You can perform a poisson regression analysis where duration of stay is the dependent variable and outcome is independent variable.

Survival analysis is not appropriate for this situation because you need a time to event variable for survival analysis.

Survival analysis is, of course, appropriate, since you have a time variable (stay). Indeed, it is a very powerful method because you can examine different patterns of stay which may not be reflected adequately in single summary measures such as mean length of stay. 

When graphing your results, you should use a 'failure' graph (starting at zero rather than at 1) to show the cumulative discharge rate. I've attached such a graph to illustrate. It shows time from arrival in accident and emergency to receiving analgesia. 

Survival analysis and you can also Logistic regression

Ronan

Could you be more specific how survival analysis is applied to this situation?

Stay time can be considered time to release from hospital. But there will be no censors in this case. One might obtain failure graphs. How will the association between patient's outcome and stay time be interpreted in this case?

Mehmet : Survival analysis does not require censored data. It's that simple. The presence of censored data is a nuisance in the analysis, but it's not required. The statistical tests and models (log rank, wilcoxon, cox) have their normal interpretations.

Oluwafemi : Note that logistic regression does not test for differences in the patient experience. It critically depends on the choice of a time point. It is not appropriate unless you specifically want to test a particular time point a priori. This can occur when the time point is of interest – for example, you might have a policy that patients should have a waiting time of less than 3 hours, so the three hour time point is an appropriate one to create a variable for logistic regression. 

Thank you so much for the valuable feedback