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!