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I am using survival analysis to model Treaty ratification, using country-treaty dyads as my primary unit. This means that I have several hundred survival spells covering different time periods (when the Treaty opened onwards).

Other research has used specific years in their survival analysis and regressions, e.g. one Treaty opens in 1960 and is ratified during 1971, another Treaty opens in 1980. The ensuing Kaplan-Meier model is incorrect, because it assumes that Treaties that opened later have been at risk since the earliest Treaty opened but only joined the dataset later. However, I do not understand why using specific years would lead to invalid Cox PH regression results.

Furthermore, I get markedly different results when I adjust by subtracting the time each Treaty opened to give each survival spell a common starting time of zero. What is the correct approach?

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If the time-to-event of interest is the time between a treaty opening and when it is ratified, then the time = 0 reference for each treaty needs to be the data of its opening. Think about clinical survival models of cancer outcomes: what you care about is the survival time of an individual after initial diagnosis, not the calendar date of death.

It can be useful to include the calendar date of treaty "opening" (resp. cancer diagnosis) as a predictor in a survival model. That helps to control for possible changes in overall outcomes over calendar time, while still keeping the correct time to event (between opening/ratification or diagnosis/death).

One potential problem in your particular application is that not all treaties are ratified. Standard survival models implicitly assume that all individuals eventually experience the event. You might need to consider a "cure" model here, which evaluates both the probability of ever experiencing the event and the time-to-event for those who do.

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  • $\begingroup$ This is incredibly helpful, thank you very much - that makes a lot of sense! $\endgroup$ Nov 2, 2023 at 13:53

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