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Event history methods analyze timing of social events—divorce, job transitions, political regime changes. These methods handle censoring (incomplete observation periods) and allow time-varying covariates. Survival curves and hazard functions describe rates of event occurrence over time.
Your training in linear regression taught you to model the *level* of an outcome — how high or low is Y given X? But many social science questions are about *timing*: not whether someone gets divorced, but when. Not whether a political regime collapses, but how long it survives. Not whether a worker finds a new job, but how quickly after being laid off. Standard regression is poorly suited to timing questions, partly because of a data problem your regression training didn't prepare you for: censoring.
Censoring occurs when you observe a subject for a period but the event has not yet occurred by the end of observation. A study tracking divorces that ends in 2020 includes couples still married at that date — they haven't experienced the event, but their marriages lasted *at least* as long as the observation window. Simply excluding these cases biases the analysis by discarding information: a marriage that has survived 15 years tells you something important even if it isn't yet ended. Survival analysis incorporates censored observations correctly by treating them as contributing information about survival *up to* the censoring point, even though the event was not observed. Your background in probability distributions — especially the exponential — will help here, since the exponential distribution describes constant-hazard survival processes and is the simplest baseline case.
The two core functions build on your probability background. The survival function S(t) gives the probability that the event has not yet occurred by time t — it starts at 1 and declines over time as events accumulate. The hazard function h(t) is the instantaneous rate of event occurrence at time t, given that the subject has survived to that point. Think of the hazard as the *risk rate right now for those still at risk* — it can vary over time. Divorce risk is highest in the early years of marriage and again around the seventh year; political regimes are often most vulnerable just after transitional periods. The hazard function captures this time-varying risk in a way that a single regression coefficient cannot.
The Cox proportional hazards model is the workhorse of event history analysis, and it generalizes linear regression in a specific way. Rather than modeling the level of an outcome, it models the *ratio of hazards* between subjects with different covariate values. The model estimates a hazard ratio for each covariate: a ratio of 2 means subjects with that characteristic experience the event at twice the rate of the reference group at any given point in time. The "proportional" assumption — that this ratio is constant over time — is a testable constraint. Extensions allow time-varying covariates (a subject's employment status can change during observation), competing risks (subjects can exit via multiple distinct events, such as retirement versus layoff), and discrete-time formulations for data where time is measured in intervals rather than continuously.
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