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I'm trying to work out the sample size needed for an RCT based on a small study looking at reoperation following index surgery. In this small study, there were 1000 patients, group 1 had 700 versus group 2 had 300 patients. In group 1 there were 20 reoperations and in group 2 there were 30 reoperations. However, survival at 10 years was 15% in group 1 and 12% in group 2. So most patients were no longer at risk of a reoperation. I'm wondering how I would work out the sample size needed for an RCT randomising 1:1 and looking at find a difference of 0.10 reduction in hazard ratio between groups if following up patients for 10 years accounting for death during the follow up period please? My stata code currently looks like this

power cox, hratio(0.90) alpha(0.05) power(0.80)

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It sounds like you have to consider a competing risks model, as many patients evidently die before they need the reoperation, with many more dying than being reoperated. It's possible that the reoperation mainly occurs at early times before there is much death, which might make a focus on reoperation reasonable, but that's not clear from your question. Before you design your prospective study, you should re-analyze your earlier study data with that in mind. The R survival vignette on competing risks shows how to do that. I suspect that Stata has such tools, although I don't use it.

That competing-risks model will give you the basis for designing the prospective study provided that surgical techniques, patient characteristics, etc., stay reasonably similar to those in place in the prior study. I'm not sure if there's any simple formula for calculating the power for this situation. Much will depend on the specific hypothesis that you want to test. For example, do you really care if one group has fewer reoperations if those patients die sooner?

Simulating data based on your competing-risks model seems like the most reliable approach. You generate a very large number of simulated events (both reoperations and death) that match the pattern of your earlier study, but with your hypothesized hazard ratio. Then repeatedly take a defined sample size from your large number of simulated events under the general design of your prospective study and perform your survival analysis. The proportion of samples of that size that show a significant difference at p<0.05 is the power for that sample size. Repeat with different sample sizes until you find that power to be 0.8. There is a survsim function for Stata that might help with this, but I don't have experience with it.

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  • $\begingroup$ thanks very much, i see your point regarding death being a competing risk. in many studies investigating time to events, death occurs before the outcome of interest. ive observed most studies dont actually account for death such as by using a Fine and Gray model. so is this an oversight by the study authors or have i missed something? perhaps it depends on other factors such as how often death occurs? $\endgroup$
    – MFA
    Commented Jul 18 at 14:24
  • $\begingroup$ @MFA it depends a lot on the particulars of the study. Unfortunately, many reports in the biomedical literature haven't been well vetted during peer review for the quality of statistical methods. I'd recommend against Fine-Gray for a situation in which death often precedes the event of interest, as it treats those who have died as still being at risk in some way for the other event. See the vignette on competing risks linked in the answer. $\endgroup$
    – EdM
    Commented Jul 18 at 15:16

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