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I am currently trying to apply survival analysis to several tree species which were monitored for growth and phenology for 4 years and separated into three treatment groups. From this data I have created a survival variable which gives me the information of whether the individual died during these 4 years or not. I have thus successfully created for each species data suitable for survival analysis using Surv and survfit functions from the "survival" package to create a R survival object and plot this object for the three treatments.

My question is about how to deal with non events in one treatment group. I have for some species a very small number of events (i.e. deaths) leaving me with quite a high number of non-events (for example, for 360 individuals, only 55 events were recorded across treatments, with one treatment with no events at all).

I have already looked up on the internet how to work with these, and I mainly found that it is ok, the likelihood ratio test is still valid (while the Wald test is not). However, this problem gives me very high values for the hazard ratio (exp(coef)) in the summary of the coxph function (like 1.012e+09 associated with a 0.996 p-value, when it is obvious that there is a significant difference between treatments when you look at the plot.)

I was wondering if anyone could help me resolve this problem :

  • is it ok to have such high estimates of the hazard ratio (exp(coef)) ?
  • does it really reflect the observed difference between treatment, or is the p-value really overestimated ?

Any help with how you would deal with this, or how you dealt with it in your previous experience would be gladly accepted.

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You've come across an issue that can occur with Cox-PH models (actually, just about all survival regression models). That is, if no events occur in one group, then the estimated effect of that group will be $-\infty$. This is very similar to the issue in general linear models with, say, the binomial family, when you have one group with all 0's or all 1's.

If you are just interested in comparing groups (without adjusting for other covariates), this can be still be done with log-rank statistics: see the function survdiff in R's survival package.

My approach would be as follows: use the Cox-PH model on all the groups that observed at least one event. Then, for the group that had no events, use the log-rank statistic to compare with some baseline group of interest. Make note in the report that the log-rank statistic was used because the Cox-PH model resulted in degenerate estimate in the group with no events.

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    $\begingroup$ +1 -- good answer covering the issue arising from the group(s) with no events at all. Also useful to note (for the OP's question) that survival analysis is totally set up to handle the groups that have some non-events (e.g. 55 events and 305 non-events in one group, as described in the question) and that these groups should be handled appropriately by the Cox PH model (as they will be treated as censored) $\endgroup$ May 19, 2015 at 20:34
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I have a similar issue and I would like to ask @Cliff AB with respect to the following:

"My approach would be as follows: use the Cox-PH model on all the groups that observed at least one event." Does this mean to re-group the category with no event with one which has events into a new one "Comorbidity A or B"? I have a categorical variable Cormobitidy and one category has no events (people alive by the end of the study) which has HR = 7.03e-21 compared to the reference and SR = 1.52e-11. The lower limit of CI is 0 and the upper limit is. (the analysis is made in Stata).

Can anyone advise how to interpret this and what to do in these cases? Can a paper be published in such a case?

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  • $\begingroup$ Welcome to CV. Please submit a new question (and make a reference to this question if needed) when you are in this situation (answer should be used only in reply to a specific question). The site works better this way and you increase your chance to get an answer. Thank you. $\endgroup$
    – Pitouille
    Oct 28, 2021 at 10:12
  • $\begingroup$ This does not really answer the question. If you have a different question, you can ask it by clicking Ask Question. To get notified when this question gets new answers, you can follow this question. Once you have enough reputation, you can also add a bounty to draw more attention to this question. - From Review $\endgroup$
    – corey979
    Oct 28, 2021 at 10:39
  • $\begingroup$ Thank you for informing me, @corey979! I appreciate that! I have posted my question under a new title, I hope someone can shed some light $\endgroup$
    – Alexandra
    Oct 28, 2021 at 16:14

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