Kaplan-Meier procedure

Kaplan-Meier procedure. A metliod of estimating survival probabilities from data on survival times for individuals in a cohort which can handle the case where a number of the individuals are still alive, so that their eventual survival times are censored. 

The Kaplan-Meier curves do not of themselves provide a formal, p-value, comparison of the treatments. This comparison of the survival curves is undertaken using either the logrank test or the Gehan-Wilcoxon test. We will look at these two test procedures in turn. 

Nonparametric analysis provides powerful results since the rehahility calculation is unconstrained to fit any particular pre-defined lifetime distribution. However, this flexibility makes nonparametric results neither easy nor convenient to use for different purposes as often encountered in engineering design (e.g., optimization). In addition, some trends and patterns are more clearly identified and recognizable with parametric analysis. Several possible methods can be used to fit a parametric distribution to the nonparametric estimated rehability functions (as provided by the Kaplan-Meier estimator), such as graphical procedures or inference procedures. See Lawless (2003) for details. We choose in this paper the maximum likelihood estimation (MLE) technique, assuming that the sateUite subsystems failure data are arising from a WeibuU piobabihly distribution, as expressed in Equations 1,2. 

Kaplan-Meier renormalization procedure (5) or the alternative procedure developed in ref. 4. If the trial is to test the later response of a patient to a short-term course of treatment (with or without a following continuous treatment), the time t = 0 is to be taken as the time at which the short-term course was completed, with only those patients who survived the course included in the cohort. 

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