| Hu Chunyan,Hu Liangping,How to use χ2 test correctly——the log-rank test and the implementation of SAS software[J].SICHUAN MENTAL HEALTH,2021,34(6):498-503 |
| How to use χ2 test correctly——the log-rank test and the implementation of SAS software |
DOI：10.11886/scjsws20211110005 |
| English keywords:Log-rank test Survival data Censored data Independent test χ2 distribution |
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| English abstract: |
| The purpose of this article was to introduce the log-rank test and the SAS implementation. There were many different expression forms for the test statistics of the log-rank tests. Among them， there were two most common expression forms： the first was similar to "Pearson?s goodness-of-fit χ2 test statistic"； the second was similar to "the test statistic of the odds ratio of high-dimensional table data， that was， the Breslow-Day?s χ2 test statistic". The log-rank test statistic had two distribution types， one was the χ2 distribution， the other was the standard normal distribution. In the process of constructing log-rank test statistics， there were four contents that needed to be paid attention to： ① the sequential multiple four-fold tables formed by stratification or partition after sorting according to the individual "survival time"； ② it was necessary to distinguish whether the "survival time of each individual" was the complete data or the censored data； ③ only the calculation of the "theoretical or expected frequency" on a specific grid ［for example， （1，1） grid］ in each four-fold table data； ④ the method of calculating the theoretical frequency was different from the one in the independent test of the data of the four-fold table. Based on two examples with the different data structures， the paper realized the log-rank tests with the help of the SAS software. |
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