survreg

survreg is a function in the survival package for R that fits parametric survival regression models using the accelerated failure time (AFT) framework. It analyzes time-to-event data typically stored in a Surv object and supports right-, left-, and interval-censored observations, as well as left truncation.

The core idea of survreg is to model the logarithm of survival time as a linear predictor: log(time) = Xβ + σε, where X are covariates, β are regression coefficients, σ is a scale parameter, and ε follows a specified error distribution. The distribution of ε is chosen with the dist argument and determines the implied survival distribution. Supported distributions include extreme (extreme value), Weibull, lognormal, log-logistic, and gamma.

Estimation is performed by maximum likelihood, allowing complex censoring and censoring-related features. The resulting object contains regression coefficients, the scale parameter, log-likelihood, and model fit statistics. Coefficients in an AFT model are interpreted in terms of effects on log time; exponentiated coefficients exp(β) are acceleration factors indicating how covariates accelerate or decelerate the time to event.

The function supports model features common to R’s modeling tools, such as stratification via strata in the formula, and inclusion of time-fixed covariates. Predictions and additional summaries can be obtained through standard methods for survreg objects, including summary, print, and coef. Compared with semi-parametric Cox models, survreg provides fully parametric survival modeling with explicit survival and hazard functions, at the cost of assuming a particular time-to-event distribution.

Example usage: fit <- survreg(Surv(time, status) ~ age + sex, dist = "lognormal"); summary(fit).