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I don't think Cox regression is going to give you a valid answer to your question. I do think it would be the best method for answering your question, but without the data on the clinical/demographic profiles of the non-revised patients it's only going to give you invalid estimates of the hazard ratios (HR). I'm presuming throughout the following that treatment group is not a randomised element (as in an RCT) but is rather a decision made by clinical providers, and thus likely to be confounded by other factors.
Now for the longer winded version: What Cox regression does is test whether there are different probabilities (hazards) of having the event of interest (revision in this instance) between the groups of interest (treatment groups in your scenario), which includes temporal elements in the analysis.
However, if you only have data for people who have had the event (revision), then your results may well end up being biased (I'd say almost definitely will be biased).
Let's take a simple example of the main comparison, which is whether rates of revision differ between treatment groups. Imagine that Treatment A has a 10% revision rate (and that pretty much all patients who require revision need it in the first 18 months); while Treatment B has a 5% revision rate (but revisions tend to happen with a similar timeframe to Treatment A, i.e. within 18 months of first surgery.)
If you analyse just the data for patients with revision (the 10% of treatment A and the 5% of treatment B groups), you would end up with a null result (a hazard ratio very close to 1) because the timing profiles of the failures look identical between the two Treatment groups -- there is important information for your question (in this scenario anyway, where the timing of failure is comparable) in the patients who didn't end up having the event (revision).
This is just for the main comparison, with no confounders in the Cox PH model. If you then want to adjust for confounders, you'd be in a similarly sticky situation, as the confounder profiles that you have for the two groups would once again be limited to just the people who had the event (revision,) and so you wouldn't be able to get any useful information about the confounder profile of people who didn't have the event. Unfortunately, this is vital to valid estimation of the adjusted hazard ratio for your main comparison (treatment A vs treatment B).
So -- if you don't have any information on potential confounders for the patients who didn't have revision then you're not going to be able to adjust for confounding of the risk of revision, regardless of what model you might take (see below). This means that you're really limited to estimating an unadjusted effect of treatment (i.e. no adjustment for confounding.)
You could either approach this using Cox regression -- in which case you'd need to work out a censoring time for the people who didn't have revision (which would usually be the time at which the people were last known to have not had revision, usually the time at which a database was extracted, depending on the study context.) Alternatively, you could use Poisson regression to estimate rates of revision in the two groups, in which case you still need to calculate person-years at risk (cumulative person-time from initial surgery to either the revision or to the end of follow up) for your two groups.
In either case, you're still missing out on one of the main advantage of regression models, which is adjusting for confounders. But unfortunately I don't think there is any way around this.
James Stanley
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