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In statistics, the log-rank test is a hypothesis test to compare the survival distributions of two samples. It is a nonparametric test and appropriate to use when the data are right skewed and censored (technically, the censoring must be non-informative). It is widely used in clinical trials to establish the efficacy of a new treatment in comparison with a control treatment when the measurement is the time to event (such as the time from initial treatment to a heart attack). The test is sometimes called the Mantel–Cox test, named after Nathan Mantel and David Cox. The log-rank test can also be viewed as a time-stratified Cochran–Mantel–Haenszel test. The test was first proposed by Nathan Mantel and was named the ''log-rank test'' by Richard and Julian Peto.〔 〕 ==Definition== The log-rank test statistic compares estimates of the hazard functions of the two groups at each observed event time. It is constructed by computing the observed and expected number of events in one of the groups at each observed event time and then adding these to obtain an overall summary across all-time points where there is an event. Let ''j'' = 1, ..., ''J'' be the distinct times of observed events in either group. For each time , let and be the number of subjects "at risk" (have not yet had an event or been censored) at the start of period in the two groups (often treatment vs. control), respectively. Let . Let and be the observed number of events in the groups respectively at time , and define . Given that events happened across both groups at time , under the null hypothesis (of the two groups having identical survival and hazard functions) has the hypergeometric distribution with parameters , , and . This distribution has expected value and variance . The log-rank statistic compares each to its expectation under the null hypothesis and is defined as : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Log-rank test」の詳細全文を読む スポンサード リンク
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