Defining time in Survival I am doing a research on ministerial stability (survival) and I am trying to explain what makes a minister to leave the office before the end of the government (cabinet). Event is defined as any ministerial resignation, which happens when the government is in power (for example, ministerial changes after elections won't be seen as an event).
However, I can't find how to properly define time variable:

*

*Days in the office, e.g. 576 days

*Minister time in the office related to the maximum numbers of days he/she could work there (because at some time the cabinet will be out because of the elections. For example, if a government was in power for 1000 days, and the certain minister left the office on day 545, the time variable should be 0,545.

Cox PH and Kaplan–Meier results with different time definition are very much different.
My first plan was to define time as a time in office related to max days, because I don't want the model to be affected by unstability of the government as such. My dataset has cases with governments lasting from 97 to 1500 days, so I am a bit confused by that. Also, I am more interested to what happens to the ministers when the government is about to end rather than what happens to the ministers after 500 days in the office.
However, if I use the first definition the governemnt change won't affect the model?
Data example:
|Max days in office  | Actual days in offcie (time1) |Actual days / Max days (time2) | Resigned (status) | X|
| -------- | ------------- | -------- | -------------- |-------------- |
| 1461| 879| 0,6016 | 1 | 0
| 1461| 180| 0,1232 | 1 | 1
| 1461| 573| 0,3922 | 1 | 0
| 719| 719| 1 | 0 | 1
| 1458| 1458| 1 | 0 | 1
| 1458 | 979| 0,6715 | 1 | 0
| 611 | 611| 1 | 0 | 1
res.cox <- coxph(Surv(time1, status) ~ x)
res.cox <- coxph(Surv(time2, status) ~ x)

 A: Choice of time scale is an important and subtle issue in survival analysis.
The basic question is which comparisons you want to do.  In the Kaplan-Meier curve, the steps are computed by looking at the number of events as a fraction of comparable individuals (under observation and at the same time since time zero).  In the Cox model, the comparisons are between individuals who are under observation and at the same time since time zero.
You will often want to do more than one analysis, so let's look at a few

*

*Time since becoming Minister.  People are most comparable when they have been in the position for a year (regardless of when they started)

*Time since start of government. People are most comparable when the government has been in office for a year (regardless of when they were appointed)

*Time until next election. People are most comparable when it's a year until the next election (regardless of when they were appointed).

For the second and third of these you need a start time and end time for each individual as well as an event indicator, because appointment doesn't happen at the same point after time zero for everyone.

*

*Surv(duration, did_resign): everyone starts at zero days of being Minister and goes until they stop at an election or resignation

*Surv(appointment_days, leaving_days, did_resign): appointment_days is the number of days after the start of the government that they were appointed, leaving_days is the number of days after the start of the government that their term ended (due to election or resignation)

*Surv(appointment_days, leaving_days, did_resign): same, but now with zero as the election date.  Software might not like negative times, so you might have to add on the maximum length of a term or something.

For the third one, you have to worry about informative censoring (depending on the political system) -- for example, in some countries an event leading to ministerial resignation might also lead to an early election, so the 'time to election' isn't predictable in advance.  If there's a well-defined 'time to routine next election' you could use that instead
I don't think fraction of available time is likely to be a good scale, but you can do it by taking the first option and dividing by the time to election. You get the informative-censoring problems of option 3 this way, though.
Differences between people that aren't automatically controlled by the time scale can still be adjusted in regression modelling, eg, you could use option 1 and a covariate giving the time since the start of the government (or the expected time remaining) at appointment.
