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LogRankTest[{data1,data2,…}]

使用对数秩类型检验，在 datai 中测试等风险率.

LogRankTest[{data1,data2,…},wspec]

执行权值为 wspec 的加权对数秩检验.

LogRankTest[{data1,…},wspec,"property"]

返回 "property" 的值.

更多信息和选项
Details and Options Details and Options
范例  
基本范例  
范围  
检验  
报告  
选项  
Method  
SignificanceLevel  
属性和关系  
参见
相关指南
历史
按以下格式引用：

LogRankTest

LogRankTest[{data1,data2,…}]

使用对数秩类型检验，在 datai 中测试等风险率.

LogRankTest[{data1,data2,…},wspec]

执行权值为 wspec 的加权对数秩检验.

LogRankTest[{data1,…},wspec,"property"]

返回 "property" 的值.

更多信息和选项

  • LogRankTest 对 datai 执行假设检验，其中零假设 为总体的真实风险率等于 （对于全部 ），而备择假设 ：对于某些 的值，至少一个 是不同的.
  • 数字 通常是 datai 中的最大的事件时间.
  • 默认情况下，返回概率值或者 值.
  • 较小的 值表明 不可能是真的.
  • datai 必须是单变量 {x1,x2,…}.
  • datai 可以是 SparseArray 或者 EventData 对象.
  • LogRankTest 基于 ，其中 、 和 分别是观测到的事件数目，基于共用的样本的期望事件数目和某些权值.
  • 对于已命名权值方法，时间 处的权值 通常基于风险 处的数目，事件数 ，共用样本的乘积极限估值 ，或者共用样本的相似估值 .
  • 可以给出下列权值指定 wspec：
  • ρFleming–Harrington 权值，其中
    {ρ,γ}完全指定的 Fleming–Harrington 权值
    "name"使用已命名权值方法
  • ρ 和 γ 的值可以是任意非负数值.
  • 指定 ρ 和 γ 产生形如 的 Fleming–Harrington 权值.
  • 可能的已命名权值指定包括：
  • "AndersenPeto"y_(i)s^~(t_(i))/(y_(i)+1)
    "Equal"
    "Gehan"
    "Peto"
    "TaroneWare"
  • 对于区间删失数据，使用 Zhao–Zhao–Sun–Kim 广义对数秩检验.
  • LogRankTest[{data1,…},wspec,"HypothesisTestData"] 返回 HypothesisTestData 对象 htd，它可以用于使用格式 htd["property"] 提取额外检验结果和属性.
  • LogRankTest[{data1,…},wspec,"property"] 可用于直接给出 "property" 的值.
  • 与检验结果报告相关的属性包括：
  • "DegreesOfFreedom"用于检验的自由度
    "EventTimes"用于检验的时间点列表
    "EventWeights"用于每个事件时间的权值列表
    "PValue" 值列表
    "PValueTable"由 值组成的格式化表格
    "ShortTestConclusion"检验结论的简短描述
    "TestConclusion"检验结论的描述
    "TestData"检验统计量和 值组成的对的列表
    "TestDataTable"由 值和检验统计量组成的格式化表格
    "TestStatistic"检验统计量的列表
    "TestStatisticTable"检验统计量的格式化表格
  • 可以给出下列选项：
  • Method Automatic用于计算 值的方法
    SignificanceLevel 0.05诊断和报告的截止

范例

打开所有单元 关闭所有单元

基本范例  (4)

使用某些样本数据比较风险率：

Wolfram Language code: d1 = {32, 34, 28, 26, 31, 25, 29, 31, 28, 25}; d2 = {30, 19, 28, 35, 35, 29, 33, 32, 31, 29};
Wolfram Language code: LogRankTest[{d1, d2}]

创建 HypothesisTestData 对象，以进行重复属性提取：

Wolfram Language code: ℋ = LogRankTest[{d1, d2}, 0, "HypothesisTestData"]
Wolfram Language code: ℋ["Properties"]

检验某些删失数据：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];

在 5% 显著性水平处检测到显著差异：

Wolfram Language code: LogRankTest[{e1, e2}]

执行加权对数秩检验：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];

使用已命名的权值方案：

Wolfram Language code: LogRankTest[{e1, e2}, "Gehan", "TestDataTable"]

使用 Fleming–Harrington 权值：

Wolfram Language code: ρ = 1;γ = 0;
Wolfram Language code: LogRankTest[{e1, e2}, {ρ, γ}, "TestDataTable"]

检验多个样本的等风险率：

Wolfram Language code: m = BlockRandom[SeedRandom[23];Table[EventData[RandomVariate[PoissonDistribution[30], 500], RandomChoice[{.1, .9} -> {0, 1}, 500]], {5}]];

生存率的可视化比较：

Wolfram Language code: Plot[Table[SurvivalModelFit[i][x], {i, m}]//Evaluate, {x, 20, 45}, Exclusions -> None]

没有显著差异：

Wolfram Language code: LogRankTest[m]

范围  (11)

检验  (7)

从对数秩检验获取 值：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: LogRankTest[{e1, e2}]

