Accelerated failure time model

In the statistical area of survival analysis, an accelerated failure time model (AFT model) is a parametric model that provides an alternative to the commonly used proportional hazards models. Whereas a proportional hazards model assumes that the effect of a covariate is to multiply the hazard by some constant, an AFT model assumes that the effect of a covariate is to accelerate or decelerate the life course of a disease by some constant. This is especially appealing in a technical context where the 'disease' is a result of some mechanical process with a known sequence of intermediary stages.

In full generality, the accelerated failure time model can be specified as

where ${\displaystyle \theta }$ denotes the joint effect of covariates, typically ${\displaystyle \theta =\exp(-[\beta _{1}X_{1}+\cdots +\beta _{p}X_{p}])}$. (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)

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