Event History Modeling, aka Survival Analysis, aka Duration Models, aka Hazard Analysis

1. Event History Modeling,aka Survival Analysis,aka Duration Models,aka Hazard Analysis

2. How Long Until …? • Given a strike, how long will it last? • How long will a military intervention or war last? • How likely is a war or intervention? • What determines the length of a Prime Minister’s stay in office? • When will a government liberalize capital controls?

3. Origins • Medical Science • Wanted to know the time of survival 0 = ALIVE 1 = DEAD • Model slightly peculiar – once you transition, there is no going back. • Many analogs in Social Sciences

4. Disadvantages of Alternatives(Cross Sections) • Assumes steady state equilibrium • Individuals may vary but overall probability is stable • Not dynamic • Can’t detect causation.

5. Disadvantages of Alternatives(Panel) • Measurement Effects • Attrition • Shape not clear • Arbitrary lags • Time periods may miss transitions

6. Event History Data • Know the transition moment • Allows for greater cohort and temporal flexibility • Takes full advantage of data

7. Data Collection Strategy(Retrospective Surveys) • Ask Respondent for Recollections • Benefit: Can “cheaply” collect life history data with single-shot survey • Disadvantages: • Only measure survivors • Retrospective views may be incorrect • Factors may be unknown to respondent

8. Logic of Model • T = Duration Time • t = elapsed time • Survival Function = S(t) = P(T≥t)

9. Logic of Model (2) • Probability an event occurs at time t • Cumulative Distribution function of f(t) • Note: S(t) = 1 – F(t)=

10. Logic of Model (3) • Hazard Rate • Cumulative Hazard Rate

11. Logic of Model (4) • Interrelationships • so knowing h(t) allows us to derive survival and probability densities.

12. Censoring and Truncation • Right truncation • Don’t know when the event will end • Left truncation • Don’t know when the event began

13. Censoring and Truncation (2)

14. Discrete vs. Continuous Time • Texts draw sharp distinction • Not clear it makes a difference • Estimates rarely differ • Need to measure time in some increment • Big problem comes for Cox Proportional Hazard Model – it doesn’t like ties

15. How to Set up Data(Single Record)

16. Choices / Distributions • Need to assume a distribution for h(t). • Decision matters • Exponential • Weibull • Cox • Many others, but these are most common

17. Distributions (Exponential) • Constant Hazard Rate • Can be made to accommodate coefficients

18. Distributions (Weibull) • Allows for time dependent hazard rates

19. Weibull Survival Functions

20. Weibull Hazard Rates

22. Distributions (Cox) • Useful when • Unsure of shape of time dependence • Have weak theory supporting model • Only interested in magnitude and direction • Parameterizing the base-line hazard rate

23. Distributions (Cox – 2) Baseline function of “t” not “X” Involves “X” but not “t”

24. Distributions (Cox –3) Why is it called proportional?

25. How to Interpret Output • Positive coefficients mean observation is at increased risk of event. • Negative coefficients mean observation is at decreased risk of event. • Graphs helpful.

26. Unobserved heterogeneity and time dependency • Thought experiment on with groups • Each group has a constant hazard rate • The group with higher hazard rate experience event sooner (out of dataset) • Only people left have lower hazard rate • Appears hazard drops over time • “Solution” akin to random effects

27. Extensions • Time Varying Coefficients • Multiple Events • Competing Risk Models