Weibull AFT — Accelerated Failure Time (parametric survival with TAF)
Coming soonAdvanced & specialized
This test is implemented and is currently going through StatMinds’ production verification: every statistic is independently checked against a trusted reference (scipy / R), locked with regression tests, and the screen is exercised across assumption-met/violated and significant/non-significant scenarios before it opens up.
See what’s live nowParametric survival regression on the time-acceleration scale: log T = β₀ + β'X + σW where W is Weibull-error distributed.
Each covariate's coefficient β yields a Time-Acceleration Factor TAF = exp(β) — a multiplicative effect on survival time directly interpretable as 'X-fold longer/shorter survival'. The engine fits Weibull, log-normal, log-logistic, and exponential AFT companions, selects by AIC/BIC, and reports per-covariate TAF with 95% CIs plus median survival predictions. Preferred over Cox when proportional hazards fails OR when survival prediction at specific time horizons (rather than hazard ratios) is the primary deliverable.
Worked example
How do covariates lengthen or shorten survival time directly?
An accelerated-failure-time (Weibull) model expresses each covariate as a time-acceleration factor — how much it multiplies survival time.
The treatment extended survival time by 45% (time-ratio = 1.45, 95% CI [1.16, 1.81], p = .001).
A Weibull AFT model showed the treatment significantly extended survival time, time-ratio = 1.45, 95% CI [1.16, 1.81], p = .001.
Try it yourself: Load this ready-made sample and follow the run above.
When to use it
- Survival regression when PH assumption failsTime-to-recurrence in a cancer trial: KM curves for treatment vs control cross at 18 months, indicating PH violation.
- Median / quantile survival prediction at horizonsBuild a prognostic tool predicting median time-to-failure for an industrial component given operating temperature and load.
When NOT to — use instead
- PH assumption HOLDSCox is semi-parametric (no distributional commitment) and is the standard when PH holds. → Cox Proportional Hazards \u2014 multivariable survival with adjusted HRs
- Multiple competing event typesAFT models a single event. → Competing Risks \u2014 Fine-Gray + Aalen-Johansen CIF (multi-cause survival)
- Time-varying covariatesStandard AFT assumes time-invariant covariates. → Cox Proportional Hazards \u2014 multivariable survival with adjusted HRs
- Few events (< 15)AFT needs at least ~15 events for stable parametric estimation. → Kaplan-Meier + log-rank \u2014 survival analysis with censoring
Hypotheses
Parameter tested: log-time acceleration coefficients β; Weibull shape ρ (or equivalent for other distributions).
Assumptions (and what to do if they fail)
Check: AIC/BIC across 4 distributions — prefer the smallest.
If violated: Mis-specified distribution biases the time-acceleration factor and survival predictions.
Check: Plot standardised Cox-Snell residuals.
If violated: Non-multiplicative effects bias the TAF estimate.
Check: Visual — martingale residuals.
If violated: Non-linearity biases TAF estimates at the extremes.
Ready to run a Weibull AFT — Accelerated Failure Time (parametric survival with TAF) on your own data?
Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.
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