This is a follow up question based on what has been explained here: Survival analysis: continuous vs discrete time but I wish to further confirm it for my case.
I have a dataset collected over a period of 2 years where we observe the degradation of a component and when it reaches a certain degradation threshold, it is considered dead. We collect the measurement of the degradation rate once a month and if the collected degradation rate falls below the threshold at the point of collecting the data, we mark it as 1 for death or if the component still did not reach the degradation threshold at the end of the study, it is considered censored. Some components may also drop out due to possible defect in the middle of the study and is considered censored as well.
So my dataset in the end contains componentid, number of days it survived, status(whether died or alive) and some stress factors that were used to observe the degradation at different stress types for example temperature.
Now what I need to decide is whether I should use a semi parametric cox model or AFT parametric models as when I tried to use the Cox regression model, I am not able to predict when the component will reach its end of life especially for censored observations and this may be due to the observation period being too short to make any estimation for future events. But when I tried using AFT models, it is able to produce predicted end of life in days (this was by using Weibull) and although this works for my case, I need to ensure that I am understanding the mathematical foundation and to consider the appropriate methods.
Picking up from the explanation between continuous and discrete models in The Statistical Analysis of Failure Time Data by JOHN D. KALBFLEISCH ROSS L. PRENTICE on Failure Time distribution and the definition of hazard functions that seem to differe for both cases makes me confused on whether I should deal with my data as a continous or discrete set and if the models I am using indeed satisfies the time distribution.
