Accelerated Failure Time model

Survival analysis is a huge topic in statistics. For a comprehensive survey, see this article from ACM. In this post, we will cover one popular model known as Accelerated Failure Time (AFT). The AFT model makes the following key assumptions:

Accelerated Failure Time assumption

1. A unit increase in each input feature multiples the log survival time by a constant factor.
2. The effects of features on the log survival time are additive.
3. Noise in the training data is random and does not depend on any particular data point.

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What is survival analysis?

Survival analysis is a discipline within statistics where the statistician models the distribution of time to an event of interest. The rest of this post will unpack this definition.

Survival analysis is a special kind of regression and differs from the conventional regression task as follows:

  • The label is always positive, since you cannot wait a negative amount of time until the event occurs.
  • The label may not be fully known, or censored, because “it takes time to measure time.”
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