Survival analysis deals with “time-to-event” outcomes: time until a machine fails, a customer churns, a patient relapses, or a loan defaults. A special challenge is that you often do not observe the event for every subject during the study window. Some observations are censored (for example, the customer is still active when the analysis ends). Traditional regression is not built for this mix of observed and censored times, which is why survival methods exist.
Many practitioners first meet survival analysis through the Cox proportional hazards model. Cox models relate predictors to the hazard (instantaneous event rate) and leave the baseline hazard unspecified. Accelerated Failure Time (AFT) models take a different approach: they directly relate predictors to the expected survival time (more precisely, to the distribution of event times), which can make results easier to interpret in operational settings—especially when you want to estimate “how much longer” or “how much sooner” an event happens.
If you are studying these ideas in a data science course in Chennai, AFT models are worth learning alongside Cox models because they answer a slightly different question and often communicate well to business stakeholders.
What Makes AFT Models Different From Cox Models?
Cox models express effects as hazard ratios. For example, a hazard ratio of 1.3 suggests a 30% higher hazard at any instant, assuming proportional hazards. AFT models express effects as time ratios (also called acceleration factors). Conceptually, an AFT model says: predictors stretch or shrink the time-to-event scale.
A common form is:
- log(T) = β₀ + β₁X₁ + … + ε
Here, T is the event time and ε follows a chosen distribution. When you exponentiate coefficients, you obtain a multiplicative effect on time. For instance, a time ratio of 1.20 can be interpreted as “the expected time-to-event is 20% longer” for a one-unit increase in a predictor (holding other variables constant). This “direct time” interpretation is often intuitive for questions like:
- How long until a subscription renewal?
- How long until a component failure?
- How long until a patient readmission?
Common Parametric Choices in AFT Modelling
AFT models are parametric, meaning you assume a distribution for survival times (or equivalently for the error term ε). Common choices include:
- Exponential: constant hazard over time (simple but often too restrictive).
- Weibull: flexible; hazard can increase or decrease over time.
- Log-normal: log time follows a normal distribution; can capture non-monotonic hazards.
- Log-logistic: can also produce non-monotonic hazard shapes and heavier tails.
Choosing a distribution is not guesswork. You compare fit using criteria like AIC, inspect residuals, and check whether predicted survival curves match observed patterns. In many real problems, Weibull or log-normal are good starting points, but the “best” option depends on the data’s shape and the underlying process.
Learners in a data science course in Chennai often practise this by fitting multiple AFT specifications and selecting the most plausible model using both statistics and domain logic.
Handling Censoring and Interpreting Coefficients
AFT models naturally incorporate right-censoring through the likelihood function. This is one of the core benefits: censored observations still contribute information (we know they survived at least up to a point).
Interpretation focuses on time ratios:
- Time ratio > 1: the predictor extends time-to-event (slower occurrence).
- Time ratio < 1: the predictor shortens time-to-event (faster occurrence).
Example (business): Suppose you model time to churn for a streaming service. If “annual plan” has a time ratio of 1.50 versus “monthly plan,” you can say annual subscribers churn later, with expected time-to-churn about 50% longer, controlling for other factors.
Example (engineering): If higher operating temperature yields a time ratio of 0.80 for time-to-failure, that suggests failures occur sooner—time-to-failure is reduced by about 20%.
When AFT Models Are a Better Fit Than Cox
AFT models are especially attractive when:
- You care about predicting time directly
- Planning maintenance cycles or forecasting customer lifetime often needs a time scale output, not only a hazard ratio.
- Proportional hazards may not hold
- Cox models rely on proportional hazards. If the effect of a predictor changes over time, Cox assumptions can break. Some AFT distributions can still fit well in such cases, depending on the pattern.
- You want clearer stakeholder communication
- “This factor increases expected time-to-event by 30%” can be simpler than explaining hazards.
That said, AFT models require choosing a distribution, and a poor choice can bias estimates. The best practice is to compare models, validate predictions, and report diagnostics.
If your aim is to become confident with these trade-offs, a data science course in Chennai that includes survival diagnostics, model comparison, and real datasets will help you move beyond “fit-and-forget” modelling.
Practical Workflow for Building an AFT Model
A sensible AFT workflow looks like this:
- Define the event and censoring clearly (what counts as the event, and when observations are censored).
- Explore survival curves (Kaplan–Meier) by key groups to understand shape and separations.
- Fit multiple AFT distributions (e.g., Weibull, log-normal, log-logistic).
- Compare fit using AIC and visual checks (predicted vs observed survival).
- Check residuals and influence to spot misfit or overly influential points.
- Validate using time-based splits where possible, since survival problems often evolve over time.
- Communicate results in time ratios and predicted time-to-event percentiles (median, 75th percentile), not only coefficients.
Conclusion
Accelerated Failure Time models provide a practical, interpretable route to survival modelling by linking predictors directly to the time-to-event scale. Unlike Cox models, which focus on hazards, AFT models describe how variables speed up or slow down the event timeline and handle censoring in a statistically sound way. With careful distribution selection, diagnostics, and validation, AFT models can be a strong choice for business, healthcare, and reliability use cases where “how long until” is the central question.
