Accelerated failure time model

Model covariates as multiplying an event-time scale—equivalently shifting log survival time—so coefficients are interpreted through time ratios rather than the constant hazard ratios of proportional-hazards regression.

Version

v2 · 2026-08-30 · History

Domain-specific #

1224

Origin domain

survival analysis

Subdomain

event time regression

Core Idea

An accelerated failure time model writes \(log T=x^{\mathsf T}\beta+\sigma\varepsilon\), or equivalently relates survival curves by \(S(t\mid x)=S_0(t\exp(-x^{\mathsf T}\beta))\) under this sign convention. Thus \(exp(\beta_j)\) is a multiplicative time ratio for a one-unit covariate change. A covariate shifts the location of log event time, which stretches or compresses the entire time axis. Choosing an extreme-value, normal, logistic, or other error distribution yields Weibull, lognormal, log-logistic, or related parametric survival families. Censoring contributes a survival rather than density term to the likelihood.

Scope of Application

Accelerated failure time model applies when the analyst can specify a positive event time (T), covariates (x), possible right censoring, and a declared baseline log-time or survival distribution and establish that event time is positive and well defined, covariates enter through a multiplicative time-scale relation or additive log-time form, censoring is represented correctly, coefficient signs and time-ratio interpretation are declared, and any parametric baseline family is part of the model rather than inferred from the acronym. The entry is a descriptive statistical specification. It does not recommend a treatment, predict an individual's survival, or license extrapolation beyond the supported population and follow-up.

Clarity

A clear claim names the carrier, governing rule, assumptions, and recognition test. This matters because authors differ on whether a positive coefficient lengthens time or increases an acceleration parameter, so every interpretation must be derived from the displayed equation rather than the word accelerated.

Identity and measurement remain separate. Model assessment reports censoring, residual diagnostics, distributional comparisons, coefficient uncertainty, time-ratio intervals, calibration horizon, and sensitivity to influential observations and extrapolation.

Manages Complexity

The abstraction compresses Weibull, exponential, lognormal, log-logistic, and generalized-gamma parametric AFT models; rank-based semiparametric AFT estimation; frailty or clustered extensions; and time-varying departures into a stable carrier, rule, invariant, and failure boundary. It makes comparison tractable while retaining the variables that control validity.

Compression can hide assumptions. A responsible use therefore declares time origin, event definition, censoring mechanism, covariates, sign convention, time ratio, baseline family, scale parameter, residuals, extrapolation horizon, and competing risks and returns to the full diagnostic whenever a convention or boundary case changes.

Abstract Reasoning

1. Type the carrier. Establish a positive event time (T), covariates (x), possible right censoring, and a declared baseline log-time or survival distribution and reject examples from a different problem. 2. Lock the rule. Express that event time is positive and well defined, covariates enter through a multiplicative time-scale relation or additive log-time form, censoring is represented correctly, coefficient signs and time-ratio interpretation are declared, and any parametric baseline family is part of the model rather than inferred from the acronym independently of one notation or implementation.

Knowledge Transfer

Transfer within survival analysis is strong when new cases preserve the same carrier, mechanism, and diagnostic. The move from If a binary treatment coefficient is \(\beta=\log 1.5\) under \(\log T=x\beta+\varepsilon\), the fitted event-time quantiles for the treated group are 1.5 times the corresponding baseline quantiles, subject to the model and covariate conditions. to A reliability analysis fits Weibull, lognormal, and log-logistic AFT models to right-censored component lifetimes and compares residual behavior, information criteria, and sensitivity of mission-time predictions. demonstrates that continuity.

Relationships to Other Abstractions

Current abstraction Accelerated failure time model Domain-specific

Parents (1) — more general patterns this builds on

• Accelerated failure time model is a kind of Proportionality Prime

  The proposed strict upward parent is prime:proportionality.

Hierarchy paths (2) — routes to 2 parentless roots

• Accelerated failure time model → Proportionality → Normativity → Constraint

Show alternative path (1)

Neighborhood in Abstraction Space

Accelerated failure time model sits in a sparse region of the domain-specific corpus (62^nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Longitudinal Models & Time-Series Structure (8 abstractions)

Nearest neighbors

• Logrank test — 0.90
• Discrete-time proportional hazards — 0.90
• Recurrent event analysis — 0.87
• Failure rate — 0.85
• Unevenly spaced time series — 0.84

Computed from structural-signature embeddings · 2026-09-08