log-rank test

ログランク検定

WordNet

1. very offensive in smell or taste; "a rank cigar"
2. relative status; "his salary was determined by his rank and seniority"
3. a row or line of people (especially soldiers or police) standing abreast of one another; "the entrance was guarded by ranks of policemen"
4. take precedence or surpass others in rank (同)outrank
5. growing profusely; "rank jungle vegetation"
6. take or have a position relative to others; "This painting ranks among the best in the Western World"
7. very fertile; producing profuse growth; "rank earth"
8. undergo a test; "She doesnt test well"
9. any standardized procedure for measuring sensitivity or memory or intelligence or aptitude or personality etc; "the test was standardized on a large sample of students" (同)mental test, mental testing, psychometric test
10. the act of undergoing testing; "he survived the great test of battle"; "candidates must compete in a trial of skill" (同)trial
11. the act of testing something; "in the experimental trials the amount of carbon was measured separately"; "he called each flip of the coin a new trial" (同)trial, run
12. a hard outer covering as of some amoebas and sea urchins
13. put to the test, as for its quality, or give experimental use to; "This approach has been tried with good results"; "Test this recipe" (同)prove, try, try out, examine, essay
14. achieve a certain score or rating on a test; "She tested high on the LSAT and was admitted to all the good law schools"
15. determine the presence or properties of (a substance)
16. show a certain characteristic when tested; "He tested positive for HIV"
17. enter into a log, as on ships and planes
18. a segment of the trunk of a tree when stripped of branches
19. measuring instrument that consists of a float that trails from a ship by a knotted line in order to measure the ships speed through the water
20. a written record of events on a voyage (of a ship or plane)
21. a written record of messages sent or received; "they kept a log of all transmission by the radio station"; "an email log"
22. cut lumber, as in woods and forests (同)lumber
23. an examination of the characteristics of something; "there are laboratories for commercial testing"; "it involved testing thousands of children for smallpox"
24. the act of subjecting to experimental test in order to determine how well something works; "they agreed to end the testing of atomic weapons"
25. having a higher rank; "superior officer" (同)superior, higher-ranking
26. position on a scale in relation to others in a sport

PrepTutorEJDIC

1. 〈C〉〈U〉『階級』,等級;)相対的な)『順位』,地位: / 〈U〉高い地位(身分) / 〈C〉〈U〉(人・物の)『列』,並び;(兵隊)の横列 / 《the ranks》(また『rank and file』)(将校たちに対して)兵卒,下士官 / …‘を'『並べる』 / …‘を'『位置づける』,評価する / 《米》…‘より'上位にある / 『位置する』・「pull one's rank on 誰々」で「(誰々に)地位を悪用する; (意見が衝突したような場合に)階級をかさに着て(誰々に)命令を押しつける」
2. (植物が)おい茂った,はびこった / (土地が)植物をおい茂らせた,肥えすぎた;(土地が)(植物を)おい茂らせた《+『with』+『名』》 / 悪臭を放つ,いやな味のする / 全くの,ひどい
3. (人の能力などの)『試験』,考査,テスト / (物事の)『試験』,検済,試錬,実験《+of+名》 / 化学分析;試薬 / =test match / …‘を'『試験する』,検査する / …‘を'化学分析する / (…の)試験を受ける,試験をする《+for+名》
4. 『丸太』,丸木 / (また『logbook』)航海(航空)日誌 / 測程儀(船の速力を測る器械) / 〈木〉‘を'丸太に切る / 〈土地〉‘の'立ち木を切り倒す / …‘を'航海(航空)日誌に記入する / (船・飛行機で)〈ある距離・時間〉‘を'航行する,飛ぶ / 木材を伐採する / 丸太の
5. 上位の,一流の,卓越した

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/05/29 11:45:29」(JST)

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[Wiki en表示]

In statistics, the logrank 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 compared to 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 logrank 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 logrank test by Richard and Julian Peto.

