the condition after that point is 0 and violates the independence assumption. A lot of these people who pass away, we don't have exact information regarding when - these people might even have to be interval censored, but have not been able to work out whether you can do multiple kinds of censoring within the same model.

Everything I've been able to find on competing risks talks about something that eliminates the risk of experiencing the event of interest. In our case, the number of people who pass away is quite small in comparison to the number of people who withdraw due to ill health or due to other reasons. We might be able to run with a "cause-specific" proportional hazards model where we consider only progression to the disease and essentially ignore everything else (which seems to basically be ignoring the independence assumption?), but am wondering if there might be a better way to run these analyses.

Any suggestions you might have would be helpful and much appreciated! Thanks.
 

hlsmith

Omega Contributor
#2
I am interested in competing risks, but haven't had an opportunity to run one, so I won't be a tremendous help to you. A comment, as for risk - is the assumption just saying the person has to have some probability of the condition > 0. So you won't have testicular cancer in women.


So are you saying your competing risk is loss-to-follow-up? But you have a few deaths not related to the event of interest?
 
#3
I am interested in competing risks, but haven't had an opportunity to run one, so I won't be a tremendous help to you. A comment, as for risk - is the assumption just saying the person has to have some probability of the condition > 0. So you won't have testicular cancer in women.


So are you saying your competing risk is loss-to-follow-up? But you have a few deaths not related to the event of interest?
Hi there,

Thanks for your comment!

Yes, we have a few deaths not related to the event of interest. Loss to follow up due to illness (as opposed to loss to follow up for other reasons) is a competing risk in this instance, yes.