Varaktighetsdata

Varaktighetsdata (duration data) are measurements that record the length of time until an event occurs or until a process ends. They are common in fields such as medicine (time to relapse or death), reliability engineering (time to failure), and social sciences (duration of unemployment). Duration data can be complete, where the exact time-to-event is observed, or censored, where the event has not occurred by the end of the study or is known only to have occurred within an interval. Right-censoring is the most common, but left- and interval-censoring also occur.

Analyses of duration data are primarily conducted through survival analysis or duration models. Nonparametric methods, such as the Kaplan-Meier estimator for the survival function and the Nelson-Aalen estimator for the cumulative hazard, require minimal model assumptions. Parametric approaches fit a specified distribution to durations, for example exponential, Weibull, log-normal, or gamma, and can be used to extrapolate beyond observed data. Semi-parametric models include Cox proportional hazards models, which relate covariates to the hazard rate without specifying a baseline duration distribution, while accelerated failure time models specify covariate effects on the time scale.

Key concepts include the survival function S(t) = P(T>t), the hazard function h(t), and the cumulative hazard H(t). In the presence of censoring or competing risks, specialized estimators and likelihood methods are used (Turnbull estimator for interval-censored data).

Software tools widely support duration-data analysis, including the R packages survival and flexsurv, Python lifelines, and Stata’s stset/stcox commands. Varaktighetsdata enable understanding not only average durations but also the distribution and factors that influence time-to-event processes across disciplines.