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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?
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?