In randomized clinical trials in the efficacy part, often survival analysis is used to analyze the time-to-event data. Since it is randomized (if randomization was done properly) one can assume that there is no confounding due to the balancing of the characteristics across the treatment groups. I quite often saw Kaplan-Meier plots and Cox regression. Of course one can put variables like age into the Cox regression model, because likely age will have an effect. This is Ok, as we have randomized, so the age will be distributed equally across the treatment groups.
In an observational study (assume we have the same setting, just no randomization) one can do the same and indeed Cox Regression is used to analyze observational studies. Cox regression allows to "adjust for confounding effects of other variables". Furthermore:
In order to obtain an effect estimate adjusted for confounders when analyzing survival data, one could use Cox regression analysis. The identification of potential confounders has been described extensively in a previous paper in this series [6,7].
As mentioned before, within our clinical example, one could suspect that age may obscure the association between eGFR at the start of dialysis and mortality because patients who start dialysis at higher eGFR levels may be older and for that reason have a higher mortality. Therefore, the association between eGFR at the start of dialysis and mortality was adjusted for the variable ‘age at the start of dialysis’. In this case age was entered as a second variable into the Cox regression model.
The output of the unadjusted and adjusted Cox regression analyses of model 1 is presented in table 3. In most statistical packages the output of the Cox regression analyses provides at least a HR, with its 95% CI and an estimate of the regression coefficient β. The β estimate is directly related to the HR because HR equals eβ. Thus the HR and β provide information on the strength of the association between eGFR and mortality. When comparing the HR or β of eGFR of the unadjusted model (HR = 1.30; β = 0.26) and adjusted model (HR = 1.21; β = 0.19) it is possible to judge how strong the confounder age affected the association between eGFR at the start of dialysis and mortality. The HR and β of high-medium eGFR in the unadjusted model are different from those in the adjusted model, meaning that age is a confounder in the association between eGFR at the start of dialysis and mortality.
1. Now I don't get why in both settings Cox regression is used?
Cox regression does make it possible to adjust for confounders. Randomization has the advantage that it allows to balance the observable plus the unobservable characteristics equally across the treatment groups. Cox regression does not do this, because we can only put in variables we observe. 2. Is it that?
Cox regression in an observational study might tell me that age does have an influence. When I put it into the model "I control for it". 3. If that was the only variable to worry about it and we can assume for the rest an "ideal world" – so age was the only potential counfounding variable – does this mean that at the end I get a perfect true estimate in terms of I completely removed the confounding out of it and in this case (only this variable makes the confounding) I get the "same result" as with randomization? 4. I don't have to randomize, because the model does the job? Assuming there are no further confounders and especially no unobservables.
Cox regression in a randomized trial where for example age is equally distributed / balanced across the treatment groups still might show me that age does have an influence, so I put it into the model and it has a significant estimate. What is the difference to the setting of having the same study as an observational study and doing the same – age as a covariate in the Cox regression – and getting the same result – age does have a significant estimate. So no matter if randomized or observational and therefore no matter if age is balanced or not: in the Cox regression using it as a covariate is something else. I don't get this point somehow.
5. I thought that if Cox regression tells me that age has an influence, so I put it into the model and get a significant estimate, this tells me that age has an influence and if the age is not distributed equally in my observational study this tells me that my analysis is worthless? Or: 6. does the Cox regression "solve this issue" – that the age is not equally distributed across treatment groups in my observational study (and assume age really is not equally distributed) – but since I take it into my model I adjust for this confounders and I can use the final estimate and I do have a good estimate for the treatment effect? 7. If age in reality has no influence then no matter if it is equally distributed or not in my observational study, when I put it into my Cox regression model it will show me no significance and the estimate will be the same as when I use the same model but without the age as a variable (to be specific: covariate) in it?
I do not get the connection of the Cox regression in an observational study to propensity score matching. I know what propensity score matching is and what it does (or at least I think so). 8. Now how is propensity score matching connected to the Cox regression? 9. When I have a Cox regression in an observational study:
- **when (in which circumstances) and **
- **should I do **
- do I have to do
- am I able to do
propensity score matching?
I could perform a propensity score matching before doing the Cox regression. So then the covariates are balanced. 10. But what advantage does this have? 11. How does that change the Cox regression? 12. After propensity score matching I still have the same variables, but now I can run the Cox regression without these covariates, because if I would put these into my model there would be no significance and the estimate of my actual variable I want to analyze would be the same as in case of using the covariates? 13. But why should I then use propensity score matching, how does make that my whole approach better? 14. In propensity score matching I can also just match on the observables, those observables I could also put into my Cox regression? If I assume that my propensity score matching was really perfect, so ideal world, why is my cox regression afterwards then better? Because then I apply it on another treatment assignment, because the treatment was due to the propensity score so to say reassigned. 15. So I can get different estimates. But this is only a benefit, if propensity score matching for whatever reasons is better – otherwise I could put the same variables into my Cox regression, so when and why is there a benefit of doing propensity score matching before? Furthermore I do not understand the following here in this case: Let's consider age again. When propensity score matching is used age is balanced. But when I put it into my Cox regression it could still be significant, because age might have an influence (although it is balanced across treatment). So it is a confounder. 16. What is the point here?