同时检验大量群：

Wolfram Language code: ng = 20;
Wolfram Language code: e = BlockRandom[SeedRandom[4];Table[EventData[RandomVariate[PoissonDistribution[30], 100], RandomChoice[{.9, .1} -> {0, 1}, 100]], {ng}]];
Wolfram Language code: LogRankTest[e]

对加权对数秩检验计算 值：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];

已命名加权方案：

Wolfram Language code: wspec = {"AndersenPeto", "Gehan", "Equal", "TaroneWare"};
Wolfram Language code: Table[{w, LogRankTest[{e1, e2}, w]}, {w, wspec}]//Grid

手动设置 Fleming–Harrington类型权值：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];

Fleming–Harrington 权值，其中 和 ：

Wolfram Language code: LogRankTest[{e1, e2}, .5]

使用完全指定的 Fleming–Harrington 类型权值：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];

Fleming–Harrington 权值，其中 和 ：

Wolfram Language code: LogRankTest[{e1, e2}, {.5, 1}]

从 HypothesisTestData 对象提取某些属性：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: ℋ = LogRankTest[{e1, e2}, 0, "HypothesisTestData"];

值和检验统计量：

Wolfram Language code: ℋ["PValue"]
Wolfram Language code: ℋ["TestStatistic"]

同时提取任意数目的属性：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: ℋ = LogRankTest[{e1, e2}, 0, "HypothesisTestData"];

值、检验统计量和自由度：

Wolfram Language code: ℋ[{"PValue", "TestStatistic", "DegreesOfFreedom"}]

报告  (4)

制作检验结果的表格：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: LogRankTest[{e1, e2}, 0, "TestDataTable"]

来自表格的数值：

Wolfram Language code: LogRankTest[{e1, e2}, 0, "TestEntries"]

获取自定义报告的属性：

Wolfram Language code: e = BlockRandom[SeedRandom[4];Table[EventData[RandomVariate[PoissonDistribution[30], 100], RandomChoice[{.9, .1} -> {0, 1}, 100]], {20}]];
Wolfram Language code: {t, p, df} = LogRankTest[e, 0, {"TestStatistic", "PValue", "DegreesOfFreedom"}];
Wolfram Language code: Grid[{{"Log‐Rank Test", SpanFromLeft}, {"SuperscriptBox[χ, 2]", "p-value", "d.o.f"}, {t, p, df}}, Frame -> All]

制作 值和检验统计量表格：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: LogRankTest[{e1, e2}, 0, "PValueTable"]
Wolfram Language code: LogRankTest[{e1, e2}, 0, "TestStatisticTable"]

可视化用于检验的规范化权值：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: wtdata = Table[{i, Transpose[LogRankTest[{e1, e2}, i, {"EventTimes", "EventWeights"}]]}, {i, {"Gehan", "TaroneWare", "Peto", "Equal"}}];

已命名的加权方案趋向于强调早期事件：

Wolfram Language code: ListLinePlot[wtdata[[All, 2]], PlotLegends -> wtdata[[All, 1]]]
Wolfram Language code: wtdata2 = Table[{i, Transpose[LogRankTest[{e1, e2}, i, {"EventTimes", "EventWeights"}]]}, {i, {{0, 0}, {0, 1}, {1, 0}, {1, .5}}}];

Fleming–Harrington 权值可用于强调其他事件区域：

Wolfram Language code: ListLinePlot[wtdata2[[All, 2]], PlotLegends -> ToString /@ wtdata2[[All, 1]]]

选项  (4)

Method  (3)

默认情况下，用检验统计量的渐近 分布来计算 值：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: LogRankTest[{e1, e2}, 0, Method -> Automatic]

基于随机排列的检验可能用较少的样本给出更好的结果：

Wolfram Language code: LogRankTest[{e1, e2}, 0, Method -> "Permutation"]

指定执行的随机排列数目：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];

指定250个随机排列：

Wolfram Language code: LogRankTest[{e1, e2}, 0, Method -> {"Permutation", "MaxSamples" -> 250}]

生成随机排列时使用同样的种子：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];

使用9作为种子：

Wolfram Language code: LogRankTest[{e1, e2}, 0, Method -> {"Permutation", "RandomSeed" -> 9}]

SignificanceLevel  (1)

在 "TestConclusion" 和 "ShortTestConclusion" 中使用显著性水平：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: LogRankTest[{e1, e2}, 0, "TestConclusion", SignificanceLevel -> .005]//TraditionalForm
Wolfram Language code: LogRankTest[{e1, e2}, 0, "TestConclusion", SignificanceLevel -> .05]//TraditionalForm
Wolfram Language code: LogRankTest[{e1, e2}, 0, "ShortTestConclusion", SignificanceLevel -> .005]
Wolfram Language code: LogRankTest[{e1, e2}, 0, "ShortTestConclusion", SignificanceLevel -> .05]

属性和关系  (7)

默认情况下，在 下，假定检验统计量服从 ChiSquareDistribution：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}]; e2 = EventData[{30, 19, 28, 35, 35, 29, 33, 32, 31, 29}, {0, 0, 1, 0, 0, 1, 0, 1, 0, 1}];
Wolfram Language code: {t, df, p} = LogRankTest[{e1, e2}, 0, {"TestStatistic", "DegreesOfFreedom", "PValue"}]
Wolfram Language code: SurvivalFunction[ChiSquareDistribution[df], t] == p

