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The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...
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A non-linear optimisation method to extract summary statistics from Kaplan-Meier survival plots using the published P

Andrew F Irvine1,2, Sara Waise3, Edward W Green4

  • 1Faculty of Medicine, University of Southampton, Southampton, UK. a.f.irvine@leeds.ac.uk.

BMC Medical Research Methodology
|October 31, 2020
PubMed
Summary

A new non-linear optimization method improves meta-analyses of survival data by accurately estimating hazard ratios from Kaplan-Meier plots and P values, enhancing evidence synthesis for time-to-event outcomes.

Keywords:
AlgorithmKaplan-Meier plotLife tableMeta-analysisNon-linear optimisationSurvival analysis

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Area of Science:

  • Biostatistics
  • Medical Informatics
  • Epidemiology

Background:

  • Meta-analyses are crucial for synthesizing evidence on survival outcomes but often lack necessary summary statistics.
  • Kaplan-Meier plots are frequently published, but inferring statistics from them can be error-prone, especially without the number at risk.

Purpose of the Study:

  • To develop a novel method for estimating key statistics for meta-analyses from Kaplan-Meier plots.
  • To improve the accuracy of meta-analyses for time-to-event data when full statistics are not reported.

Main Methods:

  • A non-linear optimization (nlopt) method was developed using only Kaplan-Meier plots and P values.
  • This method estimates the censoring pattern to calculate the natural logarithm of the hazard ratio (ln(HR)) and its variance.
  • Monte Carlo simulations were used to determine optimal data extraction points from Kaplan-Meier plots.

Main Results:

  • The nlopt method demonstrated a statistically significant improvement over the Parmar method in estimating ln(HR).
  • In validation studies, the mean absolute error was significantly lower (0.014 vs. 0.077, P=0.003).
  • For a true HR of 1.5, the nlopt method yielded limits of 1.49/1.52, compared to 1.39/1.62 for the Parmar method.

Conclusions:

  • The proposed non-linear optimization method enhances the accuracy of meta-analyses for time-to-event outcomes.
  • This method provides a valuable tool for researchers when only Kaplan-Meier plots and P values are available.
  • Source code and a web implementation are available to facilitate adoption.