Definition

The logrank 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 logrank statistic compares each to its expectation under the null hypothesis and is defined as

Asymptotic distribution

If the two groups have the same survival function, the logrank statistic is approximately standard normal. A one-sided level test will reject the null hypothesis if where is the upper quantile of the standard normal distribution. If the hazard ratio is , there are total subjects, is the probability a subject in either group will eventually have an event (so that is the expected number of events at the time of the analysis), and the proportion of subjects randomized to each group is 50%, then the logrank statistic is approximately normal with mean and variance 1. For a one-sided level test with power , the sample size required is where and are the quantiles of the standard normal distribution.

Joint distribution

Suppose and are the logrank statistics at two different time points in the same study ( earlier). Again, assume the hazard functions in the two groups are proportional with hazard ratio and and are the probabilities that a subject will have an event at the two time points where . and are approximately bivariate normal with means and and correlation . Calculations involving the joint distribution are needed to correctly maintain the error rate when the data are examined multiple times within a study by a Data Monitoring Committee.

Relationship to other statistics

• The logrank test has been shown to be too permissive a test, allowing significant results for survivorship prediction models that have low accuracy. The F* test was developed in response to these observations and has been shown to be more critical and to track accuracy of the prediction models with higher fidelity.

• The logrank statistic can be derived as the score test for the Cox proportional hazards model comparing two groups. It is therefore asymptotically equivalent to the likelihood ratio test statistic based from that model.

• The logrank statistic is asymptotically equivalent to the likelihood ratio test statistic for any family of distributions with proportional hazard alternative. For example, if the data from the two samples have exponential distributions.

• If is the logrank statistic, is the number of events observed, and is the estimate of the hazard ratio, then . This relationship is useful when two of the quantities are known (e.g. from a published article), but the third one is needed.

• The logrank statistic can be used when observations are censored. If censored observations are not present in the data then the Wilcoxon rank sum test is appropriate.

• The logrank statistic gives all calculations the same weight, regardless of the time at which an event occurs. The Peto logrank statistic gives more weight to earlier events when there are a large number of observations.

See also

• Kaplan-Meier estimator
• Hazard ratio

References

External links

• Bland, J. M.; Altman, D. G. (2004). "The logrank test". BMJ 328 (7447): 1073. doi:10.1136/bmj.328.7447.1073. PMC 403858. PMID 15117797. 

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★リンクテーブル★

リンク元	「ログランク検定」
関連記事	「rank」「testing」「RANK」「log」「test」

「ログランク検定」

　　[★]

英

log-rank test

同

log rank検定

関

一般化Wilcoxon検定、ノンパラメトリック検定、生存関数

参考

• 1.

http://aoki2.si.gunma-u.ac.jp/lecture/Survival/lr.html

• 2.

http://www012.upp.so-net.ne.jp/doi/sas/procedure/logrank/Logrank_genWil.pdf

• 3.

http://c4s.blog72.fc2.com/blog-entry-84.html

「rank」

　　[★]

• n.

• 地位、順位。下級、投球
• 後位、養殖
• 列、並び。整列

• vt.

• 並べる、整列させる。(～と)並べる、同列にする
• ～に等級(順位)をつける、ランク付けをする。評価する。分類する。
• ～より階級が上だ、～の上に立つ

• vi.

• 位する、ランク付けされる。評価される。列する、並ぶ
• 上位を占める
• 整列する

関

lie、locate、location、loci、locus、map、position、ranking、sit、situated、situation、stand、topo

　 　 　 　 　 　 　 　 　

「testing」

　　[★]

• n.

• 試験

関

assessment、data quality、exam、examination、examine、experimental design、matched group、measurement、research design、scoring method、test、trial

　 　

「RANK」

　　[★]

• NFκB活性化受容体

関

receptor activator of nuclear factor-kappa B、receptor activator of nuclear factor-kappaB

同

receptor activator for nuclear factor kB

「log」

　　[★]

• n.

• ログ、(通信などの)記録

• adj.

• 対数の

関

archive、logarithm、logarithmic、record、recording

　 　 　 　 　 　 　

「test」

　　[★] テスト