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?