Name: survival tree in time-to-event analysis
Uploaded: 2025-01-09T15:14:17.000Z
Duration: 1 min 19 s
Channel: JoVE

生存树用于建模和可视化一组协变量与感兴趣事件发生时间之间的关系。通常通过递归分割过程构建。
树的分支代表变量取值的分割。节点代表数据的子集，而终端节点则表示该节点中包含的样本数量，并可提供分析的最终预测结果。
构建生存树主要需要协变量、分割标准、最小节点大小和剪枝阈值。
协变量或预测变量可以是连续型、有序型或分类型变量。
分裂准则是一种用于在每个节点选择最佳分裂方式的方法。该准则通过最小化节点内的风险或最大化节点间的分离程度来应用。
最小节点大小是指一个节点能够进一步分裂所需的最小观测值数量。这有助于控制树的大小，并防止过拟合。
最后，剪枝阈值是决定何时停止剪枝树的一个度量标准。

生存树

Survival Tree

生存树是一种非参数方法，用于生存分析，以模拟一组协变量与感兴趣事件发生时间（通常称为“事件发生时间”或“生存时间”）之间的关系。这种方法在处理删失数据时特别有用，即在研究期结束时，某些个体尚未发生事件，或者事件的确切时间未知。

构建生存树

构建生存树始于一个数据集，该数据集包含协变量（预测变量）和生存时间，以及每个受试者的删失指示符。该过程涉及以下步骤：

<ol>
	<li>数据准备：通过确保包含所有必要的协变量并格式正确来准备数据集。缺失值可以通过插补等方法进行处理或将其视为单独的类别。</li>
	<li>树的构建：生存树是通过递归分割过程构建的。在每个步骤中，数据集都会根据最能区分生存结果的协变量分为两个子集。这通常使用分割标准（例如对数秩检验）来完成，该标准比较组之间的生存分布。</li>
	<li>节点评估：树中的每个节点代表数据的一个子集，终端节点（叶节点）根据生存函数的 Kaplan-Meier 估计进行评估。这为落入该节点的受试者提供了生存概率的估计值。</li>
	<li>剪枝：为避免过拟合，通过删除无法显着提高模型准确性的节点来修剪树。此步骤可确保树可泛化到新数据。</li>
</ol>

优点和缺点

优点：

<ol style="list-style-type: circle;">
	<li>灵活性：生存树可以处理多种数据类型，并且对异常值和缺失值具有鲁棒性。</li>
	<li>可解释性：树结构易于解释，可以直接可视化协变量与生存时间之间的关系。</li>
	<li>非参数性质：它们不需要对生存时间的分布或协变量与生存之间关系的函数形式做出假设。</li>
</ol>

缺点：

<ol style="list-style-type: circle;">
	<li>过拟合：如果没有适当剪枝，生存树可能会过度拟合训练数据，导致泛化能力差。</li>
	<li>不稳定性：数据的微小变化可能导致树结构的重大变化，与生存森林等其他方法相比，它们的稳定性较差</li>
</ol>

生存树用于建模和可视化一组协变量与感兴趣事件发生时间之间的关系。它是一种……

Education

教育

JoVE Core

Statistics

统计学

Unit 1

第一单元

Survival Analysis

生存分析

KEY TERMS AND CONCEPTS

关键术语与概念

survival tree in time-to-event analysis

A survival tree is a non-parametric tool in survival analysis that links predictor variables, or covariates, to survival time. Survival time is the time until an event of interest occurs. It is useful when some data are censored, which means the event has not happened for some people by the end of the study or the exact event time is unknown.

Building a survival tree starts with a dataset that includes covariates, survival time, and a censoring indicator for each subject. The data must be prepared so the needed covariates are included and formatted correctly. Missing values can be handled by imputation or by treating them as a separate category.

The tree is built through recursive partitioning. At each step, the data are split into two groups based on the covariate that best separates the survival outcomes. A common splitting rule is the log-rank test, which compares survival distributions between groups.

