Please help me interpret these research results

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Foot Fetish

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We conducted a retrospective cohort study to investigate 3 different treatments for the same disease. Let's call them Treatments A, B, and C. Treatment A is the "gold standard" because it's associated with the lowest rate of recurrence.

We constructed a multivariate Cox model. When compared to Treatment A (the reference standard), Treatment C was an independent risk factor for disease recurrence (Hazard ratio = 3 , p < 0.001). Treatment B was ALMOST an independent risk factor, but the p value was just shy of the 95% CI (Hazard ratio = 2, p = .08).

However, when we compared Treatment B and Treatment C head-to-head with a Chi square test, the difference in recurrence rate between them was not significant (p = 0.3).

How do you interpret these findings? Namely, what's the verdict for Treatment C? Based on the Chi square test, can we say that it's just as good as Treatment B for this disease? Or do we focus on the results of the Cox model and conclude that it's not as good as treatment B?
 
Give 95% CIs for your HRs. My guess is your sample is too small so you are losing out on precision.

Also, why do you need to evaluate B vs C if A is the gold standard? Everything should be relative to that.
 
Do you care about the time to outcome (recurrence here?) or just the proportion of outcomes? The Cox regression models the the former while the chi square provides evidence for the later. You should pre-specify a primary outcome and analyze the outcome as appropriate. You should not select the methods used based on the significance.

Make sure you are interpret the Cox model correctly. As stated it appears you have the treatment A group as the reference group and report hazard ratios and p-values comparing treatment B to treatment A and treatment C to treatment A separately. The fact B is significantly different than A but C is not significantly different from A does not mean that B is significantly different than C. You can test this separately.
 
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