We want to model the retirement of employees. We have data on a yearly base for about 20,000 employees by age and some other properties.
There are two questions:
Suitable Approach
In most cases we have only the data of one year available: We know who left at the end of that year and how old he/she was when leaving. We modelled it as a survival model where "leaving" is the event and anybody who stays is regarded as censored data. Age is regarded as event time. Observation time is actually the last day of the year. This is slightly different from textbook's survival examples, where observation takes place over a long period of time. Is our approach suitable and does not violate any assumtions of the popular survival models?
Choice between Models
For some combinations of age and properties there are no data of retirement available in the year of observation. We want to estimate the retirment rate for these combinations. For that reason we tried the Cox Proportional Hazard model. However, because no combination is completely available over all ages, the baseline hazard function seems not to be well definable.
We have the idea to use the complete data set to model the baseline hazard by duplicating the data and introducing a new value ALL for all factors which replaces the true factor value in the copied data. Is this a valid approach for Cox PH or even for the fit of parametric models?
Another idea is to use a logistic regression for the event "retirement" on the variables "age" and the other factors. However, isn't this basically equivalent to the Cox approach?
For information here is a plot of a fitted Kaplan-Meier model:
A normal logistic regression with R (family=binomial()) doesn't fit well:
When running a glm with family = binomial(link="cauchit") the regression line looks better but is still not optimal:
EDIT: I have asked this question on Quora too to get some opinion based answers aditionally.