Each node in the tree represents a subset of the data. The terminal nodes, or leaves, are evaluated with the Kaplan-Meier estimate of the survival function. This gives a survival probability estimate for subjects in that node. The tree is then pruned by removing nodes that do not improve model accuracy enough, which helps reduce overfitting and makes the model more useful for new data.

Survival trees have several strengths. They can handle many data types and are robust to outliers and missing values. They are also easy to interpret because the tree structure clearly shows how covariates relate to survival time. As a non-parametric method, they do not require assumptions about the distribution of survival times or the exact form of the relationship between covariates and survival.

They also have limits. Without pruning, survival trees can overfit the training data and perform poorly on new data. They can also be unstable, because small changes in the data may produce a very different tree. This makes them less stable than methods such as survival forests.

Survival Tree in Time-to-Event Analysis

introduction to survival analysis

Time-to-Event Data and Censoring

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life tables

Life Tables and Survival Patterns

A life table is a statistical tool that shows mortality and survival patterns in a population. It organizes data across age intervals so students can see how likely a group is to survive or die at each stage of life. The table gives a clear snapshot of population dynamics over time. Life tables are used in demography, public health, actuarial science, and ecology. They help scientists study life expectancy, plan health interventions, estimate insurance risk, and compare how species survive in...

survival curves

Kaplan-Meier Survival Curve Basics

Kaplan-Meier survival curves show how the chance of staying event-free changes over time. They are used to track survival in a population and to compare groups in medicine, public health, and reliability engineering. The Kaplan-Meier estimator is the most common way to build these curves. It is a non-parametric method, which means it does not assume a fixed pattern for the data. The result is a stepwise line that drops each time an event happens, such as death, disease recurrence, or...

actuarial approach

Life Table Method for Survival Rates

The life table method, also called the actuarial approach, is used to estimate survival rates in clinical and population studies. It began in life insurance, where risk over time must be measured carefully. In health research, it gives a clearer picture of survival when some participants are lost to follow-up or die from causes unrelated to the study. This method works by dividing the study period into set intervals, usually one year. That makes it useful for tracking outcomes over time,...

kaplan-meier approach

Survival Curves with Kaplan-Meier Data

The Kaplan-Meier estimator is a non-parametric method for estimating a survival function from time-to-event data. It is commonly used in medical research to track how many patients survive for a set time after treatment. It is also important in clinical trials, epidemiological studies, and reliability engineering. This method helps researchers study survival probabilities over time, even when some data are incomplete. That incomplete data is called censored data, which means the exact event...

assumptions of survival analysis

Survival Analysis Assumptions in Studies

Survival analysis studies the time until an event happens. The event may be death in a living organism or failure in a mechanical system. These models are used in medicine, biology, engineering, and public health to study time-to-event data. Careful study design matters because the method depends on several key assumptions. One common feature of survival times is positive skewness. This means events often happen early, while fewer cases occur later. Survival data also often include censoring,...

comparing the survival analysis of two or more groups

comparing-the-survival-analysis-of-two-or-more-groups

Kaplan-Meier Curves and Hazard Ratios

Kaplan-Meier curves and hazard ratios help researchers compare survival time between groups. Survival analysis looks at the time until an event happens, such as death, disease recurrence, or recovery. It is a key tool in medical research. A major strength of survival analysis is that it can handle censored data. Censored data means the event has not happened for some participants by the end of the study, or it has not been observed. This makes survival analysis different from standard...

the mantel-cox log-rank test

Log-Rank Test for Comparing Survival Curves

The Mantel-Cox log-rank test compares survival curves from two groups. It checks whether the groups have a statistically significant difference in survival time. This makes it useful when the timing of an event matters, such as death or disease recurrence. The log-rank test is non-parametric. That means it does not assume a specific distribution for the survival data. It is also useful in medical research, where it often helps compare a new treatment with a control or standard treatment in...

