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Non Parametric models

Non Parametric models offer a straightforward and easy-to-interpret way to compute the survival and hazard functions without imposing any assumptions. Pysurvival provides the following non-parametric models:

Kaplan-Meier model

One of the most straight-forward ways to estimate the Survival function of an entire group, is by using the Kaplan-Meier method. Given units in a cohort, let's assume that there are distinct actual event times such that with , then the Survival function estimator is given by: with:

  • is the number of individuals experiencing an event at
  • is the number of individuals at risk within - those who have not been censored or experienced an event

Smooth Kaplan-Meier

Despite its ease of use, the main drawback of the Kaplan-Meier estimator is that it is a step function with jumps. Kernel smoothing can therefore solve this issue, provided that the best kernel and bandwidth are properly chosen.

Let be a Smooth estimator of the Kaplan-Meier survival function. can be written such that:


  • , the height of the jump of the Kaplan-Meier estimator at
  • , the infinite order kernel function. Here are the most common kernel functions:

    • Biweight: if else
    • Cosine: if else
    • Epanechnikov: if else
    • Normal:
    • Triweight: if else
    • Uniform: if else
  • , the kernel function bandwidth