Is is acceptable to use cox proportional hazard regression when time-to-event is a discrete, numeric variable? I recently submitted a paper where I performed a cox proportional hazards regression model modelling the effect of group allocation in a randomised controlled trial on treatment retention. The event was dropping out of the study (non-reversible binary event) and the time to event variable was the week that the participant dropped out, which was a numeric variable with possible values 1-12. These values were discrete, i.e. no fractions of weeks.
The reviewer of my paper has stated that the outcome we used was "not continuous, so they were not an appropriate choice for time to event analysis".
Is the reviewer correct? The answer to this post indeed does suggest the the Cox PH model is not appropriate for discrete data and references Singer and Willett's Applied Longitudinal Data Analysis: Modeling Change and Event Occurence. Now I have read the book and while they do say that if the time-to-event variable is continuous you cannot use discrete-time survival analysis, I cannot find anywhere where they state that the reverse is true: that you cannot use a cox proportional hazards model for a discrete, numeric time-to-event variable. Furthermore the biostatistician we consulted advised us to use a cox regression model.
If the Cox Model is not appropriate for continuous time-to-event data can anyone tell me why?

Cox models can be fit with the type of data you are using if your true underlying response is continuous. You might model the time to when they stopped taking their assigned medication (which could have occurred at week 5.1 or 5.5) and assume that your data are interval censored (you know that the event occurred between week 5 and 6 but you don’t know exactly when).
See here for more information on interval censoring.
You might also do pooled logistic regression for your analysis. In pooled logistic regression analysis of survival data, continuous time is discretized anyway, so the fact that your data are discrete wouldn’t be an issue.
