Dear partners, Cox proportional hazards regression is a very efficient and elegant method for analyzing survival data. However, in recent months I have found several examples of authors using binary logistic regression, for the dichotomous event death, with the condition that the follow-up of all their patients is complete and have no censored data. Although it can not be ruled out, the authors do not discuss about competitive events but possibly have them. The question is, if follow-up is complete, are both methods comparable? What is the effect of competitive mortality in the odds ratios of logistic regression? In addition to that I do not find LR to be an elegant method for survival data, what mathematical argument exists against using logistic regression in this context?
In LR the impact of covariates on odds of survival/non-survival with respect to fixed time thresold say t_0 are assesed while cox model asses the impact on entire time axis. The survival function being a one-one function of the hazrd function, having estimated the hazard function through Cox model, equivalently the survival function can be estimated and the epoch t_0 at which the event of death can be considered almost certain, say S(t_0)
I feel using LR is mathematically correct but gives much limited information than Cox. LR will tell about survival below or obove a fixed time point t_0 while cox will elaborate the information on the entire time axis.
As a friend described above, employing LR in a condition that you explained is meant ignoring the role of time for the event to happen. The other problem vis-a-vis LR is the possibility that this model assumes censored events as survivors.
This is another question What about using Cox Regression (instead of Logistic Regression) when all follow up times are the same and there are no censored data? I just read a manuscript where they do that. What could the advantage be?
I think both can be mathematically correct. However, with binary logistic regression time-dependent information is lost, which may be interesting in some contexts.
Logistic Regression can be useful in making predictions - if all conditions met -, which Cox lacks. imho.
Cox regression can be used only in case of proportional hazards model . In case of non proportional hazards the 'odds model' from the Royston Parmar family of flexible survival analysis is an attractive option. However, i am not aware of methods to explore competing events with it.
My view is that with a logistic regression, although valid from a mathematical point of view, we lose the concept of instantaneous risk, expressed through hazard ratios. For me this will be an important aspect insofar as the cumulative probability, for example, in the medium term, can be conditioned by a complex clinical outcome. The professional statistician's view may be interesting here.
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