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In this project our objective was to compare the revision rates between two surgical techniques. We have time to revision (time between two surgeries), demographics, and other variables we are comparing among the two techniques. Reviewers of the article wrote that we need to use Cox regression. When using Cox regression all of the cases will have the event (revision surgery) and our covariates will be entered. Can I still look at the differences between the two techniques like I would in a KM survival by the log rank? How would I set this up in SPSS?

Additional information. The percentage of pts needing revison is extremely low, only 1.2%, out of 7400. In answer to one of the post, there are pts who may still need a revision, the last operations were in December of 2011. However, the majority will not. I am learning SAS but I haven't done any survival analysis as of yet.

Thank you for all the post. I just want to make sure I'm on the right track. We only have data for the patients that have had a revision. All pts will have the event in the cox regression. The majority of pts will not have the revision surgery, however, we don't have access to any of the data from these patients. Does this change any of your suggestions?

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    $\begingroup$ This question came up in comments to my answer - do all patients have revision times because revision is inevitable, or because only revision-needing patients are included? Those are very different problems. $\endgroup$ – Fomite Dec 13 '12 at 1:38
  • $\begingroup$ Thanks for the updated info. You would want to censor the un-revised patients at the last time for which they were known to be revision-free (e.g. if you last checked the surgical database on 31st November 2012, this would be the censored date for these not-revised-yet individuals.) SPSS should be able to handle this just fine. $\endgroup$ – James Stanley Dec 13 '12 at 23:52
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I have no idea how one would set this up in SPSS, it's not my software of choice.

To answer your question however, yes, you can use Cox regression to look at the relative difference in time-until-revision for the two techniques. There are other techniques you might try, but Cox proportional hazards models are by far the most commonly used I see in clinical literature.

Having all events isn't a problem (indeed, it lets you get around censoring, which is nice), and will let you control for your covariates, which is somewhat harder to do when using a KM-based approach. My one recommendation however is, if you're not comfortable with what you're doing, to go find someone in your department, university, etc. who is comfortable with survival analysis, and talk to them.

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    $\begingroup$ Actually, having all events in this context might be representative of a problem -- if everyone in this dataset is having revision (nobody is censored), does this mean that people who had the first surgery and haven't needed revision are not in the dataset? This will bias the results, as you're only comparing profiles of people who needed the surgery revised. $\endgroup$ – James Stanley Dec 13 '12 at 0:53
  • $\begingroup$ My impression was that revision was inevitable, its a question of time. But that would likely be a good question for the OP. $\endgroup$ – Fomite Dec 13 '12 at 0:56
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    $\begingroup$ If revision is inevitable and the OP knows the time to revision for each subject for each of the 2 treatments, then why not simply compare mean (or may be median) times to revision between the treatments? Why use methods designed to deal with censoring when there is no censoring? $\endgroup$ – RioRaider Dec 13 '12 at 1:34
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    $\begingroup$ @RioRaider Because Cox methods were not necessarily only designed to deal with censoring. The OP mentioned covariates - while you might still be able to look a median times over a small number of strata, what about a continuous covariate? Just because Cox models can handle censoring doesn't mean they're inappropriate for questions not involving censoring. $\endgroup$ – Fomite Dec 13 '12 at 1:36
  • $\begingroup$ @EpiGrad More info from the OP would help. I think in this possible scenario it then makes the lack of non-revised people a question of inefficiency -- that you are only including people once they've had a revision, and ignoring them up until such a point -- which means missing out on one of the major strengths of PH and survival models (that censored people can contribute for their known follow-up time). (I still think this could bias results, unless we're dealing with purely historical data for a closed time period with complete follow up to event for all participants, which seems unlikely.) $\endgroup$ – James Stanley Dec 13 '12 at 2:19
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I'll expand on my points in the comments above. In short, 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.

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