Application of Kaplan -Meier estimates to testing Cox power hypothesis for two progressive lycensored samples

The paper considers the problem of testing the Cox power hypothesis for two progressively censored samples. To test the hypothesis, the authors propose the Kolmogorov - Smirnov criterion as some statistics based on comparison of the Kaplan-Meier estimates of a reliability function for each sample. A method for calculating the exact distributions of statistics is based on the model of a particle random walk on a two-dimensional cell array. The method allows obtaining accurate probabilities for a considerable amount of samples. It enables one to estimate their required amount for which the exact probabilities can be replaced by the asymptotic ones. Tables of probability distributions for the proposed accurate statistics are calculated considering a wide range of possible values of the sample amount. The authors show that the statistics asymptotic distribution converges to the Kolmogorov -Smirnov standard distribution, provided the tested hypothesis is valid. The statistical characteristics for estimating the Cox model parameter are evaluated, in case the hypothesis is valid, if tested with the help of the Monte-Carlo method. The value that minimizes the proposed test statistics is considered estimation. The estimation consistency is shown.

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