加权方案允许强调特定时间点：

Wolfram Language code: m = Round@RandomVariate[WeibullDistribution[5, 30], {2, 10^4}];
Wolfram Language code: etimes = LogRankTest[m, 0, "EventTimes"];
Wolfram Language code: wspec = {"Gehan", "AndersenPeto", "Peto", "TaroneWare", "Equal"};
Wolfram Language code: wts = Table[Transpose[{etimes, LogRankTest[m, w, "EventWeights"]}], {w, wspec}];

已命名方案倾向于在更多权值放在早期事件：

Wolfram Language code: ListLinePlot[wts, PlotLegends -> wspec]

Fleming–Harrington 参数适合精细控制，而不是加权处理：

Wolfram Language code: fhw = Table[Transpose[{etimes, LogRankTest[m, w, "EventWeights"]}], {w, Tuples[Range[0, 2, 1], {2}]}];
Wolfram Language code: ListLinePlot[fhw, PlotLegends -> ToString /@ Tuples[Range[0, 2, 1], {2}]]

MannWhitneyTest 可用于没有双样本删失的情况：

Wolfram Language code: data = RandomVariate[PoissonDistribution[30], {2, 10^4}];

检验是渐近等价的：

Wolfram Language code: MannWhitneyTest[data]
Wolfram Language code: LogRankTest[data, {1, 0}]

Kruskal–Wallis 检验可用于不出现多于两个样本的删失的情况：

Wolfram Language code: data = RandomVariate[PoissonDistribution[30], {5, 10^4}];

检验是渐近等价的：

Wolfram Language code: LocationEquivalenceTest[data, "KruskalWallis", VerifyTestAssumptions -> None]
Wolfram Language code: LogRankTest[data, {1, 0}]

使用 SurvivalModelFit 估计生存概率：

Wolfram Language code: e1 = EventData[{32, 34, 28, 26, 31, 25, 29, 31, 28, 25}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}];
Wolfram Language code: mod = SurvivalModelFit[e1];

估计生存曲线：

Wolfram Language code: Plot[mod[t], {t, 20, 40}, Exclusions -> None]

关于30处的生存概率，创建 95% 置信区间：

Wolfram Language code: mod["PointwiseBands"][30]

在出现协方差时，使用 CoxModelFit 估计生存概率：

Wolfram Language code: y = EventData[{8, 22, 6, 4, 12, 11, 2, 34, 25, 15, 8, 6, 34, 6, 32, 1, 15, 9, 9, 6}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0}]; x = {{67, 1}, {11, 0}, {32, 0}, {50, 1}, {65, 1}, {44, 1}, {20, 1}, {26, 0}, {69, 1}, {50, 1}, {25, 1}, {18, 0}, {63, 1}, {41, 0}, {30, 0}, {32, 1}, {46, 1}, {35, 0}, {33, 0}, {22, 0}};
Wolfram Language code: mod = CoxModelFit[{x, y}, {a, b}, {a, b}]

获取参数估计：

Wolfram Language code: mod["ParameterTable"]

可视化协方差水平 和 处的生存估计：

Wolfram Language code: Plot[Evaluate@{mod["SF"][{50, 1}][t], mod["PointwiseBands"][{50, 1}][t]}, {t, 0, 40}, PlotPoints -> 100, Exclusions -> None]

对数秩检验可以识别 TemporalData 的路径结构：

Wolfram Language code: td = TemporalData[Automatic, {{{0.6327956976018951, 0.49307164456668334, -0.11865815946302549, -1.6346246228913748, -1.8053674367955113, -1.0171193599509663, -1.713536030590108, -0.2441834126183119, 1.468610531363788, 2.5403283801476966, 0.862 ... 135928877112, 0.8411464201445826, 0.36308201253335104, -0.45737292436875443, 0.289078430933834, 0.12996366812717347}}, {{0, 100, 1}}, 4, {"Continuous", 4}, {"Discrete", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> None}}, False, 10.1];
Wolfram Language code: LogRankTest[td]

直接使用数值：

Wolfram Language code: LogRankTest[td["ValueList"]]
Wolfram Research (2012)，LogRankTest，Wolfram 语言函数，https://reference.wolfram.com/language/ref/LogRankTest.html.

文本

Wolfram Research (2012)，LogRankTest，Wolfram 语言函数，https://reference.wolfram.com/language/ref/LogRankTest.html.

CMS

Wolfram 语言. 2012. "LogRankTest." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/LogRankTest.html.

APA

Wolfram 语言. (2012). LogRankTest. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/LogRankTest.html 年

BibTeX

@misc{reference.wolfram_2026_logranktest, author="Wolfram Research", title="{LogRankTest}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/LogRankTest.html}", note=[Accessed: 10-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_logranktest, organization={Wolfram Research}, title={LogRankTest}, year={2012}, url={https://reference.wolfram.com/language/ref/LogRankTest.html}, note=[Accessed: 10-November-2026]}