Log-rank Test Using Computational Algebraic Statistics

Abstract

Log-rank test is one of typical nonparametric test procedures in the two-sample problem for time-to-event data and is currently widely used in various fields. However, since the significance probability from log-rank test is usually computed using asymptotic chi-square approximation, it has been pointed out that the approximation precision is poor in situations where there is a large bias in the small sample size or imbalanced group allocation. In this paper, we propose a new test procedure that works well in such situations using computational algebraic statistics. The main feature of our algorithm is to estimate p-value by Markov Chain Monte Carlo method using a Markov basis on contingency tables. In order to evaluate the usefulness of the proposed method, simulation comparisons are also performed and the results show that the proposed method maintains an appropriate level of significance even in the settings where the asymptotic approximation becomes poor.