Weibull Parametric Survival Regression
Also known as: weibull aft model, weibull survival model, parametric survival regression, Weibull Regresyonu — Parametrik Hayatta Kalma
Weibull regression is a fully parametric survival model, formalised by Kalbfleisch and Prentice, that assumes survival times follow a Weibull distribution. A shape parameter controls whether the hazard increases, decreases, or remains constant over time, while covariates shift the scale of the distribution to express how predictors affect survival.
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When to use it
Use Weibull regression when you have right-censored time-to-event data, at least 30 observations, and the Weibull distributional assumption is supported by a goodness-of-fit test such as Anderson-Darling. It is appropriate when covariates are time-fixed (measured once, not updated during follow-up) and censoring is non-informative. It is especially valuable when you need absolute survival probability estimates at specific future time points — something Cox regression cannot provide without additional assumptions. If the Weibull assumption fails, consider an accelerated failure time model with an alternative distribution.
Strengths & limitations
- Produces absolute survival probability estimates at any time point, not just at observed event times.
- The shape parameter makes the hazard trajectory explicit and clinically interpretable.
- Can be interpreted both as a proportional-hazards model and as an accelerated failure time model, offering dual interpretive frames.
- More efficient than semi-parametric methods when the Weibull assumption holds, because the full distributional form is exploited.
- The Weibull distributional assumption must hold; a poor fit leads to biased hazard and survival estimates.
- Cannot accommodate time-varying covariates without model extension.
- Requires at least 30 observations for stable parameter estimation; smaller samples yield unreliable confidence intervals.
- Less familiar to general audiences than Kaplan-Meier or Cox regression, so results may need extra explanation.
Frequently asked
How does Weibull regression differ from Cox regression?
Cox regression is semi-parametric: it leaves the baseline hazard unspecified and estimates only the effect of covariates relative to that baseline. Weibull regression specifies the full distributional form — including the baseline — so it yields absolute survival probabilities at any time point but is valid only when the Weibull assumption holds. Cox is more robust to distributional misspecification; Weibull is more informative when the assumption is satisfied.
What does the shape parameter γ tell me?
The shape parameter γ describes how the event rate evolves over time. A value greater than 1 indicates an increasing hazard (subjects become progressively more likely to experience the event as time passes). A value less than 1 indicates a decreasing hazard (risk falls over time, as in post-operative mortality). A value of exactly 1 collapses the Weibull to an exponential model with a constant hazard.
How do I check whether the Weibull assumption is satisfied?
The standard graphical check is a log-log plot of the Kaplan-Meier estimate: plot log(−log S(t)) against log(t) for each covariate group. If the Weibull assumption holds, the result should be approximately linear. Formal tests such as Anderson-Darling provide a statistical assessment. If linearity is absent, consider a flexible alternative such as a log-normal or log-logistic AFT model.
What is the AFT interpretation of Weibull regression?
In the accelerated failure time interpretation, a covariate with coefficient β multiplies the expected survival time by exp(β). A negative β means the covariate accelerates the time to event (shortens survival); a positive β decelerates it. This direct interpretation of time ratios is often more intuitive in clinical settings than hazard ratios.
Sources
- Kalbfleisch, J. D. & Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data (2nd ed.). Wiley. DOI: 10.1002/9781118032985 ↗
How to cite this page
ScholarGate. (2026, June 1). Weibull Parametric Survival Regression. ScholarGate. https://scholargate.app/en/survival/weibull-regression
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