KaplanMeier

Statistical assessments with the Kaplan-Meier survival function (lower/upper limits) to test whether a measured value x0 (typically the mean of a distribution) is associated with some population x, accounting for lower limits in x. If the Kaplan-Meier survival function at x0 is outside the limits of 0.01 to 0.99, one can confidently reject the null hypothesis that the measurement x0 is associated with the measurements x.

I originally developed and implemented this script for Flury et al. 2024 in prep for tests involving a sample of 89 Lyman continuum measurements, 39 of which were upper limits requiring the censoring treatment of the Kaplan-Meier survival curve.

Examples

import matplotlib.pyplot as plt
from numpy.random import seed,rand,randn
from KaplanMeier import *

seed(123)
x = randn(100)
c = rand(100)<0.3
x0 = array([1.65])
x0_err = array([[0.3],[0.5]])

km_x,km_y = km_curve(x,c)
p_x,p_e = km_eval(x0,x,c,x0_err=x0_err)

which gives the results below

BibTeX reference

While this code is provided publicly, I request that any use thereof be cited in any publications in which this code is used. BibTeX formatted reference provided below.

@ARTICLE{Flury2024,
       author = {{Flury}, Sophia R. and {Jaskot}, Anne E. and {the LzLCS Collaboration}},
        title = "{The Low-Redshift Lyman Continuum Survey: The Roles of Stellar Feedback and ISM Geometry in LyC Escape}",
      journal = {\apjs},
     keywords = {Reionization, Galactic and extragalactic astronomy, Ultraviolet astronomy, Hubble Space Telescope, 1383, 563, 1736, 761, Astrophysics - Astrophysics of Galaxies, Astrophysics - Cosmology and Nongalactic Astrophysics},
         year = 2024,
        month = {},
       volume = {},
       number = {},
          eid = {},
        pages = {},
          doi = {},
archivePrefix = {},
       eprint = {},
          url = {https://github.com/sflury/KaplanMeier},
 primaryClass = {astro-ph.GA},
       adsurl = {https://ui.adsabs.harvard.edu/abs/},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System} }

An additional reference to consider is the original Kaplan & Meier (1958) paper which first presented the Kaplan-Meier statistic. The BibTeX entry for their paper is listed below.

@article{KaplanMeier1958,
author = {E. L. Kaplan and Paul Meier},
title = {Nonparametric Estimation from Incomplete Observations},
journal = {Journal of the American Statistical Association},
volume = {53},
number = {282},
pages = {457-481},
year = {1958},
publisher = {Taylor & Francis},
doi = {10.1080/01621459.1958.10501452},
}

DOI

Licensing

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.