applications of life tables

Life Tables in Public Policy and Science

Life tables are used in many fields to study mortality and survival rates. They give a numerical way to examine how long people or living things are likely to survive. This makes them useful for public health, business planning, and scientific research. In demography and public health, life tables help experts study population changes and predict future trends. They can show patterns such as an aging population or the effect of a health policy. In Nigeria, health officials used survival rates...

cancer survival analysis

Cancer Survival Curves and Risk Factors

Cancer survival analysis measures how long it takes from diagnosis or the start of treatment to a specific outcome, such as remission or death. It helps researchers judge treatment effectiveness and understand what affects patient outcomes. These results also support clinical decisions and prognostic evaluations. Survival data are often skewed and not normally distributed. They also include censored cases, where the full survival time is unknown because the study ends, a patient is lost to...

hazard rate

Modeling Event Risk Over Time

Hazard rate is a statistical measure that describes how event risk changes over time. It is also called the hazard function or failure rate. In survival analysis, it shows the instantaneous rate at which an event occurs, but only after the subject has not had the event yet. From a probability view, hazard rate gives the chance that a subject will have the event in a very small time interval. That chance is conditional on surviving to the start of that interval. From a frequency view, it can...

hazard ratio

Hazard Ratio in Clinical Trials

The hazard ratio is a way to compare event risk in clinical trials. It is often used to study events such as death or disease recurrence in two groups over time. The two groups are usually a treatment group and a control group. A hazard ratio compares hazard rates, which are the instantaneous risk of an event happening at a given moment. It shows how the risk in one group relates to the risk in the other group. In a cancer drug study, for example, the hazard ratio can show how a new treatment...

truncation in survival analysis

Left and Right Truncation in Survival Data

Truncation in survival analysis describes data loss caused by the timing of an event or by when a subject can enter a study. It can happen in two forms: left truncation and right truncation. In both cases, some individuals are left out of the dataset before analysis begins. Left truncation happens when people who had the event before a set time are not included in the study. This often occurs with delayed entry, which means a person is only observed if they survive until the entry point. For...

censoring survival data

Types of Censoring in Survival Analysis

Survival analysis studies time-to-event data, which tracks how long it takes for an outcome to happen. It is used in medicine, engineering, and social science. A common problem in this type of data is censoring, which means the full event time is not observed for every person or item. Censoring can happen for several reasons and in different patterns. The most common kind is right censoring. This happens when the event has not occurred by the end of the study or when a participant is lost to...

survival tree

A survival tree is a non-parametric tool in survival analysis that links predictor variables, or covariates, to survival time. Survival time is the time until an event of interest occurs. It is useful when some data are censored, which means the event has not happened for some people by the end of the study or the exact event time is unknown. Building a survival tree starts with a dataset that includes covariates, survival time, and a censoring indicator for each subject. The data must be...

parametric survival analysis: weibull and exponential methods

parametric-survival-analysis-weibull-and-exponential-methods

Modeling Survival Time with Weibull and Exponential

Parametric survival analysis models survival time by assuming a specific probability distribution for when an event occurs. The Weibull and exponential distributions are two common choices because they are flexible and relatively straightforward to use. The Weibull distribution is a flexible model in parametric survival analysis. It can describe both increasing and decreasing hazard rates, depending on its shape parameter beta. When beta is greater than 1, the hazard rate rises over time. That...

key terms and concepts

Learn how survival trees use covariates, censoring, and recursive partitioning to model time-to-event data, estimate survival, and manage overfitting.

Survival Tree in Time-to-Event Analysis | JoVE K12

statistics

JoVE Core 统计学（Statistics）向学生介绍了数据收集、分析、呈现和解释的概念和应用。 这些生动的课程提供了对来自广泛学科的学生有益的统计学的理解。 此外，"行动中的科学家"视频展示了相关概念在当今世界各地实验室进行的经典和原创研究实验中的应用

Survival Tree in Time-to-Event Analysis

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