I want to understand which model to choose for my task and advantage/disadvantage of each model. Basically, I am working on longitudinal patients data. I want to build a model to understand the factors associated with patient rehospitalisation within two years from the day they have been discharged. Some of the factors are age, location, chronic disease, number of GP visits etc.

One of the published paper which we are referencing is using cox proportional model to report hazard ratio. I don't know the model and its theory behind it. I am planning to use logistic regression and use the odd ratio to report the relative contribution of each independent variable to the dependent variable. Majority of my independent variables are categorical variables.

Could any statistician explain why I should use cox proportional hazards model instead of Logistic regression?

If I choose logistic regression over cox model, what is the disadvantage of it?

Will the strength of odd ratio report similar relative contribution of each independent variable to the dependent variable as hazard ratio?

The Cox model is used when the outcome is a number (possibly censored, such as time to death) while logistic regression is for binary events (dead/alive).

Data - Do you have data on patients by way of how many days/months after discharge they were readmitted? Or do you have binary data - readmitted within 2 years, not re admitted within 2 years.

If the latter, use logistic regression - if the former, the cox model. My hunch is you have the days information availbale.

Question - Now, Do you care if the patient returned within 1 month as compared to 23 months? If yes, use cox. If no, logistic regression.
Cox will be able to give you the risk associated with rehospitilisation over the 2 years.