Accelerated Failure Time Model (Log-normal, Log-logistic)

The accelerated failure time model regresses log survival time on covariates with log-normal or log-logistic errors, so exponentiated coefficients are time ratios that stretch or shrink survival time.

가속실패시간 모형은 로그 생존시간을 로그정규 또는 로그로지스틱 오차로 회귀해, 계수의 지수가 생존시간을 몇 배 늘리거나 줄이는지를 뜻하는 시간비가 되는 모형입니다.

Which covariates speed up or delay the event, expressed as how many times longer people survive?

어떤 변수가 사건 발생을 앞당기거나 늦추는지 생존시간 배수로 알고 싶어요.

An accelerated failure time model fits log T = Xβ + σε by maximum likelihood with censoring, and exp(β) tells how much a covariate multiplies the expected survival time. Comparing log-normal and log-logistic error distributions by AIC chooses the better-fitting form, which is useful when the hazard rises and then falls.

When to use Accelerated Failure Time Model (Log-normal, Log-logistic)

• The proportional hazards assumption is violated
• You want effects on the time scale rather than as hazard ratios
• The hazard is non-monotone, rising then falling over time

When to use something else

• Hazards are proportional and you want hazard ratios; use a Cox proportional hazards model
• The hazard is monotone and a Weibull shape is plausible; use a Weibull parametric survival model

Assumptions and requirements

• The chosen error distribution fits the log survival times
• Covariates act multiplicatively on survival time
• Censoring is independent

What the analysis reports

• AIC comparison of log-normal, log-logistic and Weibull fits
• Coefficients with standard errors and p values
• Time ratios exp(β) with confidence intervals
• Scale or shape parameter

How to report it

A [distribution] accelerated failure time model was selected by AIC ([value] vs [value]); [covariate] was associated with a time ratio of [value] (95% CI [[value], [value]], p = [value]).

Related methods

• Weibull Parametric Survival Model
• Cox Proportional Hazards Model

Run Accelerated Failure Time Model (Log-normal, Log-logistic) on Quorant