Accelerated Failure Time Model

TL;DR

• Models the time until a specified event occurs and links that time to predictor variables.
• Assumes the time-to-event is exponentially distributed and estimates a hazard rate as a function of predictors.
• Can handle censoring and competing risks in observed data.

Definition

The Accelerated Failure Time (AFT) model is a statistical model used to estimate the time until a certain event occurs, such as failure or death. The AFT model assumes that the time until an event is exponentially distributed, meaning that the probability of the event occurring is constant over time. The model estimates the rate at which the event occurs, known as the hazard rate, as a function of one or more predictor variables.

Explanation

The AFT model links observed predictor variables to an estimated hazard rate for the event of interest. Under the assumption that time-to-event follows an exponential distribution, the model treats the hazard (the instantaneous event rate) as constant over time and models how predictor variables change that rate. Estimated hazard rates from the AFT model can be used to assess the likelihood of the event occurring within a specified time frame.

The model can incorporate incomplete observations: when an event is not observed within the study period (censoring), or when other events may preclude the event of interest (competing risks), the AFT framework can still produce estimates by accounting for those data characteristics.

Examples

Medical example

In the medical field, the AFT model can be used to predict the time until death for a patient with a certain disease. The predictor variables might include the patient’s age, gender, and the stage of their disease. The AFT model would then estimate the hazard rate for the patient, which could be used to determine their likelihood of dying within a certain time frame.

Engineering example

In engineering, the AFT model can be used to predict the time until failure for a certain product or component. The predictor variables might include the product’s age, usage, and environmental conditions. The AFT model would then estimate the hazard rate for the product, which could be used to determine its likelihood of failing within a certain time frame.

Finance example

In finance, the AFT model can be used to predict the time until default for a certain loan or investment. The predictor variables might include the borrower’s credit score, income, and debt-to-income ratio. The AFT model would then estimate the hazard rate for the loan or investment, which could be used to determine its likelihood of defaulting within a certain time frame.

Use cases

• Engineering: predicting component or product time-to-failure.
• Medicine: estimating patient time-to-event (e.g., time until death) given clinical predictors.
• Finance: modeling time until default for loans or investments.

Notes or pitfalls

• Censoring: The AFT model can account for observations where the event is not observed within the study period.
• Competing risks: The AFT model can account for alternative events that may occur instead of the event of interest.

Related terms

• Hazard rate
• Censoring
• Competing risks