Cox Model vs. Logistic Regression for comparing two treatments?

Question

I am trying to choose which statistical test(s) to use for my study. It is a retrospective cohort study comparing the outcomes of 2 different surgical oncology techniques (Let's call them Treatment X and Treatment Y). The primary outcomes are local recurrence, metastasis, and mortality. Note that these are all dichotomous variables. What would be the advantage of using Cox Proportional Hazards versus Logistic Regression in this situation?

I realize that Cox is typically used used for mortality since the time to death is of interest, however the other binary variables (recurrence and metastasis), though they CAN be analyzed as a time-to-event, don't fit as neatly in that paradigm. Instead, we probably would just want to know the overall risk of local recurrence or metastasis happening, regardless of the time it takes. This makes me think that logistic regression would be more appropriate for these variables.

Finally, I was wondering how I would go about calculating a sample size for this study? Like my username states, I am a total stats noob...We would like an alpha of 0.05 and a power of 0.80. Recurrence is our primary outcome, and previous studies have shown that it occurs at a rate of ~20% following Treatment X. Recurrence rate data is not available for Treatment Y. As for the proportion of patients that will be in each group, I have no idea...How is one supposed to know this without actually collecting the data? Do you just estimate from the literature? Would it be appropriate to "fix" the ratio of subjects in Group X : Group Y at 1, i.e. get an equal number of people in each group? Or do I have to just collect the data chronologically in order to maintain internal validity?

I apologize for my lack of knowledge and the length of this post. Any help would be much appreciated. Thank you!

Answer 1

It generally makes little sense to throw away information in this type of study. Yet that is what you would do if you ignore the timing information about recurrences and metastases. And, at my age at least, there is a big difference between a recurrence or metastasis in 2 years and one in 20 years. In 2 years I won't yet have reached my biblical three-score-and-ten years; in 20 years I am likely to have died already of something else. Survival analysis is clearly called for.

You have 2 treatments, X and Y, being compared in a retrospective study. There are enough important issues hiding in this type of analysis that you really should be getting advice from a statistician with whom you can have a useful give-and-take rather than forging ahead based on what advice you can get from a site like this.

This brings to mind my first exposure to survival analysis 45 years ago, when a surgeon I was working with did a retrospective analysis of breast cancer cases. He compared radical mastectomy against lumpectomy, and found that those treated with lumpectomy did much worse. So I asked him, naively, what considerations informed the choice between the two approaches. Back then, radical mastectomy was the standard of care. He told me that lumpectomy was reserved as a palliative treatment for those who were too ill to undergo the rigors of radical mastectomy. So it wasn't so surprising that the really sick people having lumpectomies died sooner than those having adequately good clinical prognosis to receive radical mastectomies. Lumpectomy wasn't worse on its own, and now is often the standard of care.

The standard of care for surgical management of breast cancer has changed since then, but the fundamental difficulty in retrospective comparisons hasn't. Simply comparing outcomes between groups of patients who received 2 different therapies is fraught with this type of difficulty unless the therapies were chosen as part of a randomized trial. There are ways to try to take differences in the underlying status of patients into account, but these are not the type of thing that a "stats noob" should be attempting without strong support from an experienced individual. You certainly can learn how to do these things, but "do not try this at home" on your own for your first attempt.

In terms of study size, this is a retrospective study so you presumably can go back far into the past to collect case information. Again, you don't want to be throwing away information. So the size of the study should be all cases for which you have reliable data. This is different from controlled prospective trials, where pre-study power calculations are very important. If there are limitations on resources for collecting the retrospective data, and you have a reasonable estimate for recurrence rates following treatment X, then it's possible to estimate the magnitude of outcome difference you might be able to detect between the 2 treatments, given a particular number of cases and recurrence/mets/death events. Given the difficulties posed by having 2 treatments that were not assigned randomly, in a retrospective study, experienced statistical help would again be important. If this project is important enough to do, it should be important enough to do it correctly.