Accelerated Failure Time (AFT) Model
Also known as: AFT model, parametric survival regression, Hızlandırılmış Başarısızlık Zamanı Modeli (AFT)
The Accelerated Failure Time model is a parametric regression approach to survival analysis — formally reviewed and advocated by L. J. Wei in 1992 — in which covariates act as multiplicative factors that directly stretch or compress the time-to-event scale. Unlike the Cox proportional-hazards model, which models how covariates shift the hazard rate, AFT models express the covariate effect as an acceleration or deceleration of the time axis itself.
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When to use it
Use an AFT model when you have right-censored time-to-event data, a minimum of around 30 events, and you are willing to commit to a parametric distributional family (Weibull, log-normal, or log-logistic). The model is appropriate when the proportional-hazards assumption of Cox regression is suspect and when time-ratio interpretation is preferred over hazard-ratio interpretation. Before fitting, select the distribution by comparing AIC/BIC across candidate families or by inspecting log-log survival plots. Censoring must be independent of the outcome.
Strengths & limitations
- Provides direct time-ratio interpretation — easy to communicate to clinical or policy audiences.
- Fully parametric fitting gives smooth survival and hazard function estimates, not just a step function.
- Can outperform Cox regression when the chosen distribution fits the data well, yielding more precise coefficient estimates.
- Handles both continuous and categorical covariates, and allows multivariable adjustment.
- Requires correct specification of the baseline distribution; a poor choice yields biased estimates.
- Lacks the semi-parametric robustness of Cox regression — misspecified distribution cannot be fixed after the fact.
- Minimum sample requirement (~30 events) means it is unsuitable for very small studies.
- Software support is narrower than for Cox regression, and distribution selection adds an analytic step.
Frequently asked
How does AFT differ from the Cox proportional-hazards model?
Cox regression models covariates as multiplicative shifts of the hazard function at each point in time (hazard ratios), without specifying a baseline distribution. AFT models covariates as multiplicative shifts of the time axis itself (time ratios or acceleration factors), but requires the analyst to commit to a parametric distribution for survival times. The two coincide only for the Weibull distribution. AFT is preferred when the proportional-hazards assumption fails or when time-ratio communication is more useful; Cox is preferred when distributional robustness matters.
How do I choose between Weibull, log-normal, and log-logistic distributions?
Compare AIC and BIC across candidate distributions fitted by maximum likelihood — lower values indicate better fit. Graphical tools also help: log-log cumulative hazard plots that are linear support the Weibull, while other shapes suggest log-normal or log-logistic. Substantive knowledge about the expected hazard shape (monotone vs. humped) can also guide the choice.
What is the acceleration factor and how do I interpret it?
The acceleration factor ψ for a covariate change Δx is exp(β'Δx). It is the ratio of expected survival times between the two groups. ψ = 2 means the group with the higher covariate value is expected to survive twice as long; ψ = 0.5 means they survive half as long. Always report ψ with its 95% confidence interval.
Can I use AFT when I have competing risks?
Standard AFT models do not directly handle competing risks. In the presence of competing events, a cause-specific AFT approach or a Fine-Gray type model for the subdistribution hazard is preferable. Check the event structure carefully before applying a single-cause AFT.
Sources
- Wei, L. J. (1992). The Accelerated Failure Time Model: A Useful Alternative to the Cox Regression Model in Survival Analysis. Statistics in Medicine, 11(14–15), 1871–1879. DOI: 10.1002/sim.4780111409 ↗
- Kalbfleisch, J. D. & Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data (2nd ed.). Wiley. ISBN: 978-0471363576
- Kleinbaum, D. G. & Klein, M. (2012). Survival Analysis: A Self-Learning Text (3rd ed.). Springer. ISBN: 978-1441966452
How to cite this page
ScholarGate. (2026, June 1). Accelerated Failure Time (AFT) Model. ScholarGate. https://scholargate.app/en/survival/accelerated-failure-time
Which method?
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